相关论文: Integrable equations associated with the finite-te…

We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a…

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…

We study a family of unbounded solutions to the Korteweg-de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are connected to an integro-differential version of the second…

We study the finite size corrections for the magnetization and the internal energy of the 2d Ising model in a magnetic field by using transfer matrix techniques. We compare these corrections with the functional form recently proposed by…

We extend the form-factors approach to the quantum Ising model at finite temperature. The two point function of the energy is obtained in closed form, while the two point function of the spin is written as a Fredholm determinant. Using the…

The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition…

We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…

In this paper, we study the asymptotic behaviour of plane partitions distributed according to a $q^{\text{Volume}}$-weighted Muttalib--Borodin ensemble and its associated discrete point process. We establish a Large Deviation Principle for…

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the…

We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional integrable system (a quasicondensate of ultra-cold, weakly-interacting bosonic atoms being studied as a…

This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist…

We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $\alpha\in(0,1)$ in time and zero initial data. We derive a…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this…

We consider five-point differential-difference equations. Our aim is to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications…

We study the two-dimensional $t$--$J$ model at finite temperature directly in the thermodynamic limit using purification represented by an infinite projected entangled-pair state (iPEPS). We reach temperatures down to $T/t=0.1$ and hole…

Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomised initial wave functions to equilibrium. We compare our numerical…