Related papers: Cumulant methods for electron-phonon problems. II.…
We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and…
We investigate electron-phonon coupling in many-electron systems using dynamical mean-field theory in combination with the numerical renormalization group. This non-perturbative method reveals significant precursor effects to the gap…
We establish a self-consistent variational framework that allows us to study numerically the non-equilibrium evolution of non-perturbative inhomogeneous field configurations including quantum backreaction effects. After discussing the…
The self-consistent propagation of generalized $D_{1}$ [coherent-product] states and of a class of gaussian density matrix generalizations is examined, at both zero and finite-temperature, for arbitrary interactions between the localized…
The Holstein model often serves as an archetype for electron-phonon interactions and polaron formation in solids. However, precise descriptions of the Holstein polaron are difficult when the phonon frequency is small and the electron-phonon…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonators arrays in two dimensions. The resonator geometry is…
The two-dimensional many-body Holstein-Hubbard model in the T=0 normal state is examined within the framework of the self-consistent coupling of charge fluctuation correlations to the vibrational ones. The parameters of our model are the…
The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a…
In this article, we examine a stochastic partial differential equation (SPDE) driven by a symmetric $\alpha$-stable (S$\alpha$S) L\'evy noise, that is multiplied by a linear function $\sigma(u)=u$ of the solution. The solution is…
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 calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling…
Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT…
We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very…
Numerically "exact" methods addressing the dynamics of coupled electron--phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility $\mu_\mathrm{dc}$ are scarce, even for the…
The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small…
In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $\lambda$ as well as the Coulomb pseudopotential $\mu^*$ are important to determine the transition temperature $T_c$ and other properties.…
We analyze sound waves (phonons, Bogoliubov excitations) propagating on continuous wave (cw) solutions of repulsive $F=1$ spinor Bose-Einstein condensates (BECs), such as $^{23}$Na (which is antiferromagnetic or polar) and $^{87}$Rb (which…
The two-site single-polaron problem is studied within the perturbative expansions using different standard phonon basis obtained through the Lang Firsov (LF), modified LF (MLF) and modified LF transformation with squeezed phonon states…
The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on…