Related papers: Semi-classical statistical approach to Fr\"ohlich …
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
A unified semiclassical framework is presented to describe the evaporative cooling of trapped atomic gases, accounting for both classical and quantum statistics. By combining global thermodynamics with phase-space distributions, general…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb{R}^d \times \mathcal{P}_2(\mathbb{R}^d),$ where $\mathcal{P}_2(\mathbb{R}^d)$ is the Wasserstein space of probability measures on $\mathbb{R}^d$ with…
The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated $N$-phase nonlinear wave solutions to the focusing nonlinear Schr\"odinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which…
The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a…
In this paper we analyze the evolution of the time averaged energy densities associated with a family of solutions to a Schr{\"o}dinger equation on a Lie group of Heisenberg type. We use a semi-classical approach adapted to the stratified…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are…
The usual semiclassical approximation for atom-field dynamics consists in substituting the field operators by complex numbers related to the (supposedly large enough) intensity of the field. We show that a semiclassical evolution for…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of…
A detailed study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by…
We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the…
The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson ($2018$) developed a probabilistic approach…
In the first part of the paper we prove various results on regularity of Feynman-Kac functionals of Hunt processes associated with time dependent semi-Dirichlet forms. In the second part we study the Cauchy problem for semilinear parabolic…