115157994
Non-hermitian quantum mechanics in non-commutative space
AbstractA recent investigation of the possibility of having a 
$\mathcal{PT}$
-symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a 
$\mathcal{PT}$
-symmetric deformation of this space. Specifically, a 
$\mathcal{PT}$
-symmetric harmonic oscillator together with an iC(x1+x2) interaction are discussed in this space, and solutions are obtained. We show that in the 
$\mathcal{PT}$ 
deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x1+x2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not 
$\mathcal{PT}$
-symmetric. A complex interacting anisotropic oscillator system also is discussed.
119312840
'Stringy' Coherent States Inspired By Generalized Uncertainty Principle
Abstract Coherent States with Fractional Revival property, that explicitly satisfy the Generalized Uncertainty Principle (GUP), have been constructed in the context of Generalized Harmonic Oscillator. The existence of such states is essential in motivating the GUP based phenomenological results present in the literature which otherwise would be of purely academic interest. The effective phase space is Non-Canonical (or Non-Commutative in popular terminology). Our results have a smooth commutative limit, equivalent to Heisenberg Uncertainty Principle. The Fractional Revival time analysis yields an independent bound on the GUP parameter. Using this and similar bounds obtained here, we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissonian. Correspondence Principle is deformed in an interesting way. Our computational scheme is very simple as it requires only first order corrected energy values and undeformed basis states.
8406718
Motion of a spin-½ particle in shape invariant scalar and magnetic fields
We study the motion of a spin-½ particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics. We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.
119751583
On supersymmetry and random sources
We evaluate the one loop effective potential for the supersymmetric Higgs model in the presence of a gaussian random source and examine supersymmetry breaking at the one loop level.
121137215
Novel perturbation expansion for the Langevin equation
We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force with〈f(t)f(t′)〉=2δ(t−t′), andW(x) is of the formgx1+2δ. The parameterδ is a measure of the nonlinearity of the equation. We show how to obtain the correlation functions〈x(t)f(t′)〉···x(t(n))〉f as a power series inδ. We obtain three terms in theδ expansion and show how to use Padé approximants to analytically continue the answer in the variableδ. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg andδ.
14129154
A new class of PT-symmetric Hamiltonians with real spectra
Abstract We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-Hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY quantum mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.
119146278
Pseudo-Hermitian generalized Dirac oscillators
Abstract We study generalized Dirac oscillators with complex interactions in ( 1 + 1 ) dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are η -pseudo-Hermitian with respect to certain metric operators η . Exact solutions for the generalized Dirac oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with an anti-Jaynes–Cummings-type model and by spin flipping they can also be identified with a Jaynes–Cummings-type model.
122611597
Gravitino mass bounds in a general cosmological scenario
Abstract A stable gravitino is shown to respect an upper mass bound ∼1 keV and an unstable one a lower mass bound ∼10 TeV from the global hyperbolicity property alone without the assumptions of a Friedmann universe. The specific Friedmann cosmology with a critical mass density in fact reduces the upper bound for a stable gravitino to ∼0.1 keV. Complications due to inflation and the anti-de Sitter nature of the spacetime before the breakdown of local supersymmetry are also discussed.
123245921
Polarized deep inelastic sum rules
Abstract New sum-rules for the polarized deep inelastic neutrino-nucleon cross sections are derived by applying the Melosh transformation to matrix elements of local currents and of local limits of the first derivatives of bilocal currents.
13912698
Event shape discrimination of supersymmetry from large extra dimensions at a linear collider
The production of a charged lepton (l=e,μ) pair with a large missing energy at a linear collider is discussed as a means of distinguishing the minimal supersymmetry (MSSM) scenario from that with large extra dimensions (ADD) for parameter ranges where the total cross-sections are comparable for both. Analyses in terms of event shape variables, specifically sphericity and thrust, are shown to enable a clear discrimination in this regard.
15949027
CP violation and matter effect for a variable earth density in very long baseline experiments
Abstract The perturbative treatment of subdominant oscillation and matter effect in neutrino beams/superbeams, propagating over long baselines and being used to look for CP violation, is studied here for a general matter density function varying with distance. New lowest order analytic expressions are given for different flavour transition and survival probabilities in a general neutrino mixing basis and a variable earth matter density profile. It is demonstrated that the matter effect in the muon neutrino (antineutrino) flavour survival probability vanishes to this order, provided the depletion, observed for atmospheric muon neutrinos and antineutrinos at super-Kamiokande, is strictly maximal. This result is independent of the earth density profile and the distance L between the source and the detector. In the general variable density case we show that one cannot separate the matter induced asymmetry from a genuine CP effect by keeping two detectors at distances L 1 and L 2 from the source while maintaining a fixed ratio L 1 / E 1 = L 2 / E 2 . This needs to be done numerically and we estimate the asymmetry generated by the earth matter effect with particular density profiles and some chosen parameters for very long baseline neutrino oscillation experiments.