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

Chinese Physics Letters

A method for solving the equation of a ferromagnetic chain and verification of the Takhtajan equation

Huang Nianning

Published May 1, 1986• 0 citations
Publisher

Abstract

Based on the gauge equivalence, we solve the equation of a Heisenberg ferromagnetic chain by using the inverse scattering method of the nonlinear Schrodinger equation and an explicitly obtained form of the required gauge transformation. We show that the solutions of a ferromagnetic chain by the Takhtajan's method identify with that by the above mentioned method. Then we prove the correctness of the Takhtajan equation and avoid the defects in its derivations.

DOI
10.1088/0256-307x/3/5/008

Related papers

Integration of the continuous Heisenberg ferromagnet chain with an easy axis through the inverse scattering method

Nian-Ning Huang

The inverse scattering method is applied to the Heisenberg ferromagnet chain with an easy axis. The Gelfand-Levitan-Marchenko equation is found. From the equation the one-soliton solution is obtained as an example.

Chinese Physics Letters•Sep 1, 1985•0 citations

On the inhomogeneous Heisenberg chain

Раджа Балакришнан

The author derives the spin evolution equation of a classical inhomogeneous Heisenberg chain and proves its exact equivalence (in the continuum limit) to an integro-differential nonlinear Schrodinger equation whose soliton solutions have been discussed earlier. Energy transport along the chain is related to the solution of this equation. He also describes possible physical systems to which the model is applicable.

Journal of Physics C Solid State Physics•Dec 30, 1982•75 citations

A Variant form of the Takhtajan Equation for the Heisenberg Isotropic Spin Chain

Nian-Ning Huang

A variant form of the Takhtajan equation for the continuous Heisenberg isotropic spin chain is given when the asymptotic spin is along the 1-axis.

Communications in Theoretical Physics•Mar 1, 1986•0 citations

Gauge equivalence between one-dimensional Heisenberg ferromagnets with single-site anisotropy and nonlinear Schrodinger equations

Katsuhiro Nakamura, Tomohei Sasada

The concept of gauge equivalence is introduced for the classical one-dimensional Heisenberg ferromagnets with single-site anisotropy. The classical continuum version of the one-dimensional anisotropic Heisenberg antiferromagnet (ferromagnet) of spin 1 / 2 is shown to be gauge-equivalent to the nonlinear Schrodinger equation with the repulsive (attractive) interaction, which is consistent with the Yang and Yang statement on thermodynamical equivalence between the corresponding quantum systems.

Journal of Physics C Solid State Physics•Sep 20, 1982•53 citations

The transmission property of the discrete Heisenberg ferromagnetic spin chain

Qing Ding, Wei Lin

We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic (DHF) spin chain via a geometric approach. With the aid of a discrete nonlinear Schrödinger-like equation which is the discrete gauge equivalent to the DHF, we show that the determination of transmitting coefficients in the transmission problem is always bistable. Thus, a definite algorithm and general stochastic algorithms are presented. A new invariant periodic phenomenon of the nontransmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.

arXiv:0801.2060•Journal of Mathematical Physics•Sep 1, 2008•2 citations

Solitons in quantum Heisenberg chain

Marek Cieplak, Łukasz A. Turski

Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.

Journal of Physics C Solid State Physics•Nov 10, 1980•18 citations
Based on the gauge equivalence, we solve the equation of a Heisenberg ferromagnetic chain by using the inverse scattering method of the nonlinear Schrodinger equation and an explicitly obtained form of the required gauge transformation. We show that the solutions of a ferromagnetic chain by the Takhtajan's method identify with that by the above mentioned method. Then we prove the correctness of the Takhtajan equation and avoid the defects in its derivations.
We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic (DHF) spin chain via a geometric approach. With the aid of a discrete nonlinear Schrödinger-like equation which is the discrete gauge equivalent to the DHF, we show that the determination of transmitting coefficients in the transmission problem is always bistable. Thus, a definite algorithm and general stochastic algorithms are presented. A new invariant periodic phenomenon of the nontransmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.
Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.