Related papers: Wave packet dynamics in chains with delayed electr…
We studied a system of atomic Bose-Einstein condensate coupled to a ring cavity within the mean-field theory. Due to the interaction between atoms and light field, the atoms can be self-trapped. This is verified with both variational and…
We consider the cubic nonlinear Schr\"odinger equation with harmonic trapping on $\mathbb{R}^D$ ($1\leq D\leq 5$). In the case when all but one directions are trapped (a.k.a "cigar-shaped" trap), following the approach of…
We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms…
The adiabatic Born-Oppenheimer approximation is considered to be a robust approach that very rarely breaks down. Consequently, it is predominantly utilized to address various electron-phonon properties in condensed matter physics. By…
A separable $x-y$ model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly\textbf{,} adiabatically into and across a rectangular box to which an electron is confined. The time-dependent…
We study spin-phonon coupled dynamics in the vicinity of a sloped conical intersection created by laser coupling the electronic (spin) and vibrational degrees of freedom of a pair of trapped Rydberg ions. We show that the shape of the…
We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility…
Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and…
The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced…
We present an exact expression for the evolution of the wavefunction of $N$ interacting atoms in an arbitrarily time-dependent, $d$-dimensional parabolic trap potential $\omega(t)$. The interaction potential between atoms is taken to be of…
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the…
Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within N-soliton train of the nonlinear Schrodinger equation (NLS). Perturbations induced by weak quadratic and periodic external…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation…
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase boundary requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the…
We investigate the scattering of an electron by phonons in a small structure between two one-dimensional tight-binding leads. This model mimics the quantum electron transport through atomic wires or molecular junctions coupled to metallic…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
We use an adiabatic approximation in terms of instantaneous resonances to study the steady-state and time-dependent transport properties of interacting electrons in biased resonant tunneling heterostructures. This approach leads, in a…