Kinetic energy equipartition: A tool to characterize quantum thermalization

Abstract

According to both Bohmian and stochastic quantum mechanics, the standard quantum mechanical kinetic energy can be understood as consisting of two hidden-variable components. One component is associated with the current (or Bohmian) velocity, while the other is associated with the osmotic velocity (or quantum potential), and they are identified with the phase and the amplitude, respectively, of the wave function. These two components are experimentally accessible through the real and imaginary parts of the weak value of the momentum postselected in position. In this paper, a kinetic energy equipartition is presented as a signature of quantum thermalization in closed systems. This means that the expectation value of the standard kinetic energy is equally shared between the expectation values of the squares of these two hidden-variable components. Such components cannot be reached from expectation values linked to typical Hermitian operators. To illustrate these concepts, numerical results for the nonequilibrium dynamics of a few-particle harmonic trap under random disorder are presented. Furthermore, the advantages of using the center-of-mass frame of reference for dealing with systems containing many indistinguishable particles are also discussed.