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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.


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.


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.


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.


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.


Bachelard R.,University of Sao Paulo | Kastner M.,Stellenbosch University | Kastner M.,National Institute for Theoretical Physics NITheP
Physical Review Letters | Year: 2013

Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/rα with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction range α, we find evidence for the existence of a threshold at α=d/2, dependent on the spatial dimension d, at which the relaxation behavior changes qualitatively and the corresponding scaling exponents switch to a different regime. Based on analytical as well as numerical observations in systems of vastly differing nature, ranging from quantum to classical, from ferromagnetic to antiferromagnetic, and including a variety of lattice structures, we conjecture this threshold and some of its characteristic properties to be universal. © 2013 American Physical Society.


Touchette H.,National Institute for Theoretical Physics NITheP | Touchette H.,Stellenbosch University
Journal of Statistical Physics | Year: 2015

We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics—namely, thermodynamics, equilibrium macrostates, and microstate measures—whenever the microcanonical entropy is concave as a function of the energy density in the thermodynamic limit. This is proved for any classical many-particle systems for which thermodynamic functions and equilibrium macrostates exist and are defined via large deviation principles, generalizing many previous results obtained for specific classes of systems and observables. Similar results hold for other dual ensembles, such as the canonical and grand-canonical ensembles, in addition to trajectory or path ensembles describing nonequilibrium systems driven in steady states. © 2015, Springer Science+Business Media New York.


Chetrite R.,University of Nice Sophia Antipolis | Touchette H.,National Institute for Theoretical Physics NITheP | Touchette H.,Stellenbosch University
Annales Henri Poincare | Year: 2015

We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used in the conditioning is a large deviation-type event, characterized by a convex rate function. Under this assumption, we construct the driven process via a generalization of Doob’s h-transform, used in the context of bridge processes, and show that this process is equivalent to the conditioned process in the long-time limit. The notion of equivalence that we consider is based on the logarithmic equivalence of path measures and implies that the two processes have the same typical states. In constructing the driven process, we also prove equivalence with the so-called exponential tilting of the Markov process, often used with importance sampling to simulate rare events and giving rise, from the point of view of statistical mechanics, to a nonequilibrium version of the canonical ensemble. Other links between our results and the topics of bridge processes, quasi-stationary distributions, stochastic control, and conditional limit theorems are mentioned. © 2014, Springer Basel.


Uzan J.-P.,University Pierre and Marie Curie | Uzan J.-P.,University of Cape Town | Uzan J.-P.,National Institute for Theoretical Physics NITheP
Living Reviews in Relativity | Year: 2011

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.


Fantoni R.,National Institute for Theoretical Physics NITheP
Solid State Communications | Year: 2013

In a computer experiment the choice of suitable estimators to measure a physical quantity plays an important role. We propose a new direct route to determine estimators for observables which do not commute with the Hamiltonian. Our new route makes use of the Hellmann and Feynman theorem and in a diffusion Monte Carlo simulation it introduces a new bias to the measure due to the choice of the auxiliary function. This bias is independent from the usual one due to the choice of the trial wave function. We used our route to measure the radial distribution function of a spin one half Fermion fluid. © 2013 Elsevier Ltd.

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