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Kastner M.,National Institute for Theoretical Physics NITheP | Kastner M.,Stellenbosch University
Physical Review Letters | Year: 2010

Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indistinguishable from the Curie-Weiss Ising model in canonical thermodynamics, although their microcanonical thermodynamics differs. Qualitatively, the observed features of nonequivalent ensembles are expected to be relevant for long-range quantum spin systems realized in optical lattice experiments. © 2010 The American Physical Society. Source


Chetrite R.,University of Nice Sophia Antipolis | Touchette H.,National Institute for Theoretical Physics NITheP | Touchette H.,Stellenbosch University
Physical Review Letters | Year: 2013

Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here, we propose a theory of these ensembles that unifies and generalizes earlier results and show how it is fundamentally related to the large deviation properties of nonequilibrium systems. Using this theory, we provide conditions for the equivalence of nonequilibrium ensembles, generalizing those found for equilibrium systems, construct driven physical processes that generate these ensembles, and rederive in a simple way known and new product rules for their transition rates. A nonequilibrium diffusion model is used to illustrate these results. © 2013 American Physical Society. Source


Kastner M.,National Institute for Theoretical Physics NITheP | Kastner M.,Stellenbosch University | Mehta D.,Syracuse University
Physical Review Letters | Year: 2011

The stationary points of the potential energy function V are studied for the 4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of stationary points to the occurrence of thermodynamic phase transitions. We find that the phase transition potential energy of the 4 model does in general not coincide with the potential energy of any of the stationary points of V. This disproves earlier, allegedly rigorous, claims in the literature on necessary conditions for the existence of phase transitions. Moreover, we find evidence that the indices of stationary points scale extensively with the system size, and therefore the index density can be used to characterize features of the energy landscape in the infinite-system limit. We conclude that the finite-system stationary points provide one possible mechanism of how a phase transition can arise, but not the only one. © 2011 American Physical Society. Source


Kastner M.,National Institute for Theoretical Physics NITheP | Kastner M.,Stellenbosch University
Physical Review Letters | Year: 2011

The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r-α at large distances r with an exponent α not exceeding the lattice dimension. For a large class of observables and initial states, the time evolution of expectation values can be calculated. We prove analytically that, at a given instant of time t and for sufficiently large system size N, the expectation value of some observable t) will practically be unchanged from its initial value (0). This finding implies that, for large enough N, equilibration effectively occurs on a time scale beyond the experimentally accessible one and will not be observed in practice. © 2011 American Physical Society. Source


Reimann P.,Bielefeld University | Kastner M.,National Institute for Theoretical Physics NITheP | Kastner M.,Stellenbosch University
New Journal of Physics | Year: 2012

We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The main requirements are that the initial state, possibly far from equilibrium, exhibits a macroscopic population of at most one energy level and that degeneracies of energy eigenvalues and of energy gaps (differences of energy eigenvalues) are not of exceedingly large multiplicities. Our approach closely follows and extends recent works by Short and Farrelly (2012 New. J. Phys. 14 013063), in particular going beyond the realm of finite-dimensional systems and large effective dimensions. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Source

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