Related papers: Grand Canonical Evolution for the Kac Model
We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles…
In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's master equation)…
Classical thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
The interaction between an ultrarelativistic particle and a linear array made up of $N$ two-level systems (^^ ^^ AgBr" molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes…
We report model calculations of the time-dependent internal energy and entropy for a single quasi-free massive quantum particle at a constant temperature. We show that the whole process started from a fully coherent quantum state to…
Open quantum systems, when driven by a periodic field, can relax to effective statistical ensembles that resemble their equilibrium counterparts. We consider a class of problems in which a periodically- driven quantum system is allowed to…
A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…
We examine several features of Bose-Einstein condensation (BEC) in an external harmonic potential well. In the thermodynamic limit, there is a phase transition to a spatial Bose-Einstein condensed state for dimension D greater than or equal…
We identify and study classes of initial states in integrable quantum systems that, after the relaxation dynamics following a sudden quench, lead to near-thermal expectation values of few-body observables. In the systems considered here,…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
Two-particle momentum correlations of $N$ identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized…
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
The high-temperature limit of Standard Model generated by the contractions of gauge groups is discussed. Contraction parameters of gauge group $SU(2)$ of Electroweak Model and gauge group $SU(3)$ of Quantum Chromodynamics are taken…
We study, in finite volume, a grand canonical version of the McKean-Vlasov equation where the total particle content is allowed to vary. The dynamics is anticipated to minimize an appropriate grand canonical free energy; we make this notion…
We present a novel quantum stochastic evolution equation for a matter field describing the canonical state of a weakly interacting ultracold Bose gas. In the ideal gas limit our approach is exact. This numerically very stable equation…
The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environment degrees of freedom. Starting from these premises, we…
We consider the classical Kac's model for the approximation of the Boltzmann equation, and study the correlation error measuring the defect of propagation of chaos in the mean field limit. This contribution is inspired by a recent paper of…
In this paper, we address the issue of the stability of the thermal equilibrium of large quantum systems with respect to variations of the thermal contact between them. We study the Schr\"odinger time evolution of a free bosonic field in…