Related papers: Multi-Well Potentials in Quantum Mechanics and Sto…
We unravel the existence and nonequilibrium response of one-dimensional harmonically trapped droplet configurations in the presence of a central potential barrier or well. For fixed negative chemical potentials, it is shown that droplets…
We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one- dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest…
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral…
In this paper, we introduce a family of sextic potentials that are exactly solvable, and for the first time, a family of triple-well potentials with their whole energy spectrum and wavefunctions using supersymmetry method. It was suggested…
We review a recent progress in constructing the low-energy effective action of N=4 SYM theory. This theory is formulated in terms of N=2 harmonic superfields corresponding to N=2 vector multiplet and hypermultiplet. Such a formulation…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed and the various possibilities for partial supersymmetry breaking are discussed. It is shown that quantum mechanical models with one quarter, one half and…
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
Using the ${\cal N}=2$ superfield approach, we construct full ${\cal N}=4$ supersymmetric low-energy effective actions for ${\cal N}=4$ SYM models, with both ${\cal N}=2$ gauge superfield strengths and hypermultiplet superfields included.…
The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric…
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study…
After briefly reviewing the definitions of classical probability densities for position, $P_{CL}(x)$, and for momentum, $P_{CL}(p)$, we present several examples of classical mechanical potential systems, mostly variations on such familiar…
We in this paper study the quantization of a particle in an inverted potential well. The Hamiltonian is Hermitian, while the potential is unbounded below. Classically the particle moves away acceleratingly from the center of potential top.…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…