Related papers: Determinant representation for a quantum correlati…
We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space…
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 study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a rational function and the measure is supported on some…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined…
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…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
We describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum K\"ahler form, metric,…
We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation…
We investigate how the theory of self-adjoint differential equations alone can be used to provide a satisfactory solution of the inverse vatiational problem. For the discrete system, the self-adjoint form of the Newtonian equation allows…
The one loop quantum corrections to the classical reflection factor of the sinh-Gordon model are calculated partially for general boundary conditions. The model is studied under boundary conditions which are compatible with integrability,…
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral…
Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this…
In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the…
We compute lattice correlation functions for the model of critical dense polymers on a semi-infinite cylinder of perimeter $n$. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a…
Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but…
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…
A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive…
The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the…
Representations of the rotation group may be formulated in second-quantised language via Schwinger's transcription of angular momentum states onto states of an effective two-dimensional oscillator. In the case of the molecular asymmetric…
In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the time evolution of the correlation function of two…