Related papers: Two-dimensional SUSY-pseudo-Hermiticity without se…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$ dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the…
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…
We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…
In the zoo of emergent symmetries in quantum many-body physics, the previously unrealized emergent spacetime supersymmetry (SUSY) is particularly intriguing. Although it was known that spacetime SUSY could emerge at the (1+1)d tricritical…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the…
A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such…
We consider a plausible scenario in the Minimal Supersymmetric Standard Model (MSSM) where all the genuine supersymmetric (SUSY) particles are heavier than the electroweak scale. In this situation, indirect searches via their radiative…
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and…
We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy…
We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the…
We analyze the low energy spectrum of bound states of the N=1 SU(2) SUSY Yang-Mills Theory (SYM). This work continues the investigation of the non-perturbative properties of SYM by Monte Carlo simulations in the Wilson discretization with…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…
We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}.…
Hitherto, it is well known that complex PT-symmetric Scarf II has real discrete spectrum in the parametric domain of unbroken PT-symmetry. We reveal new interesting complex, non-PT-symmetric parametric domains of this versatile potential,…
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that…
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…
The relation between a N = 2 nonlinear supersymmetric (SUSY) model and a linear SUSY (free) theory for $N = 2$ vector supermultiplet accompanying the spontaneous SUSY breaking is systematically worked out in two-dimensional superfield…