Physical Review A

Alternative approach to the semiclassical description ofN-fermion systems

M. Casas, Angel Ricardo Plastino, Antonio Puente

Published Apr 1, 1994• 13 citations

Abstract

An information-theory-based approach to the semiclassical treatment of the N-fermion problem is presented which improves upon the traditional ones in two respects: It is valid beyond the turning points and is able to describe shell effects. The method is illustrated by recourse to simple one-dimensional systems.

DOI: 10.1103/physreva.49.2312

Related papers

Semiclassical Ground-State Energies of Many-Electron Systems

Brian R. Landry, Adam Wasserman, Eric J. Heller

A new semiclassical method is proposed to obtain accurate ground-state energies for many-electron systems. The method borrows its semiclassical character from Thomas-Fermi (TF) theory, but improves upon it by including exchange-correlation effects, at least approximately. We illustrate our method (correlated TF method) on simple models of 1D-interacting electrons, showing that it yields dramatic improvements over TF theory, particularly in the strongly correlated regime.

Physical Review LettersAug 4, 20094 citations

Uniform semiclassical approximations for one-dimensional fermionic systems

Raphael F. Ribeiro, Kieron Burke

A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of non-perturbative effects via an infinite resummation of the Poisson summation formula.

arXiv:1510.05676Oct 19, 20151 citation

Fisher information and semiclassical methods

Antonio Puente, M. Casas, Angel Ricardo Plastino

Using the Frieden and Soffer principle of extreme physical information we present a method for the construction of WKB wave functions that avoids the matching problem between the classically allowed and forbidden regions. When this formalism is applied in conjunction with the semiclassical methods for N-fermion systems, it provides one with Thomas-Fermi and Wigner-Kirkwood densities, valid beyond the turning points that also include shell effects. The method is illustrated with reference to both the sextic bistable and the Morse potential.

Physical Review AMay 1, 19994 citations

Semiclassical Physics

M. Brack, Rajat K. Bhaduri

This book attempts to convey to the reader that semiclassical physics can be fun, as well as useful for understanding quantum fluctuations in interacting many-body systems. It presents applications to finite fermion systems in diverse areas of physics.

CRC Press eBooksMar 5, 2018648 citations

Derivation of coupled Maxwell-Schrödinger equations describing matter-laser interaction from first principles of quantum electrodynamics

Milan Šindelka

We study the general problem of matter-laser interaction within the framework of nonrelativistic quantum electrodynamics, with particular emphasis on strong laser field effects. Consequently, we formulate a well-defined approximation leading in a straightforward manner toward the conventional semiclassical mode of description. Namely, we arrive naturally to two coupled equations of motion: (i) the Schr\"odinger equation which governs the quantum dynamics of an atomic system driven by classically described radiation field (composed of an incoming laser pulse plus radiation emitted from the atom), and (ii) the classical Maxwell wave equation which describes the emission of radiation from the mentioned atomic source. Employing the formalism of adiabatic Floquet theory, we derive a simple criterion of validity of the just described semiclassical approach. It shows that the semiclassical treatment is justified in most situations. On the other hand, it turns out that the semiclassical approximation breaks down completely in certain special but realistic cases, regardless of the fact that the incoming laser pulse contains a huge number of photons. Under such special circumstances, we anticipate new effects arising due to the quantized nature of the radiation field, to be observable, for example, in harmonic generation spectra. Our considerations are illustrated more explicitly using a simple model of a two-level atom strongly driven by a laser. The quantum dynamics of this model problem is resolved within the framework of quantum electrodynamics while adopting well-defined and physically justifiable approximations. As an outcome, analytic formulas are found serving as a quantitative criterion of (non)applicability of the semiclassical approach and demonstrating the breakdown of semiclassical theory under well-defined conditions. An illustrative numerical calculation is provided.

Physical Review AMar 18, 201015 citations

Effective Theory for Strongly Attractive One-Dimensional Fermions

Timothy G. Backert, Fabian Brauneis, Matija Čufar +3 more

We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe ansatz. This allows us to engineer effective interactions between the system's effective degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, although these interactions are strong, the resulting effective problem can be mapped onto a weakly interacting one, paving the way for the use of perturbation theory. This finding simplifies studies of many-fermion systems under confinement that are beyond reach of state-of-the-art numerical methods. We illustrate this statement by considering an impurity atom in a Fermi gas.

arXiv:2412.05915Physical Review LettersJun 26, 20251 citation