Related papers: On two-dimensional supersymmetric quantum mechanic…
We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally…
Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two…
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are…
A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence classes, have been obtained. We will re-examine two…
Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are…
The modular operator approach of Tomita-Takesaki to von Neumann algebras is elucidated in the algebraic structure of certain supersymmetric quantum mechanical systems. A von Neumann algebra is constructed from the operators of the system.…
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and…
A general strategy is provided to identify the most general metric for diagonalizable pseudo-Hermitian and anti-pseudo-Hermitian Hamilton operators represented by two-dimensional matrices. It is investigated how a permutation of the…
We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric…
The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into…
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This…
The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator…
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…
The superfield formulation of two - dimensional $N=4$ Extended Supersymmetric Quantum Mechanics (SQM) is described. It is shown that corresponding classical Lagrangian describes the motion in the conformally flat metric with additional…