相关论文: Separation of Variables in the Elliptic Gaudin Mod…

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…

We propose a new basis of spin-operators, specific for the case of planar theories, which allows a Lagrangian decomposition into spin-parity components. The procedure enables us to discuss unitarity and spectral properties of gravity models…

We study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe ansatz approach, we derive the eigenvalues of…

In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…

An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.

We study linear ordinary differential equations which are analytically parametrized on Hermitian symmetric spaces and invariant under the action of symplectic groups. They are generalizations of the classical Lam\'e equation. Our main…

Starting from a generic Lagrangian, we discuss the number of propagating degrees of freedom in the framework of generalised non-linear electrodynamics when a photon-background split is applied. We start by stating results obtained in a…

We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin models. We have found the general…

We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

Directed possibly cyclic graphs have been proposed by Didelez (2000) and Nodelmann et al. (2002) in order to represent the dynamic dependencies among stochastic processes. These dependencies are based on a generalization of…

We consider the XXX homogeneous Gaudin system with $N$ sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new…

The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary…

We propose a quantum optical implementation of a class of dissipative spin systems, including the XXZ and Ising model, with ultra-cold atoms in optical lattices. Employing the motional degree of freedom of the atoms and detuned Raman…

We use an integral quantization model based on the Heisenberg-Weyl group to describe the motion of a spinless particle in the Minkowski background spacetime. This work is a sequel to a previous paper, devoted to mathematical aspects of our…

The XXZ Gaudin model with {\it generic} integerable boundaries specified by generic {\it non-diagonal} K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues…

A conservative Newton system (d/dt)^2 q = -grad V(q) in R^n is called separable when the Hamilton--Jacobi equation for the natural Hamiltonian H = (1/2) p^2 + V(q) can be solved through separation of variables in some curvilinear…

We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…

This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…

We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length…