Searcharxiv⌕ Search

arXiv subjects

P. Roy

Publications and source records attributed to P. Roy.

At least 73 records · Page 4Linked to original sources
arXiv2013

Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (β-->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.

hep-th↗
arXiv2013

Pseudo Hermitian Generalized Dirac Oscillators

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 of 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 Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.

math-ph↗
arXiv2012

Temperature evolution of infrared- and Raman-active phonons in graphite

We perform a comparative experimental and theoretical study of the temperature dependence up to 700 K of the frequency and linewidths of the graphite E1u and E2g optical phonons (~1590 and 1580 cm-1) by infra-red (IR) and Raman spectroscopy. Despite their similar character, the temperature dependence of the two modes is quite different, being, e.g., the frequency shift of the IR-active E1u mode is almost twice as big as that of the Raman active E2g mode. Ab initio calculations of the anharmonic properties are in remarkable agreement with measurements and explain the observed behavior.

cond-mat.mtrl-sci↗
arXiv2012

Direct observation of the decay of first excited Hoyle state in $^{12}$C

An excited state of $^{12}$C having excitation energy E$_x \sim$ 9.65 $\pm$ 0.02 MeV and width (FWHM) $\sim607\pm$ 55 keV, which decays to three $ α$-particles via Hoyle state ($E_x \sim$ 7.65 MeV), has been directly identified for the first time in the exclusive inelastic scattering of 60 MeV $^{4}$He on $^{12}$C, measured in coincidence with the recoiling $^{12}$C$ ^* $ Hoyle state (decaying mostly as $^{12}$C$ ^* $ $\rightarrow \ ^{8} $Be + $ α$ $\rightarrow \ α+ α+ α$) by event-by-event kinematic reconstruction of the completely detected (4$ α$) events. This state is likely to be a candidate for 2$_2^+$ first excited Hoyle state, the existence of which has recently been indirectly evidenced from the recent inclusive inelastic scattering studies.

nucl-ex↗
arXiv2011

Pseudo Hermitian formulation of Black-Scholes equation

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

q-fin.GN↗
arXiv2011

Low temperature FIR and submm mass absorption coefficient of interstellar silicate dust analogues

Cold dust grains emission in the FIR/submm is usually expressed as a modified black body law in which the dust mass absorption coefficient (MAC), is described with a temperature- and wavelength-independent emissivity spectral index, beta. However, numerous data from space and balloon-born missions and recently from Herschel and Planck show that dust emission is not well understood, as revealed by the observed anti-correlation of beta with the grain temperature. In order to give astronomers the necessary data to interpret FIR/submm observations, we synthesised analogues of interstellar amorphous and crystalline silicate grains, rich in Mg and Ca, and having stiochiometry of olivine and pyroxene and measured their MAC, in the 100-1000/1500 \mum range for grain temperatures varying from 300 to 10 K. We find that the grain MAC decreases when the grain temperature decreases and that the local spectral index, beta, defined as the slope of the MAC curve, is anti-correlated with the grain temperature. These variations, which are not observed in the crystallised samples, are related to the amorphous nature of the samples. In addition, the spectral shape of the MAC is complex: at short wavelengths (lambda < 500/700 \mum), beta is in the range 1.6 - 2.1 for all grain temperature and grain composition whereas at longer wavelengths (lambda > 500/700 \mum), beta < 2 for samples with a pyroxene stoichiometry and beta > 2 for samples with an olivine stoichiometry. Hence, the simplifying asymptotic expression based on a single temperature- and wavelength-independent spectral index used by astronomers is not appropriate to describe the dust MAC and thus the dust emission, and may induce significant errors on the derived parameters such as the dust mass and the dust physical and chemical properties. Instead, dust emission models should use the dust MAC as a function of wavelength and temperature.

astro-ph.GA↗
arXiv2011

Information Entropy of conditionally exactly solvable potentials

We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski (BBM) inequality has also been tested for a number of states.

math-ph↗
arXiv2011

Study of classical mechanical systems with complex potentials

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature - the closed orbits become open ones.

quant-ph↗
arXiv2009

Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $η$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.

quant-ph↗
arXiv2009

Continuum states in generalized Swanson models

A one-to-one correspondence is known to exist between the spectra of the discrete states of the non Hermitian Swanson-type Hamiltonian $ H = {\cal{A}}^{\dagger} {\cal{A}} + α{\cal{A}} ^2 + β{\cal{A}}^{\dagger 2} $, ($α\neq β$), and an equivalent Hermitian Schrödinger Hamiltonian $h$, the two Hamiltonians being related through a similarity transformation. In this work we consider the continuum states of $h$, and examine the nature of the corresponding states of $H$.

quant-ph↗
arXiv2008

Pseudo supersymmetric partners for the generalized Swanson model

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., $ H_- = {\cal{A}}^{\dagger} {\cal{A}} + α{\cal{A}} ^2 + β{\cal{A}}^{\dagger 2} $, where $ αβ$ are real constants, with $ α\neq β$, and ${\cal{A}}^{\dagger}$ and ${\cal{A}}$ are generalized creation and annihilation operators. It is shown that the initial Hamiltonian $H_-$, and its partner $H_+$, are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians $H_{\pm}$, related to their respective Hermitian counterparts $h_{\pm}$, through the same similarity transformation operator $ρ$ : $ H_{\pm} = ρ^{-1} h_{\pm} ρ$. The formalism is applied to the entire class of shape-invariant models.

quant-ph↗
arXiv2008

Noncommutative oscillator, symmetry and Landau problem

Isotropic oscillator on a plane is discussed where both the coordinate and momentum space are considered to be noncommutative. We also discuss the symmetry properties of the oscillator for three separate cases when both the noncommutative parameters Θand \barΘ satisfy specific relations. We compare the Landau problem with the isotropic oscillator on noncommutative space and obtain a relation between the two noncommutative parameters with the magnetic field of the Landau problem.

hep-th↗
arXiv2007

Generalized Swanson models and their solutions

We analyze a class of non-Hermitian quadratic Hamiltonians, which are of the form $ H = {\cal{A}}^{\dagger} {\cal{A}} + α{\cal{A}} ^2 + β{\cal{A}}^{\dagger 2} $, where $ α, β$ are real constants, with $ α\neq β$, and ${\cal{A}}^{\dagger}$ and ${\cal{A}}$ are generalized creation and annihilation operators. Thus these Hamiltonians may be classified as generalized Swanson models. It is shown that the eigenenergies are real for a certain range of values of the parameters. A similarity transformation $ρ$, mapping the non-Hermitian Hamiltonian $H$ to a Hermitian one $h$, is also obtained. It is shown that $H$ and $h$ share identical energies. As explicit examples, the solutions of a couple of models based on the trigonometric Rosen-Morse I and the hyperbolic Rosen-Morse II type potentials are obtained. We also study the case when the non-Hermitian Hamiltonian is ${\cal{PT}}$ symmetric.

quant-ph↗