相关论文: Long time thermal asymptotics of nonlinear Lutting…
The correlation functions of the quantum nonlinear Schrodinger equation can be presented in terms of a Fredholm determinant. The explicit expression for this determinant is found for the large time and long distance.
We consider finite-temperature deformation of the sine kernel Fredholm determinants acting on the closed contours. These types of expressions usually appear as static two-point correlation functions in the models of free fermions and can be…
An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation…
We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related…
We study finite temperature dynamical correlation functions of the magnetization operator in the one-dimensional Ising quantum field theory. Our approach is based on a finite temperature form factor series and on a Fredholm determinant…
We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and $B(t)$ have…
We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large time and long distance behavior of these…
In the present paper, we study the asymptotics of the Fredholm determinant $D(x,s)$ of the finite-temperature deformation of the sine kernel, which represents the probability that there is no particles on the interval $(-x/\pi,x/\pi)$ in…
In this expository article we describe the asymptotics of certain Fredholm determinants which provide solutions to the cylindrical Toda equations, and we explain how these asymptotics are derived. The connection with Fredholm determinants…
We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out…
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear…
In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm…
It is shown that the Luttinger liquid is unstable to arbitrarily small transverse hopping. It becomes either a Fermi liquid or exhibits long-range order at zero temperature. The crossover temperatures below which either transverse coherent…
We consider the one-dimensional Hubbard model with the infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral…
We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this…
We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and non-intersecting paths models. By relating the logarithmic derivatives of the…
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction…
One-dimensional electrons with a linearized dispersion relation are equivalent to a collection of harmonic plasmon modes, which represent long wavelength density oscillations. An immediate consequence of this Luttinger model of…
We analyze the long-time asymptotics for the Degasperis--Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated $3 \times 3$-matrix valued Riemann--Hilbert problem, we find an explicit formula…
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.