Relaxation of kinks in the Ising chain with a transverse field interacting with a three-dimensional phonon field

The influence of phonon fluctuations on the dynamics of kink-like domain-wall excitations in the one-dimensional Ising model with a transverse field (s=1/2) was investigated. It was found that such non-linear excitations behave almost like classical Brownian particles. This is the consequence of the emission and absorption of acoustic phonons excited by domain walls propagating through the vibrating lattice. The effective friction and diffusion constants are also evaluated. It was established that the overall process has the character of Cherenkov-type radiation.

[1]  M. Sataric,et al.  Influence of phonon fluctuations on soliton dynamics in the easy-axis Heisenberg model , 1991 .

[2]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

[3]  K. Kopinga,et al.  Quasi-one-dimensional magnetic behaviour of the Ising system CsFeCl3.2aq , 1985 .

[4]  V. Ryzhov.  Magnetic solitons in a compressible Heisenberg chain , 1983 .

[5]  E. Magyari.  Solitary waves along the compressible Heisenberg chain , 1982 .

[6]  M. Schöbinger,et al.  Dynamic damping in magnetic Sine-Gordon systems , 1981 .

[7]  P. Prelovšek,et al.  Quantum versus classical domain walls in the Ising chain with a transverse field , 1981 .

[8]  M. Remoissenet.  Non-linear excitations in a compressible chain of dipoles , 1981 .

[9]  P. Kelly,et al.  Cohesive properties of CaF, and UO, in the atomic sphere approximation , 1980 .

[10]  M. Cieplak,et al.  Magnetic solitons and elastic kink-like excitations in compressible Heisenberg chain , 1980 .

[11]  S. Takeno.  Nonlinear Excitations and Coherent States in the Ising Model in a Transverse Field , 1980 .

[12]  A. R. Bishop,et al.  Solitons in condensed matter: A paradigm , 1980 .

[13]  R. Blinc,et al.  Phase Transitions in a Lipid Bilayer Embedded in a Crystalline Matrix , 1979 .

[14]  A. I. Baranov,et al.  Pseudo One-Dimensional Ferroelectric Ordering and Critical Properties of Cs H 2 P O 4 and Cs D 2 P O 4 , 1979 .

[15]  J. Kjems,et al.  Evidence for Soliton Modes in the One-Dimensional Ferromagnet CsNi F 3 , 1978 .

[16]  S. Milos̆ević,et al.  The Linear Ising Chain in the Three‐Dimensional Phonon Field , 1977 .

[17]  D. Pushkarov,et al.  Solitons in One‐Dimensional Ferromagnetic Systems , 1977 .

[18]  H. Mikeska.  Solitons in a one-dimensional magnet with an easy plane , 1977 .

[19]  C. Windsor,et al.  Theoretical and experimental studies on one-dimensional magnetic systems , 1976 .

[20]  J. R. Schrieffer,et al.  Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions , 1974 .

[21]  E. Pytte.  Lattice distortions in one-dimensional Ising chains , 1974 .

[22]  S. Takeno,et al.  A Theory of Frenkel Excitons Using a Two-Level-Atom Model , 1973 .

[23]  R. Blinc,et al.  Dynamics of order-disorder-type ferroelectrics and anti-ferroelectrics , 1972 .

[24]  P. Fulde,et al.  Some crystalline field effects in metals , 1972 .

[25]  K. Takeda,et al.  Thermal and Magnetic Properties of Linear Ferro- and Autiferro-Magnetic Substances, MCl2·2NC5H5(M; Co, Cu) , 1971 .

[26]  J. Villain,et al.  Atomic Motion in Hydrogen‐Bond Ferroelectrics , 1966 .