Related papers: Grand Canonical Evolution for the Kac Model
The grand canonical thermodynamics of a bosonic system is studied in order to identify the footprint of its own high-density quantum phase transition. The phases displayed by the system at zero temperature establish recognizable patterns at…
The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle-antiparticle pair creation occurs;…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are…
The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the Grand Canonical Ensemble (GCE) in [J. P\k{e}kalski et al. J.…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
We investigate simultaneous effects of finite system size and global charge conservation on thermal fluctuations in the vicinity of a critical point. For that we consider a finite interacting system which exchanges particles with a finite…
Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of…
This paper studies the existence, uniqueness and convergence to non-equilibrium steady states in Kac's model with an external coupling. We work in both Fourier distances and Wasserstein distances. Our methods work in the case where the…
We consider a one dimension Kac model with conservation of energy and an exclusion rule: Fix a number of particles $n$, and an energy $E>0$. Let each of the particles have an energy $x_j \geq 0$, with $\sum_{j=1}^n x_j = E$. For some…
Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems.…
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
We study whether the stationary state of two bulk-driven systems slowly exchanging particles can be described by the equality of suitably defined nonequilibrium chemical potentials. Our main result is that in a weak contact limit, chemical…
We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the…
Quantum thermodynamics with open systems is often based on the quantum optical weak-coupling master equation or on operational repeated interaction models, whereas early works on thermalisation and on decoherence theory were mostly…
A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close…
We introduce a quantum Monte Carlo method at finite temperature for interacting fermionic models in the canonical ensemble, where the conservation of the particle number is enforced. Although general thermodynamic arguments ensure the…
The thermodynamics of a system of interacting bosonic particles and antiparticles in the presence of the Bose-Einstein condensate is studied in the framework of the Skyrme-like mean-field model. It is assumed that the total charge density…
We investigate Kac's many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate…