Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

Abstract

For a certain class of isolated quantum systems, we report the existence of irreversible processes in which the energy is not dissipated. After a closed cycle in which the initial energy distribution is fully recovered, the expectation value of a symmetry-breaking observable changes from a value differing from zero in the initial state to zero in the final state. This entails the unavoidable loss of a certain amount of information and constitutes a source of irreversibility. We show that the von Neumann entropy of time-averaged equilibrium states increases in the same magnitude as a consequence of the process. We support this result by means of numerical calculations in an experimentally feasible system, the Lipkin-Meshkov-Glick model.

Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

“…For the TSEGM, the critical energy separates a region of broken parity symmetry, from another region of broken time-reversal symmetry. This feature constitutes a generalization of previous results showing that crossing an ESQPT comprises the appearance of degenerate parity doublets [18], which imply important dynamical consequences like the ones discussed in [19].…”

“…Among them, the most relevant is the absence of a clear order parameter (see, for example [4]). A promising alternative lays in the existence of symmetry-breaking equilibrium states at one side of the transition [18], entailing the irreversible restoration of the symmetry when the critical energy is crossed [19].…”

From thermal to excited-state quantum phase transition: The Dicke model

“…If the system remains isolated from any environment, the system behaves as follows. Below the critical energy, E < E c , the parity symmetry remains broken if it is broken in the initial condition; on the contrary, time evolution above the critical energy E > E c restores the symmetry [21,22]. This entails that the expected value J x keeps relevant information about the initial state.…”

“…Also, two microcanonical integrals, Eq. (22), are performed, each one restricted to the corresponding disjoint region of the energy surface. It is worth remarking that the microcanonical integrals have been performed without including the symmetry-breaking term.…”

“…First, it links ESQPTs with the breakdown of a certain symmetry, following a line of thought similar to the theory of thermal phase transitions. Second, this fact entails measurable dynamical consequences if a thermodynamic process is performed from a symmetry-breaking initial condition: the symmetry of the final equilibrium state remains broken only if the final energy is at the corresponding side of the transition, whereas the symmetry is restored on the contrary [21,22]. However, if the initial condition has a well-defined value of this symmetry, nothing similar happens when crossing the critical energy.…”