86 research outputs found
Supersymmetry Across Nanoscale Heterojunction
We argue that supersymmetric transformation could be applied across the
heterojunction formed by joining of two mixed semiconductors. A general
framework is described by specifying the structure of ladder operators at the
junction for making quantitative estimation of physical quantities. For a
particular heterojunction device, we show that an exponential grading inside a
nanoscale doped layer is amenable to exact analytical treatment for a class of
potentials distorted by the junctions through the solutions of transformed
Morse-Type potentials.Comment: 7 pages, 2 figure
Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
We develop a systematic approach to construct novel completely solvable
rational potentials. Second-order supersymmetric quantum mechanics dictates the
latter to be isospectral to some well-studied quantum systems.
symmetry may facilitate reconciling our approach to the requirement that the
rationally-extended potentials be singularity free. Some examples are shown.Comment: 13 pages, no figure, some additions to introduction and conclusion, 4
more references; to be published in Special issue of Pramana - J. Phy
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
The generalized Swanson Hamiltonian with , can be transformed into an equivalent Hermitian Hamiltonian
with the help of a similarity transformation. It is shown that the equivalent
Hermitian Hamiltonian can be further transformed into the harmonic oscillator
Hamiltonian so long as constant. However, the
main objective of this paper is to show that though the commutator of
and is constant, the generalized Swanson
Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason
for this anomaly is discussed in the frame work of position dependent mass
models by choosing as the inverse square root of the mass function.Comment: Accepted in Journal of Physics A. Comments are welcom
Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
We recall the importance of recognizing the different mathematical nature of
various concepts relating to PT-symmetric quantum theories. After clarifying
the relation between supersymmetry and pseudo-supersymmetry, we prove
generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and
Roy, is just a special case of N-fold supersymmetry. In particular, we show
that all the models constructed by these authors have type A 2-fold
supersymmetry. Furthermore, we prove that an arbitrary one-body quantum
Hamiltonian which admits two (local) solutions in closed form belongs to type A
2-fold supersymmetry, irrespective of whether or not it is Hermitian,
PT-symmetric, pseudo-Hermitian, and so on.Comment: 10 pages, no figures; typos correcte
-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
A class of spherically symmetric non-Hermitian Hamiltonians and their
\eta-weak-pseudo-Hermiticity generators are presented. An operators-based
procedure is introduced so that the results for the 1D Schrodinger Hamiltonian
may very well be reproduced. A generalization beyond the nodeless states is
proposed. Our illustrative examples include \eta-weak-pseudo-Hermiticity
generators for the non-Hermitian weakly perturbed 1D and radial oscillators,
the non-Hermitian perturbed radial Coulomb, and the non-Hermitian radial Morse
models.Comment: 14 pages, content revised/regularized to cover 1D and 3D case
(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
The effect of the built-in supersymmetric quantum mechanical language on the
spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and
complexified Lorentz scalar interactions, is re-emphasized. The signature of
the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac
particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib)
(an inversely linear plus linear, leading to a PT-symmetric oscillator model),
and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered.
Moreover, a first-order intertwining differential operator and an
-weak-pseudo-Hermiticity generator are presented and a complexified
PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise
The Quantum Effective Mass Hamilton-Jacobi Problem
In this article, the quantum Hamilton- Jacobi theory based on the position
dependent mass model is studied. Two effective mass functions having different
singularity structures are used to examine the Morse and Poschl- Teller
potentials. The residue method is used to obtain the solutions of the quantum
effective mass- Hamilton Jacobi equation. Further, it is shown that the
eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and
Poschl-Teller potentials can be obtained by using the Riccati equation without
solving a differential equation
First-order intertwining operators with position dependent mass and - weak-psuedo-Hermiticity generators
A Hermitian and an anti-Hermitian first-order intertwining operators are
introduced and a class of -weak-pseudo-Hermitian position-dependent mass
(PDM) Hamiltonians are constructed. A corresponding reference-target
-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some
-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models
are used as illustrative examples. Energy-levels crossing and flown-away states
phenomena are reported for the resulting Scarf II spectrum. Some of the
corresponding -weak-pseudo-Hermitian Scarf II- and
periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are
given as products of the reference-target map.Comment: 11 pages, no figures, Revised/Expanded, more references added. To
appear in the Int.J. Theor. Phy
Non-relativistic metrics with extremal limits
We present solutions of type IIB supergravity with z=2 Schrodinger
asymptotics that admit an extremal limit, i.e. the black hole horizon has a
double zero. These solutions are obtained as TsT transformations of the charged
planar black hole in AdS_5 \times S^5. Unlike the uncharged solution, the
Ramond-Ramond two-form is turned on. We study the thermodynamic properties of
these new solutions, and we show that the ratio of shear viscosity to entropy
density is 1/4\pi even in the extremal limit. We also consider the
TsT-transformed soliton and show that, for a special radius of the compact
circle, there is a confinement-deconfinement phase transition at zero
temperature between the soliton and black hole phases.Comment: 23 pages, references and clarifications added, typos corrected,
restriction in phase transition due to equation 6.5 emphasized; published
versio
- …