A Note on Statistical Interactions and the Thermodynamic Bethe Ansatz
نویسندگان
چکیده
We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang δ-function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics. 0∗ Member of the CNRS 0† Laboratoire de la Direction des Sciences de la Matière du Commisariat à l’Energie Atomique.
منابع مشابه
A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION
A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string hypothesis. The high temperature limit of the entropy density is expressed in terms of the solution of the osp(1|2s) version of the Q-system. In particular for fundamental representation case, we also derive a TBA equation from the osp(1|2s) ver...
متن کاملAiry Functions in the Thermodynamic Bethe Ansatz
Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painlevé III and the Toda hierarchy. In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy f...
متن کاملSimplification of thermodynamic Bethe-ansatz equations
Thermodynamic Bethe ansatz equations for XXZ model at |∆| ≥ 1 is simplified to an integral equation which has one unknown function. This equation is analytically continued to |∆| < 1.
متن کاملThermodynamic Bethe ansatz equation for osp(1|2) integrable spin chain
The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp(1|2). Using the string hypothesis, we derive a set of infinite number of non-linear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed. Modern Physics Letters A, in press. S...
متن کاملProofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel p-(u(θ)+u(θ'}}
متن کامل