2,754 research outputs found
Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'
We demonstrate that the recent paper by Abhinav and Panigrahi entitled
`Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010)
1198], which considers two different types of superpotentials for the
PT-symmetric complexified Scarf II potential, fails to take into account the
invariance under the exchange of its coupling parameters. As a result, they
miss the important point that for unbroken PT-symmetry this potential indeed
has two series of real energy eigenvalues, to which one can associate two
different superpotentials. This fact was first pointed out by the present
authors during the study of complex potentials having a complex
potential algebra.Comment: 6 pages, no figure, published versio
Diffusion of small light particles in a solvent of large massive molecules
We study diffusion of small light particles in a solvent which consists of
large heavy particles. The intermolecular interactions are chosen to
approximately mimic a water-sucrose (or water-polysaccharide) mixture. Both
computer simulation and mode coupling theoretical (MCT) calculations have been
performed for a solvent-to-solute size ratio five and for a large variation of
the mass ratio, keeping the mass of the solute fixed. Even in the limit of
large mass ratio the solute motion is found to remain surprisingly coupled to
the solvent dynamics. Interestingly, at intermediate values of the mass ratio,
the self-intermediate scattering function of the solute, F_{s}(k,t) (where k is
the wavenumber and t the time), develops a stretching at long time which could
be fitted to a stretched exponential function with a k-dependent exponent,
\beta. For very large mass ratio, we find the existence of two stretched
exponentials separated by a power law type plateau. The analysis of the
trajectory shows the coexistence of both hopping and continuous motions for
both the solute and the solvent particles. It is found that for mass ratio
five, the MCT calculations of the self-diffusion underestimates the simulated
value by about 20 %, which appears to be reasonable because the conventional
form of MCT does not include the hopping mode. However, for larger mass ratio,
MCT appears to breakdown more severely. The breakdown of the MCT for large mass
ratio can be connected to a similar breakdown near the glass transition.Comment: RevTex4, 9 pages, 10 figure
Quantum, noncommutative and MOND corrections to the entropic law of gravitation
Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde’s entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a classical setting by seeking appropriate corrections in the entropy. We estimate the correction term by using concrete coherent states in the standard and generalized versions of Heisenberg’s uncertainty principle. Using Jackiw’s direct and analytic method, we compute the explicit wavefunctions for these states, producing minimal length as well as minimal products. Subsequently, we derive a further selection criterium restricting the free parameters in the model in providing a canonical formulation of the quantum corrected Newtonian law by setting up the Lagrangian and Hamiltonian for the system
An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
The -symmetric complexified Scarf II potential V(x)= - V_1
\sech^{2}x + {\rm i} V_2 \sech x \tanh x, , is revisited
to study the interplay among its coupling parameters. The existence of an
isolated real and positive energy level that has been recently identified as a
spectral singularity or zero-width resonance is here demonstrated through the
behaviour of the corresponding wavefunctions and some property of the
associated pseudo-norms is pointed out. We also construct four different
rationally-extended supersymmetric partners to , which are -symmetric or complex non--symmetric according to the coupling
parameters range. A detailed study of one of these partners reveals that SUSY
preserves the spectral singularity existence.Comment: 14 pages, no figure, substantial additions on spectral singularities,
title change
PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework
Extending the supersymmetric method proposed by Tkachuk to the complex
domain, we obtain general expressions for superpotentials allowing generation
of quasi-exactly solvable PT-symmetric potentials with two known real
eigenvalues (the ground state and first-excited state energies). We construct
examples, namely those of complexified non-polynomial oscillators and of a
complexified hyperbolic potential, to demonstrate how our scheme works in
practice. For the former we provide a connection with the sl(2) method,
illustrating the comparative advantages of the supersymmetric one.Comment: 14 pages, LaTeX, no figur
Creation and annihilation operators and coherent states for the PT-symmetric oscillator
We construct two commuting sets of creation and annihilation operators for
the PT-symmetric oscillator. We then build coherent states of the latter as
eigenstates of such annihilation operators by employing a modified version of
the normalization integral that is relevant to PT-symmetric systems. We show
that the coherent states are normalizable only in the range (0, 1) of the
underlying coupling parameter .Comment: one additional reference, final version to be published in MPL
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
Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
We show that complex Lie algebras (in particular sl(2,C)) provide us with an
elegant method for studying the transition from real to complex eigenvalues of
a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized
P\"oschl-Teller, and Morse. The characterizations of these Hamiltonians under
the so-called pseudo-Hermiticity are also discussed.Comment: LaTeX, 14 pages, no figure, 1 reference adde
A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
We consider a PT Symmetric Partner to Khare Mandal's recently proposed
non-Hermitian potential with complex eigen values. Our potential is
Quasi-Exactly solvable and is shown to possess only real eigen values.Comment: 10 page
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