相关论文: Cumulant methods for electron-phonon problems. II.…

We study the Allen-Cahn equation with a cubic-quintic nonlinear term and a stochastic $Q$-trace-class stochastic forcing in two spatial dimensions. This stochastic partial differential equation (SPDE) is used as a test case to understand,…

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…

Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are…

We prove three theorems about the asymptotic behavior of solutions $u$ to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, under very mild hypotheses, we show that the doubling index…

We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…

In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…

We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior…

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…

A self-consistent quantum-kinetic model is developed for studying strong-field nonlinear electron transport interacting with force-driven phonons within a quantum-wire system. For this model, phonons can be dragged into motion through…

We show how to systematically improve the Momentum Average (MA)approximation for the Green's function of a Holstein polaron, bysystematically improving the accuracy of the self-energy diagrams in such a way that they can still all be summed…

Acoustic phonons in piezoelectric materials strongly couple to electrons through a macroscopic electric field. We show that this coupling leads to a momentum-dependent divergence of the Fan-Migdal electron linewidth. We then develop a…

We use the approximation-free Bold Diagrammatic Monte Carlo technique to study the effects of a finite dispersion of the optical phonon mode on the properties of the Holstein polaron, especially its effective mass. For weak electron-phonon…

The small dispersion limit of the focusing nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. First, through a comprehensive set of numerical simulations, it is demonstrated that…

Analytic continuation (AC) from the imaginary-time Green's function to the spectral function is a crucial process for numerical studies of the dynamical properties of quantum many-body systems. This process, however, is an ill-posed…

We propose a new optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems combining density-matrix and Lanczos algorithms. We demonstrate the reliablity of this approach by calculating the phase…

A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken large enough and the result gives rise to the Borel…

Simulations of lattice particle - phonon systems are fundamentally restricted by the exponential growth of the number of quantum states with the lattice size. Here, we demonstrate an algorithm that constructs the lowest eigenvalue and…

In this work, we highlight how trapped-ion quantum systems can be used to study generalized Holstein models, and benchmark expensive numerical calculations. We study a particular spin-Holstein model that can be implemented with arrays of…

We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling of the Holstein type. The bare…

The Microcanonical Ensemble computer simulation method (MCE) is used to evaluate the perturbation terms $A_i$ of the Helmholtz free energy of a Square-Well (SW) fluid. The MCE method offers a very efficient and accurate procedure for the…