Related papers: One-Dimensional Impenetrable Anyons in Thermal Equ…
We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
We study a one-dimensional multicomponent anyon model that reduces to a multicomponent Lieb-Liniger gas of impenetrable bosons (Tonks-Girardeau gas) for vanishing statistics parameter. At fixed component densities, the coordinate Bethe…
The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations…
In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix…
We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum…
We consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework. Our…
The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the…
In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric…
We present analytic formulas for the ground state energy of the two-dimensional (2D) anyon gas in the quantum limit of a perpendicular magnetic field (Landau level filling factor \nu_L\le 1). These formulas, for the cases without and with…
The recent results of [J. Dubail, J.-M. St\'ephan, J. Viti, P. Calabrese, Scipost Phys. 2, 002 (2017)], which aim at providing access to large scale correlation functions of inhomogeneous critical one-dimensional quantum systems -- e.g. a…
The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical…
We consider the non-equilibrium dynamics of the interacting Lieb-Liniger gas after instantaneously switching the interactions off. The subsequent time evolution of the space- and time-dependent correlation functions is computed exactly.…
We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose…
A nonlinear transformation approach is formulated for the correlated fermions' thermodynamics through a medium-scaling effective action. An auxiliary implicit variable-effective chemical potential is introduced to characterize the…
Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations and it is natural to expect a strong sensitivity of its solutions to variations of…
The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a non-interacting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small…
We review in detail the derivation of the dielectric response function of a noninteracting system of spin-1/2 fermions in the random-phase approximation. Results for the response function of a Fermi gas in one, two and three dimensions can…
We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any…
We derive exact closed form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics of the momentum…