Statistical Properties of Lattice Solitons

Barry M. McCoy

Nikos Theodorakopoulos, N. C. Bacalis

We examine the statistical mechanics of the classically integrable Ishimori-Faddeev-Haldane lattice spin model. Thermodynamic properties can be exactly described in terms of an interacting soliton gas. Our semiclassical scheme can be used to calculate the low-temperature thermodynamics of the S=1/2 Heisenberg chain, in very good agreement with recent numerical calculations based on the quantum-mechanical Bethe ansatz.

Alan H. Luther

Pearl J. Y. Louis, Elena A. Ostrovskaya, Yuri S. Kivshar

In this work we show that the properties of both bright and dark Bose‐Einstein condensate (BEC) solitons trapped in optical superlattices can be controlled by changing the shape of the trapping potential whilst maintaining a constant periodicity and lattice height. Using this method we can control the properties of bright gap solitons by dispersion management. We can also control the interactions between dark lattice solitons. In addition we demonstrate a method for controlled generation of matter‐wave gap solitons in stationary optical lattices by interfering two condensate wavepackets, producing a single wavepacket at a gap edge with properties similar to a gap soliton. As this wavepacket evolves, it forms a bright gap soliton.

Irina Bariakhtar, Alexander Nazarenko

Nikos Theodorakopoulos, Erich W. Weller

The thermodynamic properties of soliton-bearing systems can be obtained from the statistics of their soliton components, which reflect restrictions on phase space due to interactions. Going beyond the established agreement of the free energy with transfer-integral results, we have successfully tested first derivatives (energy, number density) and second derivatives (specific heat, compressibility) for a one-component soliton gas (corresponding to the case of the low-temperature sine-Gordon chain). A complete description of the equilibrium statistical properties of the soliton gas is given in terms of the averages of occupation numbers and their fluctuations. The latter are characterized by the absence of off-diagonal correlations.