Related papers: Semiclassical Density Matrix Near the Top of a Bar…
We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is…
The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying classical (minimal Euclidean action) path, to be referred to…
We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
We study the real time dynamics of a quantum system with potential barrier coupled to a heat-bath environment. Employing the path integral approach an evolution equation for the time dependent density matrix is derived. The time evolution…
We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which…
The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths…
Attempts to find a quantum-to-classical correspondence in a classically forbidden region leads to non-physical paths, involving, for example, complex time or spatial coordinates. Here, we identify genuine quasi-classical paths for tunneling…
We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is…
The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…