Regularized Boltzmann-Gibbs statistics for a Brownian particle in a non-confining field

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We argue that contrary to recent suggestions, non-extensive statistical mechanics has no relevance for inhomogeneous systems of particles interacting by short-range potentials. We show that these systems are perfectly well described by the usual Boltzmann-Gibbs statistical mechanics.

Vortex distribution in a confining potential

We study a model of interacting vortices in a type II superconductor. In the weak coupling limit, we constructed a mean-field theory which allows us to accurately calculate the vortex density distribution inside a confining potential. In the strong coupling limit, the correlations between the particles become important and the mean-field theory fails. Contrary to recent suggestions, this does not imply failure of the Boltzmann-Gibbs statistical mechanics, as we clearly demonstrate by comparing the results of Molecular Dynamics and Monte Carlo simulations.

Deviations from Boltzmann-Gibbs equilibrium in confined optical lattices

Cold atoms in dissipative optical lattices have long been known to exhibit anomalous kinetics due to an effective nonlinear friction force. Here we show that confining the spatial motion of the atoms will lead to an anomalous non-Boltzmann-Gibbs equilibrium state, with a power law tail at large energies. Only in the limit of deep optical lattices, do we regain the Boltzmann-Gibbs state. For strong confinement relative to the damping, we find an explicit expression for the equilibrium phase-space distribution, which generally differs from the canonical Boltzmann-Gibbs state at all energies. Bot…

受限势场中具有优先重定位的扩散

Diffusion with preferential relocation in a confining potential

本研究针对受限势场中受非马尔可夫重置协议作用的扩散粒子弛豫过程，通过分析重置时刻分布$K(τ,t)$的影响，揭示了稳态分布的两种类型及弛豫动力学特性，并通过精确案例和数值模拟验证理论。

Thermalization of random motion in weakly confining potentials

We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of t…

On Truncated Generalized Gibbs Ensembles in the Ising Field Theory

We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green's function $G(x) = \langle ψ^{\dagger}(x) ψ(0) \rangle$ of the complex fermion field $ψ(x)$. We find that both truncated GGEs are able to recover $…