Related papers: Feynman's path-integral polaron treatment approach…
A convergent perturbation method using modified Lang Firsov transformation is developed for a two-site single-polaron system. The method is applicable for the entire range of the electron-phonon coupling strength from the antiadiabatic…
Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and…
The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists' approach to this system, the present article develops a general mathematical…
The polaron model of H. Fr\"ohlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit one expects that the phonon modes may be treated classically, which leads to a…
The behavior of charge carriers in polar materials is governed by electron-phonon interactions, which affect their mobilities via phonon scattering and may localize carriers into self-induced deformation fields, forming self-trapped…
A method is presented to obtain the linear response coefficients of a system coupled to a bath. The method is based on a systematic truncation of the Liouville equation for the reduced distribution function. The first order truncation…
We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a…
We construct a general theory of operator monotonicity and apply it to the Fr\"ohlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fr\"ohlich model.
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…
A time evolution operator in the interaction picture is given by exponentiating an interaction Hamiltonian $H$. Important examples of Hamiltonians, often encountered in quantum optics, condensed matter and high energy physics, are of a…
The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
In this work we develop a theory of correlated many-electron dynamics dressed by the presence of a finite-temperature harmonic bath. The theory is based on the ab-initio Hamiltonian, and thus well-defined apart from any phenomenological…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new…
The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is…
For the description of the transport of electrons across a quantum dot, which is tunnel coupled to leads at different chemical potentials, it is usual to assume that the total Hamiltonian of the composite system of the leads and the quantum…
We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation between the spectral decomposition of the Markov additive…