相关论文: Intertwined Hamiltonians in Two Dimensional Curved…

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…

Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space $E_2$ are explored. The study is restricted to Hamiltonians allowing separation of variables $V(x,y)=V_1(x)+V_2(y)$ in Cartesian coordinates. In particular,…

Separable Hamiltonian systems either in sphero-conical coordinates on a $S^2$ sphere or in elliptic coordinates on a ${\mathbb R}^2$ plane are described in an unified way. A back and forth route connecting these Liouville Type I separable…

Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance…

A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full…

In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a…

Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are…

The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition…

In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…

In a previous paper it was shown that a one-turning-point WKB approximation gives an accurate picture of the spectrum of certain non-Hermitian PT-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to…

In this work, a connection between some spectral properties of direct integral of operators in the direct integral of Hilbert spaces and their coordinate operators has been investigated.

For a symmetric pair $(G,H)$ of reductive groups we extend to a large class of generalized principal series representations our previous construction of meromorphic families of symmetry breaking operators. These operators intertwine between…

In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on…

We construct a constant curvature analogue on the two-dimensional sphere ${\mathbf S}^2$ and the hyperbolic space ${\mathbf H}^2$ of the integrable H\'enon-Heiles Hamiltonian $\mathcal{H}$ given by $$…

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics…

A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…

We introduce a two-orbital Hamiltonian on a square lattice that contains on-site attractive interactions involving the two $e_g$ orbitals. Via a canonical mean-field procedure similar to the one applied to the well-known negative-$U$…

Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the…

We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…

We study half-space/Rindler modular Hamiltonians for excited states created by turning on sources for local operators in the Euclidean path integral in relativistic quantum field theories. We derive a simple, manifestly Lorentzian formula…