A microscopic theory of collective and independent-particle motion in many-fermion system is developed in the framework of the classical theory. The basic idea is an extension of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.A microscopic theory of collective and independent-particle motion in many-fermion system is developed in the framework of the classical theory. The basic idea is an extension of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.

Progress of Theoretical PhysicsFeb 1, 198117 citations

Free particle motion

Ted Smith, Andrew Crilley

GEMCO eBooksJan 1, 19870 citations

A Quantal Theory of Pairing Rotation, Pairing Vibrations and Independent-Particle Motions

A. Kuriyama, M. Yamamura

A microscopic theory is proposed to describe not only the pairing rotation, the pairing vibrations and the independent-particle motions, but also their mutual couplings in a consistent manner. With the aid of a BCS-type wave packet and a quasi-particle coherent state, the quantal system is translated into a corresponding classical one. First, we develop a canonical form in a classical image. This classical system obeys certain constraints, by which the double counting in the degrees of freedom is avoided. Then, the quantization is performed with the use of the Dirac theory of a canonical system with constraints. The original fermion operators themselves are expressed in terms of three types of degrees of freedom, which correspond to the pairing rotation, the pairing vibrations and the independent-quasi-particle motions, respectively.A microscopic theory is proposed to describe not only the pairing rotation, the pairing vibrations and the independent-particle motions, but also their mutual couplings in a consistent manner. With the aid of a BCS-type wave packet and a quasi-particle coherent state, the quantal system is translated into a corresponding classical one. First, we develop a canonical form in a classical image. This classical system obeys certain constraints, by which the double counting in the degrees of freedom is avoided. Then, the quantization is performed with the use of the Dirac theory of a canonical system with constraints. The original fermion operators themselves are expressed in terms of three types of degrees of freedom, which correspond to the pairing rotation, the pairing vibrations and the independent-quasi-particle motions, respectively.

Progress of Theoretical PhysicsApr 1, 19820 citations

Motion of Particles

Pieter Kok

Undergraduate lecture notes in physicsJan 1, 20230 citations

Quantum mechanics of a constrained electrically charged particle in the presence of electric currents

Bjørn Jensen, Rossen Dandoloff

We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a nonsingular static surface in ordinary three-dimensional space in the presence of arbitrary configurations of time independent electric currents. Starting from the canonical action in the embedding space we show that a charged particle with charge $q$ couples to a term linear in $q{A}^{3}M$ , where ${A}^{3}$ is the transverse component of the electromagnetic vector potential and $M$ is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion nonseparable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally nonseparable independently of the coupling to the geometry and the boundary constraints.We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a nonsingular static surface in ordinary three-dimensional space in the presence of arbitrary configurations of time independent electric currents. Starting from the canonical action in the embedding space we show that a charged particle with charge $q$ couples to a term linear in $q{A}^{3}M$, where ${A}^{3}$ is the transverse component of the electromagnetic vector potential and $M$ is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion nonseparable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally nonseparable independently of the coupling to the geometry and the boundary constraints.

arXiv:0911.0144Physical Review ANov 17, 200934 citations

Motion of Particles

Pieter Kok

Undergraduate lecture notes in physicsJan 1, 20180 citations

q

couples to a term linear in

q{A}^{3}M

, where

{A}^{3}

is the transverse component of the electromagnetic vector potential and

M

is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion nonseparable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally nonseparable independently of the coupling to the geometry and the boundary constraints.