To resolve the mystery of superfluidity and supersolidity superfluidity as a Bose exchange effect 余永乐 武汉物理与数学研究所 山西大学理论物理研究所
To resolve the mystery of superfluidity and supersolidity: superfluidity as a Bose exchange effect 余永乐 武汉物理与数学研究所
P Kapitza upertluldity in liquid He-4, 1938 DD. Osheroff, R C. Richardson, D M.Lee Superfluidity in liquid He-3, 1972 E. Kim and M. h.W. Chan Superfluidity in Solid He-4, 2004
P. Kapitza Superfluidity in liquid He-4, 1938. D. D. Osheroff, R. C. Richardson, D. M. Lee Superfluidity in liquid He-3, 1972. E. Kim and M. H.W. Chan Superfluidity in Solid He-4, 2004
Microscopic mechanism of Superfluidity F. London, related Superfluidity with BEC, 1938 O. Penrose, L Onsager. C. N. Yang, off-diagonal long-range order *N.N. Bogoliubov's theory
Microscopic mechanism of Superfluidity : F. London, related Superfluidity with BEC, 1938 * O. Penrose, L. Onsager. C. N. Yang, off-diagonal long-range order * N. N. Bogoliubov’s theory
h2、0 H ∑n+27g∑8( 2MR480
2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + −
h2、0 H ∑n+27g∑8( 2MR480 E: in unit of h/2mR L: in unit of h L N=10g=1
N=10 g=1 2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + − 2 2 E mR L : / 2 , : in unit of in unit of
h2、0 H ∑n+27g∑8( 2MR480 a metastable state at l=n It carries a persistent current E: in unit of h/2mR L: in unit of h L N=10g=1
N=10 g=1 A metastable state at L=N, It carries a persistent current. 2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + − 2 2 E mR L : / 2 , : in unit of in unit of
h2、0 H ∑n+27g∑8( 2MR480 a metastable state at l=n It carries a persistent current (Leggett, Rev. Mod. Phys. 73, (2001) E: in unit of h/2mR L: in unit of h See also, F. Bloch, Phys. Rev. A, 7 (1973) L N=10g=1
(Leggett, Rev. Mod. Phys. 73,(2001) See also, F. Bloch, Phys. Rev. A,7 (1973)) N=10 g=1 A metastable state at L=N, It carries a persistent current. 2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + − 2 2 E mR L : / 2 , : in unit of in unit of
h2、0 H ∑n+27g∑8( 2MR480 a metastable state at L=N It carries a persistent current (Leggett, Rev. Mod. Phys. 73, (2001) E: in unit of h/2mR L: in unit of h See also, F. Bloch, Phys. Rev. A, 7 (1973) Rotating frame with Q2=l L E=E-QL N=10g=1
(Leggett, Rev. Mod. Phys. 73,(2001) See also, F. Bloch, Phys. Rev. A,7 (1973)) N=10 g=1 Rotating frame with = 1 E E L = − A metastable state at L=N, It carries a persistent current. 2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + − 2 2 E mR L : / 2 , : in unit of in unit of
h2、0 H ∑n+27g∑8( 2MR480 fv(1,2,…,6) is an eigenstate with0≤L<N, then o(122,…,、)=e i(1+2+…+ v(1,O2…,O) is an eigenstate, with L=L +kN E=E +L/N-L2/N=E +kN+2KL See also: F. Bloch, Phys. Rev. A, 7, 2187(1973) G M. Kavoulakis. et al. cond-mat/0510315
2 2 2 2 1 2 ( ) 2 N N i j i i j i H g MR = = − + − 1 2 ' 1 2 ( ... ) 1 2 1 2 ' 2 '2 2 ' if ( , ,..., ) is an eigenstate with 0 , then ( , ,..., ) ( , ,..., ) is an eigenstate, with , / / 2 N N ik N N L N e L L kN E E L N L N E k N kL + + + = = + = + − = + + See also: F. Bloch, Phys. Rev. A, 7,2187(1973) G. M. Kavoulakis, et al. cond-mat/0510315
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