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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…

Some years ago, Fendley found an explicit solution to Thermodynamic Bethe Ansatz (TBA) equation for a N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek for explicit solutions for other super-potential cases…

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear…

We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single}…

The basics of the thermodynamic Bethe ansatz equation are given. The simplest case is repulsive delta function bosons, the thermodynamic equation contains only one unknown function. We also treat the XXX model with spin 1/2 and the XXZ…

We present a new method of obtaining nonlinear integral equations characterizing the thermodynamics of one-dimensional multi-component gases interacting via a delta-function potential. In the case of the repulsive two-component Bose gas we…

A Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms has recently been proposed. Using a numerical procedure developed by McCoy et al., we find significant evidence that this solution can yield…

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…

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are…

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…

In the case of the heat equation $u_t=u_{xx}+Vu$ on the real line there are some remarkable potentials $V$ for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a…

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of…

The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…

We present a multi-grid algorithm in order to solve numerically the thermodynamic Bethe ansatz equations. We specifically adapt the program to compute the data of the conformal field theory reached in the ultraviolet limit. Submitted to…

We give the exact solution of orbit dependent nuclear pairing problem between two non-degenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including…

The thermodynamic Bethe Ansatz equations that have been proposed to describe massive integrable deformations of the coset conformal field theories $g_k\times g_l/g_{k+l}$ are shown to result directly by applying the usual thermodynamic…

We give integral equations for the generating function of the cummulants of the work done in a quench for the Kondo model in the thermodynamic limit. Our approach is based on an extension of the thermodynamic Bethe ansatz to non-equilibrium…

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference operator in a discrete variable $n$. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients…

Using the thermodynamical Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in arXiv:0901.3753 for the spectrum of all operators in…