{"id":15490,"date":"2026-04-10T17:19:05","date_gmt":"2026-04-10T10:19:05","guid":{"rendered":"https:\/\/rosetta.vn\/nguyenxuanxanh\/?p=15490"},"modified":"2026-04-10T22:08:44","modified_gmt":"2026-04-10T15:08:44","slug":"phep-gap-trong-toan-va-vat-ly-gs-phan-thanh-nam-lmu-munich","status":"publish","type":"post","link":"https:\/\/rosetta.vn\/nguyenxuanxanh\/phep-gap-trong-toan-va-vat-ly-gs-phan-thanh-nam-lmu-munich\/","title":{"rendered":"Ph\u00e9p g\u1eadp trong to\u00e1n v\u00e0 v\u1eadt l\u00fd (GS Phan Th\u00e0nh Nam, LMU Munich)"},"content":{"rendered":"

T\u1eeb<\/em>\u00a0GAUSS\u00a0\u0111\u1ebfn<\/em>\u00a0BOSE\u2013FERMI:<\/span><\/h1>\n

PH\u00c9P G\u1eacP TRONG TO\u00c1N V\u00c0 V\u1eacT L\u00dd<\/span><\/h2>\n

Phan Th\u00e0nh Nam<\/strong>, Gi\u00e1o s\u01b0 Ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc Ludwig Maximilian, Munich<\/em><\/span><\/p>\n

Nguy\u1ec5n Xu\u00e2n Xanh<\/strong> gi\u1edbi thi\u1ec7u<\/em><\/span><\/p>\n

M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadt l\u00fd h\u1ecdc to\u00e1n (mathematical physics) kh\u00f4ng ch\u1ec9 l\u00e0 t\u1ea1o \u0111i\u1ec1u ki\u1ec7n cho nh\u00e0 v\u1eadt l\u00fd t\u00ednh to\u00e1n s\u1ed1 l\u01b0\u1ee3ng c\u00e1c h\u1eb1ng s\u1ed1 nh\u1ea5t \u0111\u1ecbnh ho\u1eb7c ph\u00e9p l\u1ea5y t\u00edch ph\u00e2n c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh vi ph\u00e2n nh\u1ea5t \u0111\u1ecbnh. M\u00e0 \u0111\u00fang h\u01a1n, n\u00f3 ti\u1ebft l\u1ed9 cho anh ta bi\u1ebft s\u1ef1 h\u00e0i h\u00f2a ti\u1ec1m \u1ea9n c\u1ee7a s\u1ef1 v\u1eadt b\u1eb1ng c\u00e1ch khi\u1ebfn anh ta nh\u00ecn ch\u00fang theo m\u1ed9t c\u00e1ch m\u1edbi.<\/span><\/p>\n

\u2014 Henri Poincar\u00e9<\/strong>,\u00a0The Value of Science<\/em><\/span><\/p>\n

\"\"<\/p>\n

Gi\u00e1o s\u01b0 Phan Th\u00e0nh Nam ph\u00e1t bi\u1ec3u trong ch\u01b0\u01a1ng tr\u00ecnh k\u1ef7 ni\u1ec7m Ng\u00e0y To\u00e1n h\u1ecdc Qu\u1ed1c t\u1ebf<\/strong> t\u1ea1i H\u00e0 N\u1ed9i ng\u00e0y 14 th\u00e1ng 3 n\u0103m 2026. \u1ea2nh: VnExpress\/Tung Dinh<\/p>\n

L\u1eddi gi\u1edbi thi\u1ec7u<\/em><\/strong><\/span><\/p>\n

T\u00f4i h\u1ebft s\u1ee9c vui m\u1eebng \u0111\u01b0\u1ee3c l\u00e0m quen v\u1edbi Phan Th\u00e0nh Nam, m\u1ed9t nh\u00e0 v\u1eadt l\u00fd to\u00e1n t\u00e0i n\u0103ng tr\u1ebb, hi\u1ec7n l\u00e0 gi\u00e1o s\u01b0 to\u00e1n t\u1ea1i \u0110\u1ea1i h\u1ecdc Ludwig Maximilian (LMU), Munich, m\u1ed9t \u0111\u1ea1i h\u1ecdc h\u00e0ng \u0111\u1ea7u c\u1ee7a \u0110\u1ee9c v\u1edbi nhi\u1ec1u t\u00ean tu\u1ed5i t\u1eebng l\u00e0 nh\u1eefng ng\u01b0\u1eddi kh\u1ed5ng l\u1ed3 s\u1ed1ng v\u00e0 l\u00e0m vi\u1ec7c \u1edf \u0111\u00e2y nh\u01b0 Werner Heisenberg, Wolfgang Pauli, Arnold Sommerfeld. Sau m\u1ed9t s\u1ed1 trao \u0111\u1ed5i email, anh Nam \u0111\u00e3 cho t\u00f4i vinh d\u1ef1 \u0111\u0103ng b\u00e0i Ph\u00e9p g\u1eadp trong to\u00e1n v\u00e0 v\u1eadt l\u00fd<\/em>: T\u1eeb Gauss \u0111\u1ebfn Bose-Fermi <\/strong>tr\u00ean trang rosetta. Ph\u00e9p g\u1eadp n\u00f3i chung l\u00e0 folding. V\u1edbi b\u00e0i n\u00e0y anh Nam mu\u1ed1n n\u00f3i v\u1ec1 nh\u1eefng \u00fd t\u01b0\u1edfng v\u00e0 ph\u01b0\u01a1ng ph\u00e1p t\u00f4i t\u1ea1m g\u1ecdi l\u00e0 “engineering” c\u1ee7a m\u1ed9t c\u00f4ng tr\u00ecnh nghi\u00ean c\u1ee9u l\u1edbn k\u00e9o d\u00e0i n\u0103m n\u0103m c\u1ee7a anh v\u00e0 c\u00e1c \u0111\u1ed3ng nghi\u1ec7p v\u1ec1 m\u1ed9t hi\u1ec7n t\u01b0\u1ee3ng v\u1eadt l\u00fd m\u00e0 anh r\u1ea5t t\u00e2m \u0111\u1eafc. V\u00e2ng, x\u00e2y m\u1ed9t t\u00f2a nh\u00e0 ph\u1ee9c t\u1ea1p, c\u1ea7n c\u00f3 \u00fd t\u01b0\u1edfng, ki\u1ebfn tr\u00fac v\u00e0 engineering.<\/p>\n

V\u1ec1 anh Nam c\u00f3 nhi\u1ec1u c\u00e2u chuy\u1ec7n th\u00fa v\u1ecb c\u1ea7n ph\u1ea3i k\u1ec3. N\u0103m 2018, H\u1ed9i qu\u1ed1c t\u1ebf v\u1ec1 v\u1eadt l\u00fd \u1ee9ng d\u1ee5ng v\u00e0 l\u00fd thuy\u1ebft (vi\u1ebft t\u1eaft IUPAP) \u0111\u00e3 trao t\u1eb7ng gi\u1ea3i th\u01b0\u1edfng nh\u00e0 khoa h\u1ecdc tr\u1ebb trong l\u0129nh v\u1ef1c v\u1eadt l\u00fd to\u00e1n cho GS Phan Th\u00e0nh Nam v\u00ec \u0111\u00e3 \u0111\u1ea1t c\u00e1c k\u1ebft qu\u1ea3 ti\u00ean phong v\u1edbi ch\u1ea5t l\u01b0\u1ee3ng khoa h\u1ecdc xu\u1ea5t s\u1eafc trong v\u1eadt l\u00fd to\u00e1n.<\/p>\n

N\u0103m 2020 anh \u0111\u01b0\u1ee3c trao Gi\u1ea3i th\u01b0\u1edfng c\u1ee7a H\u1ed9i To\u00e1n h\u1ecdc Ch\u00e2u \u00c2u<\/strong> (EMS). \u0110\u00e2y l\u00e0 m\u1ed9t hi\u1ec7p h\u1ed9i r\u1ea5t l\u1edbn, c\u00f3 3000 c\u00e1 nh\u00e2n th\u00e0nh vi\u00ean, kho\u1ea3ng 60 hi\u1ec7p h\u1ed9i to\u00e1n h\u1ecdc qu\u1ed1c gia \u1edf ch\u00e2u \u00c2u, 40 trung t\u00e2m v\u00e0 b\u1ed9 ph\u1eadn nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc. Gi\u1ea3i th\u01b0\u1edfng n\u00e0y r\u1ea5t danh gi\u00e1 \u0111\u01b0\u1ee3c trao cho nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc t\u00e0i n\u0103ng. C\u1ee9 b\u1ed1n n\u0103m m\u1ed9t l\u1ea7n, gi\u1ea3i th\u01b0\u1edfng \u0111\u01b0\u1ee3c x\u00e9t v\u00e0 trao t\u1eb7ng t\u1ea1i \u0110\u1ea1i h\u1ed9i To\u00e1n h\u1ecdc ch\u00e2u \u00c2u cho c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc d\u01b0\u1edbi 35 tu\u1ed5i c\u00f3 \u0111\u00f3ng g\u00f3p xu\u1ea5t s\u1eafc cho to\u00e1n h\u1ecdc. Nh\u1eefng quy \u0111\u1ecbnh gi\u1ed1ng nh\u01b0 quy \u0111\u1ecbnh c\u1ee7a gi\u1ea3i Fields. Gi\u00e1o s\u01b0 Jan Philip Solovej, nh\u00e0 to\u00e1n h\u1ecdc \u0110an M\u1ea1ch gi\u1ea3i Henri Poincar\u00e9 n\u0103m 2021, nghi\u00ean c\u1ee9u v\u1ec1 l\u00fd thuy\u1ebft to\u00e1n h\u1ecdc v\u1ec1 c\u01a1 h\u1ecdc l\u01b0\u1ee3ng t\u1eed, l\u00e0 ng\u01b0\u1eddi \u0111\u01b0\u1ee3c b\u1ea7u l\u00e0m ch\u1ee7 t\u1ecbch c\u1ee7a h\u1ed9i EMS n\u0103m 2023. \u00d4ng c\u0169ng l\u00e0 ng\u01b0\u1eddi h\u01b0\u1edbng d\u1eabn lu\u1eadn \u00e1n ti\u1ebfn s\u0129 c\u1ee7a Nam n\u0103m 2011. \u00d4ng c\u00f3 nh\u1eadn x\u00e9t v\u1ec1 c\u00e1c c\u00f4ng tr\u00ecnh c\u1ee7a Nam nh\u01b0 sau:<\/p>\n

Phan Thanh Nam \u0111\u00e3 c\u00f3 nh\u1eefng \u0111\u00f3ng g\u00f3p xu\u1ea5t s\u1eafc trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc v\u1ec1 c\u00e1c h\u1ec7 nhi\u1ec1u h\u1ea1t l\u01b0\u1ee3ng t\u1eed, bao g\u1ed3m nguy\u00ean t\u1eed, ph\u00e2n t\u1eed c\u0169ng nh\u01b0 kh\u00ed Bose v\u00e0 kh\u00ed Fermi. C\u00e1c k\u1ebft qu\u1ea3 c\u1ee7a \u00f4ng li\u00ean quan \u0111\u1ebfn c\u1ea3 tr\u1ea1ng th\u00e1i c\u00e2n b\u1eb1ng v\u00e0 t\u00ednh ch\u1ea5t \u0111\u1ed9ng h\u1ecdc c\u1ee7a c\u00e1c h\u1ec7 n\u00e0y. Nhi\u1ec1u k\u1ebft qu\u1ea3 n\u1ed5i ti\u1ebfng nh\u1ea5t trong l\u0129nh v\u1ef1c n\u00e0y l\u00e0 do \u00f4ng th\u1ef1c hi\u1ec7n. Trong s\u1ed1 \u0111\u00f3 c\u00f3 gi\u1edbi h\u1ea1n t\u1ed1t nh\u1ea5t v\u1ec1 \u0111\u1ed9 ion h\u00f3a t\u1ed1i \u0111a c\u1ee7a nguy\u00ean t\u1eed v\u00e0 h\u1eb1ng s\u1ed1 \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn l\u00e0 t\u1ed1t nh\u1ea5n cho \u0111\u1ebfn nay trong b\u1ea5t \u0111\u1eb3ng th\u1ee9c Lieb-Thirring.<\/p>\n

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H\u01a1n n\u1eefa, \u00f4ng v\u00e0 c\u00e1c c\u1ed9ng s\u1ef1 \u0111\u00e3 ph\u00e1t tri\u1ec3n m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p r\u1ea5t t\u1ed5ng qu\u00e1t \u0111\u1ec3 thi\u1ebft l\u1eadp gi\u1edbi h\u1ea1n tr\u01b0\u1eddng trung b\u00ecnh c\u1ee7a c\u00e1c h\u1ec7 Boson d\u1ef1a tr\u00ean \u0110\u1ecbnh l\u00fd de Finetti l\u01b0\u1ee3ng t\u1eed. \u0110\u00e2y hi\u1ec7n l\u00e0 ti\u00eau chu\u1ea9n v\u00e0ng trong l\u0129nh v\u1ef1c n\u00e0y.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

T\u00ednh \u0111\u1ebfn n\u0103m 2020, anh l\u00e0 t\u00e1c gi\u1ea3 c\u1ee7a h\u01a1n 40 c\u00f4ng tr\u00ecnh v\u1ec1 to\u00e1n h\u1ecdc.<\/p>\n

Phan Th\u00e0nh Nam, sinh n\u0103m 1985 t\u1ea1i Tuy H\u00f2a, Ph\u00fa Y\u00ean, theo h\u1ecdc ng\u00e0nh To\u00e1n h\u1ecdc v\u00e0 Khoa h\u1ecdc m\u00e1y t\u00ednh t\u1eeb n\u0103m 2003 t\u1ea1i \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc T\u1ef1 nhi\u00ean thu\u1ed9c \u0110\u1ea1i h\u1ecdc Qu\u1ed1c gia Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh, n\u01a1i anh nh\u1eadn b\u1eb1ng c\u1eed nh\u00e2n n\u0103m 2007. \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc n\u00e0y l\u00e0 m\u1ea3nh \u0111\u1ea5t \u0111\u00e3 c\u00f3 truy\u1ec1n th\u1ed1ng to\u00e1n h\u1ecdc t\u1eeb nh\u1eefng n\u0103m 1960 c\u1ee7a th\u1ebf k\u1ef7 tr\u01b0\u1edbc, v\u1edbi s\u1ef1 d\u1eabn d\u1eaft c\u1ee7a gi\u00e1o s\u01b0 \u0110\u1eb7ng \u0110\u00ecnh \u00c1ng, ng\u01b0\u1eddi h\u1ea7u nh\u01b0 \u0111\u00e0o t\u1ea1o t\u1ea5t c\u1ea3 nh\u00e0 to\u00e1n h\u1ecdc \u1edf ph\u00eda Nam. Sau \u0111\u00f3 Nam h\u1ecdc th\u1ea1c s\u0129 n\u0103m 2008 t\u1ea1i \u0110\u1ea1i h\u1ecdc Orl\u00e9ans, Ph\u00e1p, d\u01b0\u1edbi s\u1ef1 h\u01b0\u1edbng d\u1eabn c\u1ee7a Gi\u00e1o s\u01b0 Alain Ph\u1ea1m Ng\u1ecdc \u0110\u1ec9nh (con c\u1ee7a B\u00e1c s\u0129 Ph\u1ea1m Ng\u1ecdc Th\u1ea1ch), v\u00e0 ti\u1ebfp t\u1ee5c h\u1ecdc ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc Copenhagen, \u0110an M\u1ea1ch, n\u01a1i \u00f4ng b\u1ea3o v\u1ec7 lu\u1eadn \u00e1n ti\u1ebfn s\u0129 n\u0103m 2011 d\u01b0\u1edbi s\u1ef1 h\u01b0\u1edbng d\u1eabn c\u1ee7a Gi\u00e1o s\u01b0 Jan Philip Solovej. L\u00e0 nghi\u00ean c\u1ee9u sinh sau ti\u1ebfn s\u0129, \u00f4ng l\u00e0m vi\u1ec7c v\u1edbi Mathieu Lewin t\u1ea1i \u0110\u1ea1i h\u1ecdc Cergy-Pontoise, Ph\u00e1p, v\u00e0 CNRS Paris cho \u0111\u1ebfn n\u0103m 2013 v\u00e0 t\u1ea1i Vi\u1ec7n Khoa h\u1ecdc v\u00e0 C\u00f4ng ngh\u1ec7 \u00c1o (IST) v\u1edbi Robert Seiringer cho \u0111\u1ebfn n\u0103m 2016. N\u0103m 2016, \u00f4ng tr\u1edf th\u00e0nh gi\u00e1o s\u01b0 tr\u1ee3 l\u00fd t\u1ea1i \u0110\u1ea1i h\u1ecdc Masaryk, v\u00e0 n\u0103m 2017 ch\u00ednh th\u1ee9c tr\u1edf th\u00e0nh gi\u00e1o s\u01b0 t\u1ea1i \u0110\u1ea1i h\u1ecdc Ludwig Maximilian, Munich. Nh\u00ecn chung, Gi\u00e1o s\u01b0 Nam l\u00e0 nh\u00e0 v\u1eadt l\u00fd to\u00e1n, v\u1edbi c\u00e1c chuy\u00ean m\u00f4n bao g\u1ed3m c\u01a1 h\u1ecdc l\u01b0\u1ee3ng t\u1eed nhi\u1ec1u h\u1ea1t, l\u00fd thuy\u1ebft ph\u1ed5, ph\u00e9p t\u00ednh bi\u1ebfn ph\u00e2n, ph\u01b0\u01a1ng tr\u00ecnh vi ph\u00e2n ri\u00eang ph\u1ea7n v\u00e0 ph\u00e2n t\u00edch s\u1ed1. L\u00e3nh v\u1ef1c nghi\u00ean c\u1ee9u c\u1ee7a anh l\u00e0 r\u1ea5t \u0111a d\u1ea1ng.<\/p>\n

Anh Nam ngo\u00e0i ra c\u00f2n l\u00e0 c\u00e2y vi\u1ebft t\u00edch c\u1ef1c cho \u0111\u1ea1i ch\u00fang, \u0111\u00e3 c\u00f3 b\u00e0i \u0111\u0103ng tr\u00ean t\u1ea1p ch\u00ed Tia S\u00e1ng, v\u00e0 c\u0169ng v\u1ec1 n\u01b0\u1edbc di\u1ec5n thuy\u1ebft nhi\u1ec1u l\u1ea7n, t\u1ea1i \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc, TP H\u1ed3 Ch\u00ed Minh, c\u0169ng nh\u01b0 c\u00e1ch \u0111\u00e2y m\u1ea5y h\u00f4m t\u1ea1i H\u1ed9i V\u1eadt l\u00fd Vi\u1ec7t Nam, H\u00e0 N\u1ed9i. Anh s\u1ebd c\u00f2n “giao thoa” v\u1edbi Vi\u1ec7t Nam nhi\u1ec1u h\u01a1n n\u1eefa. T\u00f4i tin anh s\u1ebd l\u00e0 m\u1ed9t “nh\u00e0 tr\u00ed th\u1ee9c \u0111\u1ea1i ch\u00fang” v\u00e0 d\u1ea5n th\u00e2n nh\u01b0 ki\u1ec3u tr\u00ed th\u1ee9c ph\u01b0\u01a1ng T\u00e2y. T\u00f4i li\u00ean t\u01b0\u1edfng ngay \u0111\u1ebfn nh\u00e0 v\u1eadt l\u00fd \u00c1o Ludwig Boltzmann cu\u1ed1i th\u1ebf k\u1ef7 XIX v\u1edbi “Popul\u00e4re Schriften” (C\u00e1c b\u00e0i vi\u1ebft \u0111\u1ea1i ch\u00fang) n\u1ed5i ti\u1ebfng c\u1ee7a \u00f4ng nh\u1eb1m ph\u1ed5 bi\u1ebfn tri\u1ebft l\u00fd khoa h\u1ecdc \u0111\u1ebfn \u0111\u00f4ng \u0111\u1ea3o sinh vi\u00ean v\u00e0 c\u00f4ng ch\u00fang. N\u00f3 \u0111\u00f3ng vai tr\u00f2 l\u00e0 c\u1ea7u n\u1ed1i quan tr\u1ecdng gi\u1eefa c\u01a1 h\u1ecdc c\u1ed5 \u0111i\u1ec3n th\u1ebf k\u1ef7 19 v\u00e0 v\u1eadt l\u00fd, tri\u1ebft h\u1ecdc hi\u1ec7n \u0111\u1ea1i th\u1ebf k\u1ef7 20, c\u0169ng nh\u01b0 mu\u1ed1n truy\u1ec1n t\u1ea3i tri\u1ebft h\u1ecdc t\u1ef1 nhi\u00ean cho nh\u1eefng ng\u01b0\u1eddi kh\u00f4ng ph\u1ea3i nh\u00e0 v\u1eadt l\u00fd, x\u00e2y d\u1ef1ng c\u00e1c “h\u00ecnh \u1ea3nh” nh\u01b0 m\u00f4 h\u00ecnh v\u1ec1 t\u1ef1 nhi\u00ean (Bild). Quy\u1ec3n s\u00e1ch \u0111\u01b0\u1ee3c \u0111\u00f3n nh\u1eadn r\u1ea5t n\u1ed3ng nhi\u1ec7t. Boltzmann l\u00e0 m\u1ed9t trong nh\u1eefng nh\u00e0 v\u1eadt l\u00fd c\u00f3 \u1ea3nh h\u01b0\u1edfng l\u00ean Einstein v\u1ec1 nhi\u1ec1u quan \u0111i\u1ec3m, nh\u01b0 quan ni\u1ec7m v\u1ec1 nguy\u00ean t\u1eed, c\u00e1ch nh\u00ecn th\u1ed1ng k\u00ea, tri\u1ebft h\u1ecdc t\u1ef1 nhi\u00ean. C\u00e1c \u00fd t\u01b0\u1edfng trong t\u00e1c ph\u1ea9m Popul\u00e4re Schriften<\/em> c\u0169ng \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u00e3 \u1ea3nh h\u01b0\u1edfng s\u00e2u s\u1eafc \u0111\u1ebfn nh\u00e0 tri\u1ebft h\u1ecdc Ludwig Wittgenstein. V\u1eadt l\u00fd c\u1ea7n \u0111\u1ebfn tri\u1ebft h\u1ecdc t\u1ef1 nhi\u00ean nh\u01b0 \u00fd t\u01b0\u1edfng \u0111\u1ecbnh h\u01b0\u1edbng, to\u00e1n h\u1ecdc, v\u00e0 th\u00ed nghi\u1ec7m nh\u01b0 c\u00f4ng c\u1ee5 th\u1ef1c hi\u1ec7n. Nh\u1eefng y\u1ebfu t\u1ed1 n\u00e0y \u0111\u00e3 d\u1eabn d\u1eaft c\u00e1c nh\u00e0 khoa h\u1ecdc ch\u00e2u \u00c2u t\u1eeb Quadrivium<\/em> c\u1ee7a gi\u00e1o d\u1ee5c khai ph\u00f3ng \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n m\u1ea1nh m\u1ebd \u1edf c\u00e1c \u0111\u1ea1i h\u1ecdc trung c\u1ed5 \u0111\u1ec3 cu\u1ed1i c\u00f9ng \u0111\u1ea1t t\u1edbi v\u1eadt l\u00fd hi\u1ec7n \u0111\u1ea1i m\u00e0 ti\u00eau bi\u1ec3u l\u00e0 Galileo Galilei. Xem th\u00eam Gi\u00e1o d\u1ee5c khai ph\u00f3ng \u2013 Kit\u00f4 gi\u00e1o v\u00e0 Di s\u1ea3n v\u0103n h\u00f3a Hy l\u1ea1p.<\/a><\/em><\/strong><\/p>\n

Anh c\u0169ng \u0111\u1eb7c bi\u1ec7t tham gia ch\u01b0\u01a1ng tr\u00ecnh mang t\u00ean “H\u1ecdc gi\u1ea3 h\u1ed9i t\u1ee5” \u0111\u00e3 \u0111\u01b0\u1ee3c Gi\u00e1o s\u01b0 Ng\u00f4 B\u1ea3o Ch\u00e2u c\u00f4ng b\u1ed1 th\u00e0nh l\u1eadp ng\u00e0y 6 th\u00e1ng 3. Theo ch\u01b0\u01a1ng tr\u00ecnh, m\u1ed7i gi\u00e1o s\u01b0 tham gia s\u1ebd d\u00e0nh t\u1eeb hai \u0111\u1ebfn ba th\u00e1ng m\u1ed7i n\u0103m l\u00e0m vi\u1ec7c v\u1edbi VIASM trong th\u1eddi gian ba n\u0103m ban \u0111\u1ea7u. H\u1ecd c\u0169ng s\u1ebd c\u00f9ng h\u01b0\u1edbng d\u1eabn c\u00e1c nghi\u00ean c\u1ee9u sinh ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc Khoa h\u1ecdc. Ch\u01b0\u01a1ng tr\u00ecnh n\u00e0y r\u1ea5t c\u00f3 \u00fd ngh\u0129a, m\u00e0 m\u1ed9t trong nh\u1eefng m\u1ee5c ti\u00eau s\u1ebd l\u00e0 \u0111\u00e0o t\u1ea1o ti\u1ebfn s\u0129 trong n\u01b0\u1edbc (home-made) m\u1ed9t tr\u0103m ph\u1ea7n tr\u0103m. C\u00e1c sinh vi\u00ean t\u00e0i n\u0103ng gi\u1ea3i Olympic c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y \u1edf \u0111\u00e2y m\u1ed9t m\u00f4i tr\u01b0\u1eddng h\u1ecdc h\u1ecfi v\u00e0 ph\u00e1t tri\u1ec3n ti\u1ebfp thu\u1eadn l\u1ee3i. H\u1ecd l\u00e0 nh\u1eefng ch\u00fa r\u1ed3ng con, gi\u1edd s\u1ebd c\u00f3 c\u01a1 h\u1ed9i \u0111\u1ec3 c\u1ea5t c\u00e1nh ngay tr\u00ean ch\u00ednh \u0111\u1ea5t n\u01b0\u1edbc m\u00ecnh, hi\u1ec7n th\u1ef1c h\u00f3a truy\u1ec1n thuy\u1ebft th\u0103ng long\u00a0<\/em><\/strong>ngh\u00ecn n\u0103m c\u1ee7a Vi\u1ec7t Nam.<\/span>\u00a0M\u1ed9t giai \u0111o\u1ea1n ph\u00e1t tri\u1ec3n m\u1edbi c\u1ee7a ng\u00e0nh to\u00e1n h\u1ecdc, v\u00e0 hy v\u1ecdng l\u00e0 h\u00ecnh m\u1ea9u cho t\u1ea5t c\u1ea3 c\u00e1c ng\u00e0nh kh\u00e1c. Xem th\u00eam tr\u01b0\u1eddng h\u1ee3p c\u1ee7a Hideki Yukawa\u2013Ng\u01b0\u1eddi l\u1eef h\u00e0nh c\u00f4 \u0111\u01a1n <\/a><\/em><\/strong>v\u00e0 s\u1ef1 \u0111\u00e0o t\u1ea1o home-made c\u1ee7a ng\u01b0\u1eddi Nh\u1eadt ngay t\u1eeb \u0111\u1ea7u th\u1eddi Minh Tr\u1ecb. H\u1ecd \u00fd th\u1ee9c s\u00e2u s\u1eafc thua k\u00e9m ph\u01b0\u01a1ng T\u00e2y v\u00ec khoa h\u1ecdc v\u00e0 gi\u00e1o d\u1ee5c t\u1ee5t h\u1eadu, n\u00ean \u0111\u00e3 ra s\u1ee9c h\u1ecdc h\u1ecfi t\u1ed1i \u0111a, \u0111em v\u0103n h\u00f3a khoa h\u1ecdc gieo tr\u1ed3ng t\u1ea1i tr\u00ean \u0111\u1ea5t n\u01b0\u1edbc h\u1ecd.<\/p>\n

Con \u0111\u01b0\u1eddng c\u1ee7a Phan Th\u00e0nh Nam<\/strong> c\u00f2n r\u1ea5t r\u1ed9ng v\u00e0 nhi\u1ec1u h\u00e0o h\u1ee9ng tr\u01b0\u1edbc m\u1eb7t. L\u00e3nh v\u1ef1c nghi\u00ean c\u1ee9u c\u1ee7a anh r\u1ea5t r\u1ed9ng v\u00e0 anh c\u00f3 \u0111\u1ed9 k\u1ebft n\u1ed1i cao v\u1edbi c\u00e1c nh\u00e0 khoa h\u1ecdc qu\u1ed1c t\u1ebf. \u1ede tu\u1ed5i \u0111\u1eddi m\u1edbi ch\u1ec9 41, anh c\u00f2n m\u1ed9t t\u01b0\u01a1ng lai \u0111\u1ea7y h\u1ee9a h\u1eb9n. Anh l\u00e0 ng\u01b0\u1eddi khi\u00eam t\u1ed1n v\u00e0 c\u1edfi m\u1edf, c\u00f3 m\u1ed9t background v\u0103n h\u00f3a khai s\u00e1ng, learned culture, t\u1ea1m g\u1ecdi nh\u01b0 th\u1ebf. Anh c\u00f3 m\u1ed9t facebook tr\u00ecnh b\u00e0y nh\u1eefng suy ngh\u0129 c\u1ee7a m\u00ecnh v\u1ec1 tri\u1ebft l\u00fd, v\u0103n h\u00f3a, khoa h\u1ecdc v\u00e0 c\u1ea3 nh\u1eefng c\u00e1i t\u1ea1m g\u1ecdi thu\u1ed9c l\u00e3nh v\u1ef1c si\u00eau h\u00ecnh: https:\/\/www.facebook.com\/ptnam373<\/a>. B\u00e0i vi\u1ebft c\u1ee7a anh tr\u00ean Tia S\u00e1ng v\u1ec1 \u0111\u1ec1 t\u00e0i Entropy v\u00e0 \u0110\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc l\u00e0 xu\u1ea5t s\u1eafc. \u0110\u1ecbnh lu\u1eadt n\u00e0y quan tr\u1ecdng \u0111\u1ebfn n\u1ed7i nh\u00e0 khoa h\u1ecdc, h\u1ecdc gi\u1ea3 C.P. Snow trong t\u00e1c ph\u1ea9m “Hai n\u1ec1n v\u0103n h\u00f3a” (1959) \u0111\u00e3 l\u1eadp lu\u1eadn r\u1eb1ng ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai c\u1ee7a nhi\u1ec7t \u0111\u1ed9ng l\u1ef1c h\u1ecdc l\u00e0 m\u1ed9t th\u00e0nh ph\u1ea7n thi\u1ebft y\u1ebfu kh\u00f4ng th\u1ec3 thi\u1ebfu c\u1ee7a n\u0103ng l\u1ef1c v\u0103n h\u00f3a (literacy) trong th\u1ebf gi\u1edbi hi\u1ec7n \u0111\u1ea1i. \u00d4ng kh\u1eb3ng \u0111\u1ecbnh, vi\u1ec7c kh\u00f4ng bi\u1ebft \u0111\u1ecbnh lu\u1eadt th\u1ee9 hai n\u00e0y c\u0169ng t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi vi\u1ec7c ch\u01b0a t\u1eebng \u0111\u1ecdc m\u1ed9t t\u00e1c ph\u1ea9m n\u00e0o c\u1ee7a Shakespeare.<\/p>\n

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Johann Carl Friedrich Gauss<\/strong> (1777\u20131855), m\u1ed9t nh\u00e0 b\u00e1c h\u1ecdc ng\u01b0\u1eddi \u0110\u1ee9c \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t trong nh\u1eefng nh\u00e0 to\u00e1n h\u1ecdc c\u00f3 \u1ea3nh h\u01b0\u1edfng nh\u1ea5t trong l\u1ecbch s\u1eed. L\u00e3nh v\u1ef1c c\u1ee7a \u00f4ng bao tr\u00f9m: to\u00e1n h\u1ecdc, l\u00fd thuy\u1ebft s\u1ed1, gi\u1ea3i t\u00edch, h\u00ecnh h\u1ecdc, th\u1ed1ng k\u00ea v\u00e0 x\u00e1c su\u1ea5t, thi\u00ean v\u0103n h\u1ecdc, tr\u1eafc \u0111\u1ecba h\u1ecdc v\u00e0 v\u1eadt l\u00fd . \u00d4ng l\u00e0 m\u1ed9t th\u1ea7n \u0111\u1ed3ng. Khi ba tu\u1ed5i, c\u1eadu b\u00e9 Gauss \u0111\u00e3 m\u1ed9t l\u1ea7n k\u00eau l\u00ean “B\u1ed1 \u01a1i, b\u1ed1 t\u00ednh sai r\u1ed3i!” khi ph\u00e1t hi\u1ec7n l\u1ed7i trong b\u1ea3ng danh s\u00e1ch ph\u00e1t ti\u1ec1n cho c\u00e1c ph\u1ee5 t\u00e1 trong nh\u00e0 tr\u1ebb. Ki\u1ec3m tra l\u1ea1i, b\u1ed1 th\u1ea5y con m\u00ecnh n\u00f3i \u0111\u00fang. Gauss th\u01b0\u1eddng n\u00f3i vui r\u1eb1ng \u00f4ng \u0111\u00e3 h\u1ecdc \u0111\u1ebfm tr\u01b0\u1edbc khi h\u1ecdc n\u00f3i <\/em><\/strong>(nh\u01b0 Einstein t\u1eadp suy ngh\u0129 b\u1eb1ng h\u00ecnh \u1ea3nh tr\u01b0\u1edbc khi h\u1ecdc n\u00f3i). Th\u1eadt s\u1ef1 \u00f4ng \u0111\u00e3 tr\u1edf th\u00e0nh \u00f4ng ho\u00e0ng c\u1ee7a to\u00e1n h\u1ecdc, \u0111\u1eb7c bi\u1ec7t c\u1ee7a ng\u00e0nh s\u1ed1 h\u1ecdc v\u1edbi t\u00e1c ph\u1ea9m \u0111\u1eb7c bi\u1ec7t c\u1ee7a \u00f4ng: Disquisitiones Arithmeticae<\/strong>, <\/em>m\u1ed9t lo\u1ea1i s\u00e1ch gi\u00e1o khoa kh\u1ea3o s\u00e1t v\u1ec1 s\u00f4 h\u1ecdc mang t\u00ednh c\u00e1ch m\u1ea1ng. L\u00fac \u0111\u00f3 \u00f4ng 24 tu\u1ed5i (1801). Con s\u1ed1 \u0111\u00e3 tr\u1edf th\u00e0nh nh\u1eefng n\u1ed1t nh\u1ea1c c\u1ee7a \u00f4ng, thay v\u00ec l\u00e0 n\u1ed1t nh\u1ea1c c\u1ee7a Amadeus Mozart. Ngo\u00e0i ra \u00f4ng c\u0169ng tham gia t\u1ea1o ra kh\u00f4ng gian phi-Euclid hai chi\u1ec1u, m\u00e0 h\u1ecdc tr\u00f2 \u00f4ng Bernhard Riemann sau \u0111\u00f3 \u0111\u00e3 n\u00e2ng l\u00ean th\u00e0nh nhi\u1ec1u chi\u1ec1u. N\u0103m m\u01b0\u01a1i n\u0103m sau, Einstein \u0111\u00e3 s\u1eed d\u1ee5ng lo\u1ea1i kh\u00f4ng gian n\u00e0y cho thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i r\u1ed9ng c\u1ee7a \u00f4ng.<\/p>\n

Xem th\u00eam Con \u0111\u01b0\u1eddng c\u1ee7a Einstein th\u1eddi trai tr\u1ebb<\/em><\/a><\/strong> \u0111\u01b0\u1ee3c vi\u1ebft g\u1ea7n \u0111\u00e2y.<\/p>\n

Xin nhi\u1ec7t li\u1ec7t gi\u1edbi thi\u1ec7u anh ch\u1ecb b\u00e0i vi\u1ebft c\u1ee7a Phan Th\u00e0nh Nam<\/strong>. Nh\u1eefng c\u00e2u chuy\u1ec7n k\u1ec3 c\u1ee7a anh di\u1ec5n ra trong th\u1ebf gi\u1edbi l\u01b0\u1ee3ng t\u1eed \u0111\u1ed1i v\u1edbi ng\u01b0\u1eddi th\u01b0\u1eddng tuy l\u1ea1 l\u1eabm, nh\u01b0ng c\u00f3 s\u1ee9c h\u00fat m\u1ea1nh m\u1ebd nh\u01b0 nh\u1eefng c\u00e2u chuy\u1ec7n ch\u01b0\u1edfng c\u1ee7a Kim Dung, ho\u1eb7c h\u01a1n. “Ph\u00e9p g\u1eadp s\u1ed1” c\u1ee7a c\u1eadu b\u00e9 Gauss gi\u1edd \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng m\u1ed9t c\u00e1ch s\u00e1ng t\u1ea1o th\u00e0nh “ph\u00e9p g\u1eadp l\u01b0\u1ee3ng t\u1eed” b\u1eaft \u0111\u01b0\u1ee3c c\u00e2y c\u1ea7u gi\u1eefa hai th\u1ebf gi\u1edbi kh\u00e1c bi\u1ec7t boson v\u00e0 fermion \u0111\u1ec3 h\u00f3a gi\u1ea3i nh\u1eefng kh\u00f3 kh\u0103n. C\u00f3 l\u1ebd ch\u00fang ta c\u1ea7n th\u00eam m\u1ed9t quy\u1ec3n s\u00e1ch<\/em> c\u1ee7a anh Nam \u0111\u1ec3 hi\u1ec3u nhi\u1ec1u h\u01a1n nh\u1eefng c\u00e1i huy\u1ec1n b\u00ed trong th\u1ebf gi\u1edbi l\u01b0\u1ee3ng t\u1eed.<\/p>\n

T\u01b0 duy v\u00e0 \u00f3c engineering s\u00e1ng t\u1ea1o c\u1ee7a con ng\u01b0\u1eddi d\u1ea7n d\u1ea7n l\u00e0m tan ch\u1ea3y nh\u1eefng b\u00e0i to\u00e1n t\u01b0\u1edfng ch\u1eebng kh\u00f4ng v\u01b0\u1ee3t \u0111\u01b0\u1ee3c, c\u00f3 th\u1ec3 m\u1edf ra nh\u1eefng th\u1ebf gi\u1edbi ho\u00e0n to\u00e0n m\u1edbi. C\u00e2u n\u00f3i cu\u1ed1i b\u00e0i c\u1ee7a anh Nam “Bi\u1ebft \u0111\u00e2u, ch\u00ednh nh\u1eefng c\u00fa g\u1eadp ng\u1eabu nhi\u00ean trong \u0111\u1eddi l\u1ea1i l\u00e0 \u0111i\u1ec3m kh\u1edfi \u0111\u1ea7u cho nh\u1eefng h\u00e0nh tr\u00ecnh th\u00fa v\u1ecb nh\u1ea5t.<\/em><\/strong>” V\u00e2ng, ch\u00fang ta r\u1ea5t hy v\u1ecdng nh\u01b0 th\u1ebf, v\u00e0 ch\u00fac anh Nam g\u1eb7t h\u00e1i th\u00eam nhi\u1ec1u th\u00e0nh c\u00f4ng tr\u00ean c\u00e1nh \u0111\u1ed3ng m\u00e0 anh v\u00e0 c\u00e1c b\u1ea1n v\u1eeba gieo h\u1ea1t.<\/p>\n

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Nguy\u1ec5n Xu\u00e2n Xanh<\/strong><\/span><\/p>\n

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T\u1eeb<\/em>\u00a0GAUSS\u00a0\u0111\u1ebfn<\/em> BOSE\u2013FERMI:<\/span><\/h1>\n

PH\u00c9P G\u1eacP TRONG TO\u00c1N V\u00c0 V\u1eacT L\u00dd<\/span><\/h1>\n

Phan Th\u00e0nh Nam<\/span><\/strong><\/h1>\n

Trong l\u1ecbch s\u1eed to\u00e1n h\u1ecdc, c\u00f3 l\u1ebd chi\u00eau \u201cg\u1eadp s\u1ed1\u201d c\u1ee7a c\u1eadu b\u00e9 Gauss l\u00e0 m\u1ed9t trong nh\u1eefng tuy\u1ec7t k\u1ef9 n\u1ed5i ti\u1ebfng nh\u1ea5t. C\u00e2u chuy\u1ec7n k\u1ec3 r\u1eb1ng khi m\u1edbi 7 tu\u1ed5i, Gauss b\u1ecb th\u1ea7y gi\u00e1o giao cho m\u1ed9t \u201ch\u00ecnh ph\u1ea1t\u201d: c\u1ed9ng 1+2+3+…+100. T\u01b0\u1edfng r\u1eb1ng c\u1eadu h\u1ecdc tr\u00f2 s\u1ebd ng\u1ed3i c\u1ed9ng m\u1ecfi tay, n\u00e0o ng\u1edd ch\u1ec9 trong ch\u1edbp m\u1eaft c\u1eadu \u0111\u00e3 \u0111\u01b0a ra k\u1ebft qu\u1ea3 5050. B\u00ed quy\u1ebft c\u1ee7a Gauss kh\u00f4ng n\u1eb1m \u1edf t\u1ed1c \u0111\u1ed9 c\u1ed9ng, m\u00e0 \u1edf m\u1ed9t ph\u00e1t hi\u1ec7n \u0111\u1ed1i x\u1ee9ng: n\u1ebfu vi\u1ebft d\u00e3y s\u1ed1 1,2,…,100 theo th\u1ee9 t\u1ef1 th\u1eb3ng h\u00e0ng tr\u00ean m\u1ed9t t\u1edd gi\u1ea5y r\u1ed3i g\u1eadp l\u1ea1i, th\u00ec s\u1ed1 1 g\u1eb7p s\u1ed1 100, s\u1ed1 2 g\u1eb7p s\u1ed1 99, …, m\u00e0 m\u1ed7i c\u1eb7p nh\u01b0 v\u1eady \u0111\u1ec1u c\u00f3 t\u1ed5ng l\u00e0 101, cho n\u00ean 50*101=5050 ch\u00ednh l\u00e0 t\u1ed5ng to\u00e0n b\u1ed9. M\u1ed9t ph\u00e9p g\u1eadp \u0111\u01a1n gi\u1ea3n \u0111\u00e3 bi\u1ebfn m\u1ed9t c\u00f4ng vi\u1ec7c c\u01a1 b\u1eafp th\u00e0nh m\u1ed9t l\u1eddi gi\u1ea3i thanh tho\u00e1t.<\/p>\n

\u0110i\u1ec1u th\u00fa v\u1ecb l\u00e0 h\u01a1n hai th\u1ebf k\u1ef7 sau, tinh th\u1ea7n c\u1ee7a Gauss v\u1eabn t\u1ecfa s\u00e1ng trong nhi\u1ec1u nghi\u00ean c\u1ee9u hi\u1ec7n \u0111\u1ea1i. G\u1ea7n \u0111\u00e2y, c\u00f9ng v\u1edbi c\u00e1c \u0111\u1ed3ng nghi\u1ec7p \u1edf LMU v\u00e0 ISTA (arXiv:2505.22340), ch\u00fang t\u00f4i nghi\u00ean c\u1ee9u gi\u1ea3 thuy\u1ebft Huang\u2013Yang (1957) v\u1ec1 c\u00f4ng th\u1ee9c n\u0103ng l\u01b0\u1ee3ng cho kh\u00ed Fermi lo\u00e3ng, trong \u0111\u00f3 s\u1eed d\u1ee5ng m\u1ed9t \u00fd t\u01b0\u1edfng \u0111\u1eb9p t\u1eeb v\u1eadt l\u00fd: ph\u00e9p g\u1eadp l\u01b0\u1ee3ng t\u1eed. Kh\u00f4ng ph\u1ea3i “g\u1eadp s\u1ed1” nh\u01b0 Gauss, m\u00e0 l\u00e0 “g\u1eadp nh\u1eefng h\u1ea1t l\u01b0\u1ee3ng t\u1eed” \u0111\u1ec3 k\u1ebft n\u1ed1i hai th\u1ebf gi\u1edbi t\u01b0\u1edfng ch\u1eebng \u0111\u1ed1i l\u1eadp: th\u1ebf gi\u1edbi fermion c\u1ee7a Pauli v\u00e0 Fermi n\u01a1i nguy\u00ean l\u00fd lo\u1ea1i tr\u1eeb nghi\u00eam c\u1ea5m m\u1ecdi s\u1ef1 chen ch\u00fac, v\u00e0 th\u1ebf gi\u1edbi boson c\u1ee7a Bose v\u00e0 Einstein n\u01a1i c\u00e1c h\u1ea1t c\u00f3 th\u1ec3 ch\u1ed3ng l\u1ea5n l\u00ean nhau v\u00f4 t\u1eadn. B\u1eb1ng c\u00e1ch gh\u00e9p \u0111\u00f4i c\u00e1c h\u1ea1t fermion \u0111\u1ec3 bi\u1ebfn ch\u00fang th\u00e0nh boson, ph\u01b0\u01a1ng ph\u00e1p n\u00e0y cho ph\u00e9p \u00e1p d\u1ee5ng nh\u1eefng c\u00f4ng c\u1ee5 quen thu\u1ed9c t\u1eeb th\u1ebf gi\u1edbi \u0111\u1ed1i x\u1ee9ng Bose gas \u0111\u1ec3 hi\u1ec3u v\u1ec1 th\u1ebf gi\u1edbi ph\u1ea3n \u0111\u1ed1i x\u1ee9ng Fermi gas.<\/p>\n

N\u0103m 1924, Bose vi\u1ebft m\u1ed9t b\u00e0i b\u00e1o v\u1ec1 th\u1ed1ng k\u00ea photon, trong \u0111\u00f3 \u00f4ng \u0111\u01b0a ra m\u1ed9t c\u00e1ch di\u1ec5n gi\u1ea3i ho\u00e0n to\u00e0n m\u1edbi cho \u0111\u1ecbnh lu\u1eadt b\u1ee9c x\u1ea1 c\u1ee7a Planck (1900). Trong c\u00f4ng tr\u00ecnh \u0111\u01b0\u1ee3c xem l\u00e0 khai sinh ra c\u01a1 h\u1ecdc l\u01b0\u1ee3ng t\u1eed (Nobel V\u1eadt l\u00fd 1918), \u0111\u1ec3 gi\u1ea3i th\u00edch ph\u1ed5 b\u1ee9c x\u1ea1 c\u1ee7a v\u1eadt \u0111en, Planck gi\u1ea3 \u0111\u1ecbnh l\u00e0 n\u0103ng l\u01b0\u1ee3ng c\u1ee7a dao \u0111\u1ed9ng t\u1eed l\u00e0 l\u01b0\u1ee3ng t\u1eed ho\u00e1 theo b\u1ed9i s\u1ed1 r\u1eddi r\u1ea1c E = nhv,<\/em>\u00a0trong \u0111\u00f3 m\u1ed7i photon gi\u1ed1ng nh\u01b0 m\u1ed9t vi\u00ean g\u1ea1ch c\u00f3 n\u0103ng l\u01b0\u1ee3ng b\u1eb1ng h\u1eb1ng s\u1ed1 Planck h<\/em> nh\u00e2n v\u1edbi t\u1ea7n s\u1ed1 dao \u0111\u1ed9ng c\u1ee7a \u00e1nh s\u00e1ng v<\/em>, c\u00f2n n<\/em> ch\u00ednh l\u00e0 s\u1ed1 vi\u00ean g\u1ea1ch.\u00a0 Kh\u00f4ng \u0111\u1eb7t gi\u1ea3 thi\u1ebft nh\u01b0 Planck, Bose \u0111\u00e3 xu\u1ea5t ph\u00e1t t\u1eeb nguy\u00ean l\u00fd \u0111\u1ebfm vi m\u00f4, nh\u01b0ng thay v\u00ec coi photon l\u00e0 c\u00e1c h\u1ea1t ph\u00e2n bi\u1ec7t (nh\u01b0 trong th\u1ed1ng k\u00ea Maxwell\u2013Boltzmann), \u00f4ng xem ch\u00fang l\u00e0 kh\u00f4ng ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c. \u0110i\u1ec1u n\u00e0y d\u1eabn t\u1edbi c\u00e1ch \u0111\u1ebfm m\u1edbi, sau n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 th\u1ed1ng k\u00ea Bose\u2013Einstein, c\u00f3 th\u1ec3 m\u00f4 t\u1ea3 b\u1eb1ng \u0111\u1ed1i x\u1ee9ng ho\u00e1n v\u1ecb trong to\u00e1n h\u1ecdc: n\u1ebfu \u0111\u1ed5i ch\u1ed7 hai boson th\u00ec h\u00e0m s\u00f3ng to\u00e0n th\u1ec3 kh\u00f4ng thay \u0111\u1ed5i.<\/p>\n

Bose g\u1eedi b\u00e0i b\u00e1o c\u1ee7a m\u00ecnh t\u1edbi m\u1ed9t t\u1ea1p ch\u00ed c\u1ee7a Anh (Philosophical Magazine) nh\u01b0ng b\u1ecb t\u1eeb ch\u1ed1i, c\u00f3 l\u1ebd v\u00ec khi \u1ea5y \u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t gi\u1ea3ng vi\u00ean tr\u1ebb \u1edf \u1ea4n \u0110\u1ed9 thu\u1ed9c \u0111\u1ecba. Tuy v\u1eady, \u00f4ng \u0111\u00e3 vi\u1ebft th\u01b0 cho Einstein b\u1eb1ng ti\u1ebfng Anh, g\u1eedi k\u00e8m b\u1ea3n th\u1ea3o b\u00e0i b\u00e1o. \u0110\u00e2y c\u00f3 th\u1ec3 xem l\u00e0 m\u1ed9t h\u00e0nh \u0111\u1ed9ng d\u0169ng c\u1ea3m v\u00ec khi \u0111\u00f3 Einstein \u0111ang l\u00e0 “\u0111\u1ea1i hi\u1ec7p v\u00f5 l\u00e2m” sau khi c\u00f4ng b\u1ed1 thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i h\u1eb9p (1905), thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i r\u1ed9ng (1915) v\u00e0 nh\u1eadn gi\u1ea3i Nobel v\u1eadt l\u00fd 1921 cho c\u00f4ng tr\u00ecnh gi\u1ea3i th\u00edch hi\u1ec7u \u1ee9ng quang \u0111i\u1ec7n. Einstein \u0111\u00e3 kh\u00f4ng ph\u1edbt l\u1edd m\u00e0 tr\u00e1i l\u1ea1i r\u1ea5t h\u1ee9ng th\u00fa: \u00f4ng t\u1ef1 d\u1ecbch ra ti\u1ebfng \u0110\u1ee9c, g\u1eedi \u0111\u0103ng gi\u00f9m Bose tr\u00ean t\u1edd “Zeitschrift f\u00fcr Physik”, r\u1ed3i c\u00f2n vi\u1ebft th\u00eam hai b\u00e0i b\u00e1o m\u1edf r\u1ed9ng. Trong b\u00e0i b\u00e1o th\u1ee9 hai, vi\u1ebft c\u00e1ch \u0111\u00e2y \u0111\u00fang 100 n\u0103m, Einstein \u0111\u00e3 ti\u00ean \u0111o\u00e1n m\u1ed9t tr\u1ea1ng th\u00e1i m\u1edbi c\u1ee7a v\u1eadt ch\u1ea5t l\u00e0 ng\u01b0ng t\u1ee5 Bose\u2013Einstein (BEC), n\u01a1i v\u00f4 s\u1ed1 h\u1ea1t l\u01b0\u1ee3ng t\u1eed r\u01a1i v\u00e0o c\u00f9ng m\u1ed9t tr\u1ea1ng th\u00e1i \u1edf nhi\u1ec7t \u0111\u1ed9 c\u1ef1c th\u1ea5p (g\u1ea7n 0 \u0111\u1ed9 K = \u2212273 \u0111\u1ed9 C). C\u00f9ng v\u1edbi vi\u1ec7c t\u1ea1o ra BEC trong ph\u00f2ng th\u00ed nghi\u1ec7m n\u0103m 1995, d\u1eabn t\u1edbi gi\u1ea3i Nobel V\u1eadt l\u00fd 2001 cho Cornell, Wieman v\u00e0 Ketterle, vi\u1ec7c hi\u1ec3u r\u00f5 BEC v\u00e0 c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng l\u01b0\u1ee3ng t\u1eed li\u00ean quan tr\u1edf th\u00e0nh “ch\u1ee7 \u0111\u1ec1 n\u00f3ng trong kh\u00ed l\u1ea1nh”: nghi\u00ean c\u1ee9u th\u1ee9 x\u1ea3y ra g\u1ea7n \u0111\u1ed9 0 tuy\u1ec7t \u0111\u1ed1i nh\u01b0ng l\u00e0m s\u00f4i \u0111\u1ed9ng c\u1ea3 gi\u1edbi khoa h\u1ecdc.<\/p>\n

H\u00e3y th\u1eed h\u00ecnh dung tr\u00ean m\u1ed9t s\u00e2n v\u1eadn \u0111\u1ed9ng h\u00e0ng v\u1ea1n ng\u01b0\u1eddi, n\u1ebfu m\u1ed7i ng\u01b0\u1eddi ch\u01a1i m\u1ed9t n\u1ed1t nh\u1ea1c ri\u00eang th\u00ec ch\u00fang ta ch\u1ec9 nghe th\u1ea5y s\u1ef1 h\u1ed7n lo\u1ea1n. Nh\u01b0ng n\u1ebfu c\u1ea3 s\u00e2n b\u1ed7ng \u0111\u1ed3ng lo\u1ea1t ng\u00e2n c\u00f9ng m\u1ed9t n\u1ed1t, \u00e2m thanh \u1ea5y s\u1ebd r\u1ea5t d\u00e0y v\u00e0 vang xa. \u0110\u00f3 ch\u00ednh l\u00e0 h\u00ecnh \u1ea3nh c\u1ee7a Bose\u2013Einstein condensation: t\u1eeb h\u1ed7n lo\u1ea1n th\u00e0nh h\u1ee3p x\u01b0\u1edbng khi t\u1ea5t c\u1ea3 c\u00f9ng \u0111\u1ed3ng l\u00f2ng h\u00e1t m\u1ed9t b\u1ea3n nh\u1ea1c chung. \u0110i\u1ec1u n\u00e0y ph\u00f9 h\u1ee3p v\u1edbi lu\u1eadt s\u1ed1 l\u1edbn trong x\u00e1c su\u1ea5t, n\u00f3i r\u1eb1ng khi s\u1ed1 \u0111\u00f4ng \u0111\u1ee7 l\u1edbn th\u00ec trung b\u00ecnh s\u1ebd l\u1ea5n \u00e1t kh\u00e1c bi\u1ec7t. T\u1eeb \u0111\u00e2y, ph\u01b0\u01a1ng tr\u00ecnh Gross\u2013Pitaevskii (m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh Schr\u00f6dinger phi tuy\u1ebfn) ra \u0111\u1eddi, tr\u1edf th\u00e0nh n\u1ed1t nh\u1ea1c ch\u1ee7 c\u1ee7a d\u00e0n boson.<\/p>\n

Nh\u01b0ng m\u1ed9t b\u1ea3n nh\u1ea1c \u0111\u00e2u th\u1ec3 ch\u1ec9 c\u00f3 m\u1ed9t n\u1ed1t. Khi c\u00f3 s\u1ef1 t\u01b0\u01a1ng t\u00e1c gi\u1eefa nh\u1eefng ngh\u1ec7 s\u0129, ch\u1eafn ch\u1eafn s\u1ebd c\u00f3 s\u1ef1 l\u1ec7ch pha, v\u00e0 \u0111i\u1ec1u th\u00fa v\u1ecb ch\u00ednh l\u00e0 nh\u1eefng dao \u0111\u1ed9ng xung quanh n\u1ed1t ch\u1ee7. N\u0103m 1947, Bogoliubov \u0111\u01b0a ra m\u1ed9t l\u00fd thuy\u1ebft n\u1ec1n t\u1ea3ng cho kh\u00ed Bose, m\u00f4 t\u1ea3 ph\u00e2n b\u1ed1 dao \u0111\u1ed9ng quanh tr\u1ea1ng th\u00e1i ng\u01b0ng t\u1ee5 Bose\u2013Einstein nh\u01b0 m\u1ed9t \u0111\u1ecbnh l\u00fd gi\u1edbi h\u1ea1n trung t\u00e2m trong x\u00e1c su\u1ea5t. V\u1ec1 m\u1eb7t to\u00e1n h\u1ecdc, l\u00fd thuy\u1ebft Bogoliubov c\u00f3 th\u1ec3 hi\u1ec3u nh\u01b0 l\u00e0 d\u1ea1ng l\u01b0\u1ee3ng t\u1eed ho\u00e1 cho ph\u00e9p khai tri\u1ec3n Taylor b\u1eadc hai c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh Gross\u2013Pitaevskii. V\u1ec1 m\u1eb7t v\u1eadt l\u00fd, l\u00fd thuy\u1ebft Bogoliubov cho th\u1ea5y ph\u1ed5 dao \u0111\u1ed9ng (excitation spectrum) c\u1ee7a boson l\u00e0 tuy\u1ebfn t\u00ednh \u1edf v\u1eadn t\u1ed1c nh\u1ecf, t\u1eeb \u0111\u00f3 gi\u1ea3i th\u00edch ti\u00eau chu\u1ea9n “si\u00eau l\u1ecfng” c\u1ee7a Landau (Nobel V\u1eadt l\u00fd 1962), hi\u1ec7n t\u01b0\u1ee3ng m\u00e0 c\u00e1c h\u1ea1t l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 ch\u1ea3y nh\u01b0 ch\u1ea5t l\u1ecfng m\u00e0 kh\u00f4ng c\u00f3 ma s\u00e1t, t\u01b0\u01a1ng t\u1ef1 nh\u01b0 m\u1ed9t cao th\u1ee7 c\u00f3 khinh c\u00f4ng \u1edf m\u1ee9c “thu\u1ef7 th\u01b0\u1ee3ng phi\u00eau” c\u00f3 th\u1ec3 l\u01b0\u1edbt \u0111i tr\u00ean n\u01b0\u1edbc m\u00e0 kh\u00f4ng \u0111\u1ec3 l\u1ea1i g\u1ee3n s\u00f3ng.<\/p>\n

Vi\u1ec7c hi\u1ec3u \u0111\u01b0\u1ee3c ng\u01b0ng t\u1ee5 Bose-Einstein v\u00e0 l\u00fd thuy\u1ebft Bogoliubov\u00a0 d\u1ef1a tr\u00ean nguy\u00ean l\u00fd c\u0103n b\u1ea3n c\u1ee7a v\u1eadt l\u00fd l\u01b0\u1ee3ng t\u1eed nhi\u1ec1u h\u1ea1t lu\u00f4n l\u00e0 m\u1ed9t \u00e1m \u1ea3nh \u0111\u1eb9p v\u1edbi t\u00f4i t\u1eeb nh\u1eefng ng\u00e0y l\u00e0m PhD. C\u00e2u h\u1ecfi t\u1ef1 nhi\u00ean l\u00e0 li\u1ec7u ch\u00fang ta c\u00f3 th\u1ec3 bi\u1ebfn tr\u1ef1c gi\u00e1c \u0111\u1ea7y ch\u1ea5t nh\u1ea1c th\u00e0nh m\u1ed9t \u0111\u1ecbnh l\u00fd to\u00e1n h\u1ecdc, v\u1edbi c\u00e1c \u0111\u00e1nh gi\u00e1 sai s\u1ed1 t\u01b0\u1eddng minh. \u0110\u00f3 l\u00e0 m\u1ed9t ch\u1eb7ng \u0111\u01b0\u1eddng d\u00e0i v\u1edbi r\u1ea5t nhi\u1ec1u b\u00e0i to\u00e1n m\u1edf, v\u00e0 m\u1ed7i b\u01b0\u1edbc ti\u1ebfn \u0111\u1ec1u h\u00e9 l\u1ed9 th\u00eam chi\u1ec1u s\u00e2u v\u00f4 h\u1ea1n c\u1ee7a th\u1ebf gi\u1edbi l\u01b0\u1ee3ng t\u1eed.<\/p>\n

N\u1ebfu boson l\u00e0 d\u00e0n \u0111\u1ed3ng ca ngoan ngo\u00e3n, th\u00ec fermion l\u1ea1i l\u00e0 \u0111o\u00e0n qu\u00e2n k\u1ef7 lu\u1eadt. Do tu\u00e2n theo th\u1ed1ng k\u00ea Fermi\u2013Dirac, ch\u00fang bu\u1ed9c ph\u1ea3i ph\u1ea3n \u0111\u1ed1i x\u1ee9ng: kh\u00f4ng hai h\u1ea1t n\u00e0o \u0111\u01b0\u1ee3c \u1edf c\u00f9ng m\u1ed9t tr\u1ea1ng th\u00e1i. Nh\u1edd v\u1eady, electron m\u1edbi theo nguy\u00ean l\u00fd lo\u1ea1i tr\u1eeb Pauli, nguy\u00ean t\u1eed m\u1edbi c\u00f3 c\u1ea5u tr\u00fac l\u1edbp v\u1ecf, v\u00e0 v\u1eadt ch\u1ea5t m\u1edbi b\u1ec1n v\u1eefng. Nh\u01b0ng \u0111\u1ed1i v\u1edbi to\u00e1n h\u1ecdc, s\u1ef1 ph\u1ea3n \u0111\u1ed1i x\u1ee9ng n\u00e0y l\u00e0 m\u1ed9t r\u00e0o c\u1ea3n l\u1edbn v\u00ec nhi\u1ec1u k\u1ef9 thu\u1eadt \u0111\u1eb9p c\u1ee7a boson kh\u00f4ng c\u00f2n \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c.<\/p>\n

\u1ede t\u00ecnh tr\u1ea1ng kh\u00f4ng c\u00f3 t\u01b0\u01a1ng t\u00e1c, kh\u00ed Fermi l\u00fd t\u01b0\u1edfng \u1edf tr\u1ea1ng th\u00e1i n\u0103ng l\u01b0\u1ee3ng th\u1ea5p nh\u1ea5t t\u1ea1o th\u00e0nh m\u1ed9t Fermi ball trong kh\u00f4ng gian \u0111\u1ed9ng l\u01b0\u1ee3ng: t\u1ea5t c\u1ea3 c\u00e1c h\u1ea1t l\u01b0\u1ee3ng t\u1eed l\u1ea5p k\u00edn b\u00ean trong qu\u1ea3 c\u1ea7u, b\u00ean ngo\u00e0i th\u00ec ho\u00e0n to\u00e0n tr\u1ed1ng r\u1ed7ng. Khi c\u00f3 l\u1ef1c t\u01b0\u01a1ng t\u00e1c, c\u00e1c h\u1ea1t l\u01b0\u1ee3ng t\u1eed s\u1ebd dao \u0111\u1ed9ng m\u1ed9t t\u00fd \u0111\u1ec3 ph\u00e1 v\u1ee1 c\u1ea5u tr\u00fac nh\u1ecb nguy\u00ean n\u00e0y, v\u00e0 hi\u1ec3u r\u00f5 vi\u1ec7c ch\u00fang v\u01b0\u1ee3t qua ng\u0103n c\u00e1ch v\u00f4 h\u00ecnh c\u1ee7a m\u1eb7t c\u1ea7u Fermi nh\u01b0 th\u1ebf n\u00e0o l\u00e0 m\u1ed9t c\u00e2u h\u1ecfi tr\u1ecdng t\u00e2m trong v\u1eadt l\u00fd l\u00fd thuy\u1ebft, li\u00ean quan t\u1edbi b\u1ea3n ch\u1ea5t s\u00e2u s\u1eafc c\u1ee7a t\u01b0\u01a1ng quan l\u01b0\u1ee3ng t\u1eed (quantum correlation).<\/p>\n

Trong m\u1ed9t b\u00e0i b\u00e1o c\u1ee7a Huang v\u00e0 Yang vi\u1ebft n\u0103m 1957, c\u00f9ng n\u0103m khi Yang (D\u01b0\u01a1ng Ch\u1ea5n Ninh) nh\u1eadn gi\u1ea3i Nobel V\u1eadt l\u00fd, thay v\u00ec x\u1eed l\u00fd tr\u1ef1c ti\u1ebfp c\u00e1c t\u01b0\u01a1ng t\u00e1c ph\u1ee9c t\u1ea1p, h\u1ecd d\u00f9ng m\u1ed9t m\u1eb9o do Fermi kh\u1edfi x\u01b0\u1edbng g\u1ecdi l\u00e0 “th\u1ebf gi\u1ea3” (pseudopotential). \u0110\u00e2y l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p r\u1ea5t tinh vi, trong \u0111\u00f3 thay v\u00ec t\u00ednh t\u1ea5t c\u1ea3 nh\u1eefng t\u01b0\u01a1ng t\u00e1c ph\u1ee9c t\u1ea1p, ta ch\u1ec9 c\u1ea7n d\u1ef1 \u0111o\u00e1n l\u00e0 sau t\u01b0\u01a1ng t\u00e1c th\u00ec h\u00e0m s\u00f3ng b\u1ecb “l\u1ec7ch pha” bao nhi\u00eau, v\u00e0 gom t\u1ea5t c\u1ea3 th\u00f4ng tin \u1ea5y v\u00e0o m\u1ed9t th\u1ebf n\u0103ng gi\u1ea3 \u0111\u1ecbnh. Nh\u1edd k\u1ef9 thu\u1eadt n\u00e0y, h\u1ecd \u0111\u00e3 t\u00ednh \u0111\u01b0\u1ee3c x\u1ea5p x\u1ec9 c\u00e1c m\u1ee9c n\u0103ng l\u01b0\u1ee3ng cho kh\u00ed Fermi theo m\u1ed9t c\u00e1ch r\u1ea5t gi\u1ed1ng v\u1edbi c\u00e1ch t\u00ednh c\u00e1c m\u1ee9c n\u0103ng l\u01b0\u1ee3ng cho kh\u00ed Bose \u1edf nhi\u1ec7t \u0111\u1ed9 th\u1ea5p. Tuy nhi\u00ean, ch\u1ee9ng minh ch\u1eb7t ch\u1ebd d\u1ef1 \u0111o\u00e1n c\u1ee7a Huang v\u00e0 Yang l\u00e0 kh\u00f4ng t\u1ea7m th\u01b0\u1eddng, v\u00ec c\u00f3 v\u1ebb nh\u01b0 hai lo\u1ea1i h\u1ea1t boson v\u00e0 fermion r\u1ea5t kh\u00e1c nhau v\u1ec1 m\u1eb7t v\u1eadt l\u00fd v\u00e0 vi\u1ec7c b\u1eaft m\u1ed9t c\u00e2y c\u1ea7u to\u00e1n h\u1ecdc gi\u1eefa hai th\u1ebf gi\u1edbi n\u00e0y nghe c\u00f3 v\u1ebb kh\u00e1 h\u00e3o huy\u1ec1n.<\/p>\n

Th\u1ebf nh\u01b0ng \u0111i\u1ec1u b\u1ea5t ng\u1edd l\u00e0 v\u1edbi m\u1ed9t ph\u00e9p \u201cg\u1eadp h\u1ea1t” th\u00ec ta v\u1eabn l\u00e0m \u0111\u01b0\u1ee3c. Do nguy\u00ean l\u00fd b\u1ea3o to\u00e0n, h\u1ec5 m\u1ed9t h\u1ea1t fermion nh\u1ea3y ra ngo\u00e0i Fermi ball th\u00ec ch\u1eafc ch\u1eafn n\u00f3 s\u1ebd \u0111\u1ec3 l\u1ea1i m\u1ed9t l\u1ed7 tr\u1ed1ng b\u00ean trong. \u00dd t\u01b0\u1edfng “g\u1eadp h\u1ea1t” l\u00e0 khi ta gh\u00e9p b\u1ea5t k\u1ef3 m\u1ed9t “h\u1ea1t” b\u00ean ngo\u00e0i v\u1edbi m\u1ed9t “l\u1ed7” b\u00ean trong th\u00ec c\u1ea3 c\u1eb7p \u1ea5y c\u01b0 x\u1eed nh\u01b0 m\u1ed9t boson.\u00a0 \u0110\u00f3 ch\u00ednh l\u00e0 bosonization \u2013 ngh\u1ec7 thu\u1eadt “g\u1eadp fermion th\u00e0nh boson”. Ch\u1eef “b\u1ea5t k\u1ef3” r\u1ea5t quan tr\u1ecdng, v\u00ec ch\u00fang ta kh\u00f4ng bi\u1ebft \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c “h\u1ea1t” n\u00e0o s\u1ebd gh\u00e9p c\u1eb7p v\u1edbi “l\u1ed7” n\u00e0o, n\u00ean theo nguy\u00ean t\u1eafc “c\u00e1i g\u00ec kh\u00f3 qu\u00e1 th\u00ec b\u1ecf”, ch\u00fang ta bu\u00f4ng b\u1ecf vi\u1ec7c t\u00ecm hi\u1ec3u ch\u00ednh x\u00e1c c\u00e1ch gh\u00e9p t\u1eebng c\u1eb7p \u0111\u01a1n l\u1ebb, m\u00e0 x\u00e9t ch\u00fang nh\u01b0 m\u1ed9t t\u1ed5ng th\u1ec3. K\u1ef9 thu\u1eadt “g\u1eadp b\u1ea5t k\u1ef3” cho ph\u00e9p ch\u00fang ta qu\u00ean c\u00e1i c\u1ee5 th\u1ec3 \u0111\u1ec3 \u0111\u1ea1t c\u00e1i tr\u1eebu t\u01b0\u1ee3ng, ch\u00ednh l\u00e0 \u0111i\u1ec3m m\u1ea1nh nh\u1ea5t c\u1ee7a to\u00e1n h\u1ecdc, \u0111\u1ed3ng th\u1eddi \u0111\u00e2y c\u0169ng l\u00e0 \u00fd t\u01b0\u1edfng m\u1ea5u ch\u1ed1t trong ph\u00e9p “x\u1ea5p x\u1ec9 pha ng\u1eabu nhi\u00ean” (random phase approximation) \u0111\u01b0\u1ee3c \u0111\u1ec1 x\u01b0\u1edbng b\u1edfi Bohm v\u00e0 Pines \u0111\u1ea7u th\u1eadp ni\u00ean 1950.<\/p>\n

V\u1ec1 m\u1eb7t k\u1ef9 thu\u1eadt, vi\u1ec7c t\u1ea1o c\u1ea7u n\u1ed1i gi\u1eefa 2 h\u1ea1t fermion v\u00e0 1 h\u1ea1t boson nh\u01b0 \u0111\u1ec1 xu\u1ea5t t\u1eeb v\u1eadt l\u00fd l\u00e0 m\u1ed9t ph\u00e9p x\u1ea5p x\u1ec9 kh\u00f4ng ho\u00e0n h\u1ea3o, c\u00f3 ch\u1ed7 \u0111\u00fang, c\u00f3 ch\u1ed7 sai, c\u00f3 ch\u1ed7 v\u1eeba \u0111\u00fang v\u1eeba sai, nh\u01b0ng \u00fd t\u01b0\u1edfng v\u1ec1 m\u1ed9t ph\u00e9p k\u1ebft n\u1ed1i nh\u01b0 v\u1eady l\u00e0 \u0111\u1ee7 m\u1ea1nh \u0111\u1ec3 c\u00f3 th\u1ec3 ho\u00e0n ch\u1ec9nh ho\u00e1 v\u1ec1 m\u1eb7t to\u00e1n h\u1ecdc. T\u1eeb \u0111\u00f3, ta c\u00f3 th\u1ec3 m\u1edf c\u00e1nh c\u1eeda quay l\u1ea1i v\u1edbi c\u00e1c c\u00f4ng c\u1ee5 quen thu\u1ed9c c\u1ee7a boson, \u0111\u1eb7c bi\u1ec7t l\u00e0 l\u00fd thuy\u1ebft Bogoliubov, v\u00e0 \u0111\u01b0a ra m\u1ed9t phi\u00ean b\u1ea3n to\u00e1n h\u1ecdc ch\u1eb7t ch\u1ebd cho c\u00f4ng th\u1ee9c Huang\u2013Yang.<\/p>\n

Nh\u01b0 v\u1eady, b\u00e0i to\u00e1n Huang\u2013Yang c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ti\u1ebfp c\u1eadn theo tinh th\u1ea7n “chi\u00eau g\u1eadp” c\u1ee7a Gauss: b\u1eb1ng c\u00e1ch g\u1eadp \u0111\u00fang ch\u1ed7, ta c\u00f3 th\u1ec3 bi\u1ebfn ph\u1ea3n \u0111\u1ed1i x\u1ee9ng th\u00e0nh \u0111\u1ed1i x\u1ee9ng. H\u00ecnh \u1ea3nh n\u00e0y l\u00e0m t\u00f4i nh\u1edb t\u1edbi th\u01a1 Nguy\u1ec5n B\u00ednh:<\/p>\n

Nh\u00e0 n\u00e0ng \u1edf c\u1ea1nh nh\u00e0 t\u00f4i<\/em><\/p>\n

C\u00e1ch nhau c\u00e1i gi\u1eadu m\u1ed3ng t\u01a1i xanh r\u1eddn<\/em><\/p>\n

C\u00e1i gi\u1eadu m\u1ed3ng t\u01a1i nh\u01b0 m\u1ed9t b\u1ee9c t\u01b0\u1eddng v\u00f4 h\u00ecnh ng\u0103n \u0111\u00f4i t\u00ecnh nh\u00e2n, nh\u01b0ng n\u1ebfu g\u1eadp hai ph\u00eda l\u1ea1i, m\u1ed9t b\u00ean trong m\u1ed9t b\u00ean ngo\u00e0i, th\u00ec ranh gi\u1edbi bi\u1ebfn m\u1ea5t, hai n\u1eeda ho\u00e1 m\u1ed9t. Trong v\u1eadt l\u00fd to\u00e1n c\u0169ng v\u1eady: ranh gi\u1edbi v\u00f4 h\u00ecnh c\u1ee7a m\u1eb7t c\u1ea7u Fermi ball t\u01b0\u1edfng nh\u01b0 kh\u00f4ng th\u1ec3 v\u01b0\u1ee3t qua, nay nh\u1edd m\u1ed9t ph\u00e9p g\u1eadp, hai h\u1ea1t fermion xa c\u00e1ch h\u1ee3p th\u00e0nh m\u1ed9t boson d\u1ec5 ch\u1ecbu.<\/p>\n

T\u1eeb Gauss “g\u1eadp s\u1ed1” \u0111\u1ebfn Huang-Yang “g\u1eadp h\u1ea1t”, t\u1ea5t c\u1ea3 \u0111\u1ec1u cho th\u1ea5y \u0111\u00f4i khi trong khoa h\u1ecdc, ch\u00fang ta kh\u00f4ng c\u1ea7n nhi\u1ec1u binh kh\u00ed mi\u1ec5n l\u00e0 m\u1ed7i th\u1ee9 \u0111\u1ee7 tinh. \u1ede \u0111\u00e2y ch\u1ec9 c\u1ea7n m\u1ed9t “ph\u00e9p g\u1eadp” \u0111\u00fang ch\u1ed7 l\u00e0 \u0111\u1ee7 \u0111\u1ec3 bi\u1ebfn m\u1ed9t b\u1ee9c tranh ph\u1ee9c t\u1ea1p th\u00e0nh m\u1ed9t b\u1ea3n nh\u1ea1c gi\u1ea3n d\u1ecb s\u00e2u l\u1eafng.<\/p>\n

V\u00e0 c\u00f3 l\u1ebd trong \u0111\u1eddi s\u1ed1ng c\u0169ng v\u1eady. B\u00e0i b\u00e1o n\u0103m 1924 Bose t\u1eebng b\u1ecb m\u1ed9t t\u1ea1p ch\u00ed t\u1eeb ch\u1ed1i v\u00ec \u00f4ng v\u1eabn c\u00f2n v\u00f4 danh, nh\u01b0ng c\u00fa t\u1eeb ch\u1ed1i \u1ea5y h\u00f3a ra ch\u1ec9 l\u00e0 m\u1ed9t “ph\u00e9p g\u1eadp ng\u1eabu nhi\u00ean”, \u0111\u01b0a \u00fd t\u01b0\u1edfng c\u1ee7a \u00f4ng t\u1edbi v\u1edbi Einstein \u0111\u1ec3 r\u1ed3i m\u1edf ra m\u1ed9t n\u1eeda th\u1ebf gi\u1edbi trong v\u1eadt l\u00fd l\u01b0\u1ee3ng t\u1eed. Bi\u1ebft \u0111\u00e2u, ch\u00ednh nh\u1eefng c\u00fa g\u1eadp ng\u1eabu nhi\u00ean trong \u0111\u1eddi l\u1ea1i l\u00e0 \u0111i\u1ec3m kh\u1edfi \u0111\u1ea7u cho nh\u1eefng h\u00e0nh tr\u00ecnh th\u00fa v\u1ecb nh\u1ea5t.<\/p>\n

Phan Th\u00e0nh Nam<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

T\u1eeb\u00a0GAUSS\u00a0\u0111\u1ebfn\u00a0BOSE\u2013FERMI: PH\u00c9P G\u1eacP TRONG TO\u00c1N V\u00c0 V\u1eacT L\u00dd Phan Th\u00e0nh Nam, Gi\u00e1o s\u01b0 Ti\u1ebfn s\u0129 t\u1ea1i \u0110\u1ea1i h\u1ecdc Ludwig Maximilian, Munich Nguy\u1ec5n Xu\u00e2n Xanh gi\u1edbi thi\u1ec7u M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadt l\u00fd h\u1ecdc to\u00e1n (mathematical physics) kh\u00f4ng ch\u1ec9 l\u00e0 t\u1ea1o \u0111i\u1ec1u ki\u1ec7n cho nh\u00e0 v\u1eadt l\u00fd t\u00ednh to\u00e1n s\u1ed1 l\u01b0\u1ee3ng c\u00e1c h\u1eb1ng s\u1ed1 nh\u1ea5t \u0111\u1ecbnh ho\u1eb7c<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/15490"}],"collection":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/comments?post=15490"}],"version-history":[{"count":44,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/15490\/revisions"}],"predecessor-version":[{"id":15545,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/posts\/15490\/revisions\/15545"}],"wp:attachment":[{"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/media?parent=15490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/categories?post=15490"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rosetta.vn\/nguyenxuanxanh\/wp-json\/wp\/v2\/tags?post=15490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}