Related papers: Canonical Temperature Control by Molecular Dynamic…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying temperature is not constant. The aim of this…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
The dynamic properties of fluid, including density, surface tension, diffusivity and viscosity, are temperature-dependent and can significantly influence the flow dynamics of mesoscopic non-isothermal systems. To capture the correct…
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
The well-known formal analogy between time and absolute temperature, existing on the quantum level, is considered as a profound duality relationship requiring some modifications in the conventional quantum dynamics. They consist of tiny…
Dynamics of collisionless plasma described by the Poisson-Vlasov equations is connected with the Hamiltonian motions of particles and their symmetries. The Poisson equation is obtained as a constraint arising from the gauge symmetries of…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
We study the time evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in arXiv:2009.00992 that the one-particle density matrix…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum…
We show direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperature molecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and molecular…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…