Statistical mechanics of kinks in 1+1 dimensions: Numerical simulations and double-Gaussian approximation

Journal Article · Wed Dec 01 00:00:00 EST 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.4284· OSTI ID:5727415

Alexander, F J; Habib, S; Kovner, A ^[1]

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1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) T-6, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) T-8, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We investigate the thermal equilibrium properties of kinks in a classical [Phi][sup 4] field theory in 1+1 dimensions. From large-scale Langevin simulations we identify the temperature below which a dilute-gas description of kinks is valid. The standard dilute-gas or WKB description is shown to be remarkably accurate below this temperature. At higher intermediate'' temperatures, where kinks still exist, this description breaks down. By introducing a double-Gaussian variational ansatz for the eigenfunctions of the statistical transfer operator for the system, we are able to study this region analytically. In particular, our predictions for the number of kinks and the correlation length are in agreement with the simulations. The double Gaussian prediction for the characteristic temperature at which the kink description ultimately breaks down is also in accord with the simulations. We also analytically calculate the internal energy and demonstrate that the peak in the specific heat near the kink characteristic temperature is indeed due to kinks. In the neighborhood of this temperautre there appears to be an intricate energy-sharing mechanism operating between nonlinear phonons and kinks.

• OSTI ID: 5727415
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 48:6; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PHI4-FIELD THEORY
SOLITONS
ANALYTICAL SOLUTION
EIGENFUNCTIONS
ENERGY TRANSFER
GAUSS FUNCTION
LANGEVIN EQUATION
NONLINEAR PROBLEMS
PHONONS
SIMULATION
STATISTICAL MECHANICS
TACHYONS
TEMPERATURE DEPENDENCE
THERMAL EQUILIBRIUM
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
WKB APPROXIMATION
CALCULATION METHODS
ELEMENTARY PARTICLES
EQUATIONS
EQUILIBRIUM
FIELD THEORIES
FUNCTIONS
MECHANICS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUASI PARTICLES
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)