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

International Journal of Modern Physics B

SEMICLASSICAL EXPRESSION OF THE SPIN PROPAGATOR

Kee-Su Park, Michael Stone, Anupam Garg

Published Oct 10, 2001• 2 citations
Publisher

Abstract

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay attention to the extra phase. This extra correction of phase is related to an anomaly in the fluctuation determinant. We show that if this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T2), and demonstrate its consistency under dissection of the path.

DOI
10.1142/s0217979201007518

Related papers

The Semiclassical Propagator for Spin Coherent States

Michael Stone, W. Green St

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the “extra phase ” discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T 2), and demonstrate its consistency under dissection of the path.

•Jan 1, 2000•56 citations

The semiclassical propagator for spin coherent states

Michael Stone, Kee-Su Park, Anupam Garg

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the “extra phase” discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behavior to O(T2), and demonstrate its consistency under dissection of the path.

arXiv:cond-mat/0004247•Journal of Mathematical Physics•Dec 1, 2000•84 citations

Semiclassical propagators for quantum coherent states and applications of extra quantum phase to large-spin tunneling of magnetic molecules

Kee-Su Park

A continuous path integral is used to obtain the semiclassical expressions of quantum propagators by means of coherent states in the holomorphic representation together with the appropriate boundary conditions. It allows us to express the total actions including boundary terms, classical trajectories, and extra phases in the stationary phase approximation. In particular, in the semiclassical expression for the quantum spin propagator, we pay attention to the extra quantum phase discovered by Solari and Kochetov. It is shown that this extra phase is related to an anomaly in the fluctuation determinant. It is verified that once this extra phase is included, the semiclassical propagator leads to the correct short time behaviour to O(T²), and shows its consistency under dissection of the path. In the application to the instanton methods, the extra quantum phase yields the correct formula for the tunnel splitting including both the exponential factor and the prefactor. The quantum phase leads to the correct spectrum with a shift of the spin quantum number by 1/2. We apply the semiclassical propagators and the tunnel splitting to a few models in magnetic molecular systems. It is shown that the formula gives the correct exponential factor and prefactors for quantum tunneling of a large spin if the extra quantum phase is taken into account.

•Jan 1, 2001•0 citations

On the extra phase in the semiclassical spin coherent-state propagator

Mikhail Pletyukhov

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.

arXiv:cond-mat/0304114•Apr 4, 2003•0 citations

A semiclassical treatment of path integrals for the spin system

Hiroshi Kuratsuji, Yutaka Mizobuchi

Starting with path integrals in the SU(2) coherent state representation, the semiclassical approximation of the propagator for the spin system is investigated. By extending the idea of the semiclassical expansion method, which was developed in the usual phase-space path integrals, to the path integrals in the curved phase space, which is characteristic of the SU(2) coherent states, we obtain a closed form for the semiclassical propagator. As an application, we discuss the semiclassical quantization condition for the spin system.

Journal of Mathematical Physics•Apr 1, 1981•40 citations

The semiclassical coherent state propagator in the Weyl representation

Carol Braun, Feifei Li, Anupam Garg +1 more

It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need for a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection between the discrete fluctuation determinant and the discrete Jacobi equation.

arXiv:1509.01640•Journal of Mathematical Physics•Dec 1, 2015•6 citations
We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay attention to the extra phase. This extra correction of phase is related to an anomaly in the fluctuation determinant. We show that if this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T2), and demonstrate its consistency under dissection of the path.
A continuous path integral is used to obtain the semiclassical expressions of quantum propagators by means of coherent states in the holomorphic representation together with the appropriate boundary conditions. It allows us to express the total actions including boundary terms, classical trajectories, and extra phases in the stationary phase approximation. In particular, in the semiclassical expression for the quantum spin propagator, we pay attention to the extra quantum phase discovered by Solari and Kochetov. It is shown that this extra phase is related to an anomaly in the fluctuation determinant. It is verified that once this extra phase is included, the semiclassical propagator leads to the correct short time behaviour to O(T²), and shows its consistency under dissection of the path. In the application to the instanton methods, the extra quantum phase yields the correct formula for the tunnel splitting including both the exponential factor and the prefactor. The quantum phase leads to the correct spectrum with a shift of the spin quantum number by 1/2. We apply the semiclassical propagators and the tunnel splitting to a few models in magnetic molecular systems. It is shown that the formula gives the correct exponential factor and prefactors for quantum tunneling of a large spin if the extra quantum phase is taken into account.
The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.
Starting with path integrals in the SU(2) coherent state representation, the semiclassical approximation of the propagator for the spin system is investigated. By extending the idea of the semiclassical expansion method, which was developed in the usual phase-space path integrals, to the path integrals in the curved phase space, which is characteristic of the SU(2) coherent states, we obtain a closed form for the semiclassical propagator. As an application, we discuss the semiclassical quantization condition for the spin system.
It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need for a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection between the discrete fluctuation determinant and the discrete Jacobi equation.