Statistical Mechanics of Superfluid Systems in a Moving Frame

Jinwu Ye

In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical mechanics in the context of a moving sample with a velocity $ v $. Our investigation reveals significant disparities between the two ensembles when considering relativistic effects up to the order of $ (v/c)^2 $. While the temperature remains the same in the former, it experiences an increase in the latter. If the system undergoes a finite-temperature phase transition, the critical temperature decreases in the co-moving frame of the latter ensemble. The implications of these findings on the thermodynamic zeroth to the third laws and the eigenstate thermalization hypothesis are analysed. The potential for the experimental detection of these novel effects in condensed matter systems are discussed.

Pierre M. V. Résibois, I. Prigogine

David M. Ceperley

In 1953, Richard Feynman showed how superfluidity can be understood from the point of view of imaginary-time path integrals. In this picture, each atom becomes a cyclic polymer and the superfluid transition occurs when the atomic paths join up to make larger units which stretch a macroscopic distance. Boson statistics imply that all possible ways of connecting or "permuting" the "polymers" have equal weight. Feynman's path integrals are an exact isomorphism between quantum statistical mechanics of bosons and the classical statistical mechanics of these special "polymers". We have implemented Feynman's path integral method on a computer. Efficient methods, based on the Metropolis algorithm have been developed to move the paths quickly through path configuration space and permutation space. In addition, accurate approximations to the many-body off-diagonal density matrix involving pairs and triplets of atoms have been calculated.

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Fad Sun, Jinwu Ye

In material science, it was established that as the number of particles $ N $ in a material gets more and more, especially in the thermodynamic limit, various macroscopic quantum phenomena such as superconductivity, superfluidity, quantum magnetism, Fractional quantum Hall effects and various quantum or topological phase transitions (QPT) emerge in such non-relativistic quantum many-body systems. There is always a reservoir which exchanges energy and particles with the material. This is the essence of P. W. Anderson's great insight `` More is different ''. However, there is still a fundamental component missing in this general picture: How the `` More is different '' becomes different in a moving inertial frame or a moving sample? Here we address this outstanding problem.We demonstrate our claims by studying one of the simplest QPTs: Superfluid (SF)-Mott transitions of interacting bosons in a square lattice in a sample moving with a constant velocity $ \vec{v} $. We first elaborate the crucial difference between a moving sample and a moving inertial frame, stressing the crucial roles played by a reservoir in a grand canonical ensemble which is needed to study the SF-Mott transition in the first place. In this work, we mainly present the moving sample case and only discuss very briefly the moving inertial frame case. It is the moving which mixes the space and time. We also stress the important roles played by the underlying lattice. Doing various light or neutron scattering measurements in a moving sample may become an effective way not only measure various intrinsic properties of the materials, tune various quantum and topological phases through phase transitions, but also probe the new emergent space-time structure near any QPT.