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SUMMARY:Is the superfluidity of a Bose gas related to the spontaneous brea
 king of $U(1)$ symmetry?
DTSTART;VALUE=DATE-TIME:20260924T134000Z
DTEND;VALUE=DATE-TIME:20260924T140000Z
DTSTAMP;VALUE=DATE-TIME:20260914T044802Z
UID:indico-contribution-503@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Maksim Tomchenko (Bogolyubov Institute for Theoretic
 al Physics)\nIt is widely accepted that phonons in a superfluid Bose gas a
 re Goldstone bosons\, and that the spontaneous breaking of $U(1)$ symmetry
  is the primary cause of superfluidity. The first statement is justified b
 y spontaneous symmetry breaking (SSB)\, which is usually defined as follow
 s: the Hamiltonian of the system is invariant under the $U(1)$ transformat
 ion $\\hat{\\Psi}(\\mathbf{r}\,t)\\rightarrow e^{i\\alpha}% \\hat{\\Psi}(\
 \mathbf{r}\,t)$\, but the order parameter $\\Psi(\\mathbf{r}\,t)$ is not. 
 However\, the strict definition of SSB is different: the Hamiltonian and t
 he boundary conditions are invariant under a symmetry transformation\, whi
 le the $\\it{ground~ state}$ is not. Based on the latter criterion\, we st
 udy a finite system of spinless\, weakly interacting bosons using three ap
 proaches: the standard Bogoliubov method\, the particle-number-conserving 
 Bogoliubov method\, and the approach based on the exact ground-state wave 
 function. Our results show that SSB does not occur in a real-world (finite
 ) superfluid Bose gas. Therefore\, the phonons in such a gas are not Golds
 tone bosons and are similar to sound in a classical gas\, and the superflu
 idity of such a system is not related to the spontaneous breaking of the $
 U(1)$ symmetry. In the case of an infinite Bose gas\, however\, the situat
 ion becomes paradoxical: the ground state can be regarded as either infini
 tely degenerate or non-degenerate\; this means that the phonon is both sim
 ilar to a Goldstone boson and different from it. [1] \n\n[1] M. Tomchenko\
 , Is a phonon excitation of a superfluid\nBose gas a Goldstone boson? J. P
 hys. A: Math. Theor. 59\, 305202 (2026). https://doi.org/10.1088/1751-8121
 /ae8c94\n\nhttps://indico.bitp.kiev.ua/event/18/contributions/503/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/503/
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