Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Path integral evaluation of the Bloch density matrix for an oscillator in a magnetic field

J M Manoyan

Published Oct 21, 1986• 20 citations
Publisher

Abstract

The non-relativistic propagator for a localised oscillator in a magnetic field of arbitrary strength is evaluated analytically by performing the path integral in polar coordinates. The result is then used to obtain the Bloch density matrix for the system as well as the eigenvalues of the Hamiltonian concerned.
DOI
10.1088/0305-4470/19/15/024

Related papers

Path integral evaluation of the Bloch density matrix for an oscillator in an electric and magnetic field

M. L. Glasser

The Bloch density matrix for an electron in a three-dimensional oscillator potential in the presence of parallel electric and magnetic fields is presented in cylindrical coordinates.

Journal of Physics A Mathematical and General•Feb 21, 1987•5 citations

The Bloch density matrix for a localised oscillator in a magnetic field

Norman Henry March, M. P. Tosi

A closed analytic form is obtained for the Bloch or canonical density matrix of a localised oscillator in a magnetic field of arbitrary strength, by solving the Bloch equation with the completeness boundary condition.

Journal of Physics A Mathematical and General•Aug 1, 1985•27 citations

An operator method of evaluating the Bloch density matrix for an oscillator in a constant magnetic field

Katsumi Yonei

A new method is proposed in evaluating the Bloch density matrix for a three-dimensional charged harmonic oscillator placed in a constant magnetic field. The method first reduces the operator exp (- beta H) to a product of several factors of a simple nature by using the commutation relations among the Hamiltonian components and by performing some transformations on the Hamiltonian, and then calculates the matrix element. The method is especially efficient when the system has a rotational symmetry around the axis parallel to the magnetic field, but it is also useful in other cases. A generalised problem in which a uniform electric field coexists is also discussed. To make the whole discussion consistent, the density matrix for a one-dimensional harmonic oscillator, which plays an essential role in the whole problem, is recalculated in the spirit of this method, and it is shown that the present method derives the well known form of the Bloch density matrix for this system in a quite elementary way, without reference to any advanced knowledge of eigenfunctions.

Journal of Physics A Mathematical and General•Jul 7, 1989•8 citations

Evaluation of the Bloch density matrix for a charged oscillator in a magnetic field by canonical transformations

Mohammed A. Z. Habeeb

The problem of a charged particle moving in an anisotropic harmonic oscillator potential in the presence of a constant external magnetic field is reduced to that of a particle in an anisotropic oscillator by using canonical transformations. The Bloch density matrix for the original problem is then exactly evaluated by transforming the well known result for the anisotropic oscillator with the aid of the integral kernel corresponding to the canonical transformation under consideration.

Journal of Physics A Mathematical and General•Nov 11, 1987•6 citations

PATH INTEGRALS IN POLAR COORDINATES: CHARGED PARTICLES IN A UNIFORM MAGNETIC FIELD.

Akira Inomata

The statistical density matrix for a system of charged particles in a uniform magnetic field is derived by Feyman's path integral method. The integrations over all paths are directly carried out by use of cylindrical coordinates. As limiting cases, the density matrices for free particles, rigid rotators, and harmonic oscillators are also discussed. (Author)

•Feb 1, 1967•0 citations

The coherent-state method of evaluating the density matrix for an oscillator in a constant magnetic field

Gong Ren-shan

The coherent-state method is proposed for evaluating the Bloch density matrix for a charged isotropic oscillator placed in a constant magnetic field. The method first reduces the Bloch equation, satisfied by the density matrix e - beta H , to a partial differential equation by means of the coherent-state representation, and then calculates the density matrix. A generalised problem in which a uniform electric field coexists is also discussed.

Journal of Physics A Mathematical and General•Jun 7, 1990•1 citation
A new method is proposed in evaluating the Bloch density matrix for a three-dimensional charged harmonic oscillator placed in a constant magnetic field. The method first reduces the operator exp (- beta H) to a product of several factors of a simple nature by using the commutation relations among the Hamiltonian components and by performing some transformations on the Hamiltonian, and then calculates the matrix element. The method is especially efficient when the system has a rotational symmetry around the axis parallel to the magnetic field, but it is also useful in other cases. A generalised problem in which a uniform electric field coexists is also discussed. To make the whole discussion consistent, the density matrix for a one-dimensional harmonic oscillator, which plays an essential role in the whole problem, is recalculated in the spirit of this method, and it is shown that the present method derives the well known form of the Bloch density matrix for this system in a quite elementary way, without reference to any advanced knowledge of eigenfunctions.