Related papers: Construction and exact solution of a nonlinear qua…
The Schwinger model is perhaps the simplest non-trivial exactly-solvable QFT. In this note we examine the perturbative structure of the theory on the sphere and show that its quantum corrections match those predicted by the expansion of the…
A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the…
Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are…
The quantum Lattice Boltzmann equation (QLBe), a new variant of the lattice Boltzmann equation, specifically designed to describe non relativistic quantum motion, is validated for the case of a free-particle in (1+1) space-time dimensions.…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2…
Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…
A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch…
We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a point-like defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels.…
We introduce a new technique for constructing three-dimensional (3D) models of incompressible Riemann S-type ellipsoids and compressible triaxial configurations that share the same velocity field as that of Riemann S-type ellipsoids. Our…
We express the discrete 1+1-dimensional $O(3)$ non-linear sigma model (NL$\sigma$M) in a form well-suited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes…
This paper addresses the focusing cubic-quintic nonlinear Schrodinger equation in three space dimensions. Especially, we study the global dynamics of solutions whose energy and mass equal to those of the ground state in the sprits of…
The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an infinite number of quasi-conserved charges which present intriguing…
Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…
A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S. Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in 2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial of two…
We consider an integrable, nonlocal and nonlinear, Schr\"odinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those…
A new system of coupled higher-order nonlinear Schroedinger equations is proposed which passes the Painleve test for integrability well. A Lax pair and a multi-field generalization are obtained for the new system.
We introduce two new families of quasi-exactly solvable (QES) extensions of the oscillator in a $d$-dimensional constant-curvature space. For the first three members of each family, we obtain closed-form expressions of the energies and…