arXiv subjects

Anjana Sinha

Publications and source records attributed to Anjana Sinha.

15 recordsLinked to original sources

arXiv2020

Dust-Ion-Acoustic Waves in unmagnetized 4-component plasma

A theoretical study is presented for the propagation of Dust Ion Acoustic Waves in an unmagnetized four-component plasma, consisting of Maxwellian negative ions, cold mobile positive ions, $κ$-distributed electrons and positively charged dust grains. Based on the characteristics of Sagdeev pseudopotential and phase portraits, three types of nonlinear waves are observed --- solitons, double layers and supersolitons. The conditions for the existence of such nonlinear waves are highly sensitive to the plasma parameters. The results obtained in this study may be of wide relevance in the field of space plasma as well as ultrasmall semiconductor devices in the laboratory.

physics.plasm-ph↗

arXiv2017

Dissipative nonlinear waves in a gravitating quantum fluid

Nonlinear wave propagation is studied analytically in a dissipative, self-gravitating Bose Einstein condensate, in the framework of Gross-Pitaevskii model. The linear dispersion relation shows that the effect of dissipation is to suppress dynamical instabilities that destabilize the system. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation. The soliton energy, amplitude and velocity are found to decay with time, whereas the soliton width increases, such that the soliton exists for a finite time only

cond-mat.quant-gas↗

arXiv2013

Spectral Singularity in confined PT symmetric optical potential

We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $ confined within the region $0 \leq x \leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral multiple of the period $ π$. We give some new and interesting results. Scattering is observed to be normal ($|T| ^2 \leq 1, \ |R|^2 \leq 1$) for $V_0 \leq 0.5 $, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point ($ V_0 > 0.5 $) scattering is found to be anomalous ($|T| ^2, \ |R|^2 $ not necessarily $ \leq 1 $). Additionally, in this parameter regime of $V_0$, one observes infinite number of spectral singularities $E_{SS}$ at different values of $V_0$. Furthermore, for $L= 2 n π$, the transition point $V_0 = 0.5$ shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side ($Im [V(x)] < 0$) but finite reflection when the beam is incident from the emissive side ($Im [V(x)] > 0$), transmission being identically unity in both cases. Finally, the scattering coefficients $|R|^2$ and $|T|^2 $ always obey the generalized unitarity relation : $ ||T|^2 - 1| = \sqrt{|R_R|^2 |R_L|^2}$, where subscripts $R$ and $L$ stand for right and left incidence respectively.

quant-ph↗

arXiv2013

Scattering in a varying mass PT symmetric double heterojunction

We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no spontaneous breakdown of PT symmetry. The potential profile in the intermediate layer is considered such that it has a non vanishing imaginary part near the heterojunctions. Exact analytical solutions for the wave function are obtained, and the reflection and transmission coefficients are plotted as a function of energy, for both left as well as right incidence. As expected, the spatial dependence on mass changes the nature of the scattering solutions within the heterojunctions, and the space-time (PT) symmetry is responsible for the left-right asymmetry in the reflection and transmission coefficients. However, the non vanishing imaginary component of the potential near the heterojunctions gives new and interesting results.

quant-ph↗

arXiv2012

Classical Trajectories of the Continuum States of the ${\cal{PT}}$ symmetric Scarf II potential

We apply the factorization technique developed by Kuru et. al. [Ann. Phys. {\bf 323} (2008) 413] to obtain the exact analytical classical trajectories and momenta of the continuum states of the non Hermitian but ${\cal{PT}}$ symmetric Scarf II potential. In particular, we observe that the strange behaviour of the quantum version at the spectral singularity has an interesting classical analogue.

quant-ph↗

arXiv2012

Scattering states of a particle, with position-dependent mass, in a ${\cal{PT}}$ symmetric heterojunction

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.

quant-ph↗

arXiv2011

Scattering states of a particle, with position-dependent mass, in a double heterojunction

In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the heterojunctions. It is observed that the spatial dependence of mass within the well / barrier introduces a nonlinear component in the plane wave solutions of the continuum states. Additionally, the transmission coefficient is found to increase with increasing energy, finally approaching unity, whereas the reflection coefficient follows the reverse trend and goes to zero.

quant-ph↗

arXiv2004

PT symmetry of a conditionally exactly solvable potential

A conditionally exactly solvable potential, the supersymmetric partner of the harmonic oscillator is investigated in the PT-symmetric setting. It is shown that a number of properties characterizing shape-invariant and Natanzon-class potentials generated by an imaginary coordinate shift $x-{\rm i}ε$ also hold for this potential outside the Natanzon class.

quant-ph↗

arXiv2003

New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to higher states of an exactly solvable PT symmetric potential. It is shown that the resulting hamiltonian and the original one are pseudo supersymmetric partners. We also discuss application of Darboux transformation to hamiltonians with spontaneously broken PT symmetry.

quant-ph↗

arXiv2003

Generation of exactly solvable non-Hermitian potentials with real energies

A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.

quant-ph↗

arXiv2003

Three Dimensional Confinement : WKB Revisited

An alternate formalism is developed to determine the energy eigenvalues of quantum mechanical systems, confined within a rigid impenetrable spherical box of radius $r_0$, in the framework of Wentzel-Kramers-Brillouin (WKB) approximation. Instead of considering the Langer correction for the centrifugal term, the approach adopted here is that of Hainz and Grabert : The centrifugal term is expanded perturbatively (in powers of $\hbar$), decomposing it into 2 terms -- the classical centrifugal potential and a quantum correction. Hainz and Grabert found that this method reproduced the exact energies of the hydrogen atom, to the first order in $\hbar$, with all higher order corrections vanishing. In the present study, this formalism is extended to the case of radial potentials under hard wall confinement, to check whether the same argument holds good for such confined systems as well. As explicit examples, 3 widely known potentials are studied, which are of considerable importance in the theoretical treatment of various atomic phenomena involving atomic transitions, viz., the 3-dimensional harmonic oscillator, the hydrogen atom, and the Hulthen potential.

quant-ph↗

arXiv2002

Energy spectra of two electrons in a circular quantum dot

The electron interaction energy of two interacting electrons in a circular quantum dot (with hard wall confinement) is investigated in the framework of the semi-classical Wentzel-Kramers-Brillouin (WKB) approximation. The two electrons are assumed to be in an infinitely deep well of radius $r_0$, in a simple configuration with one electron fixed at the origin. The corresponding Schrodinger equation, with hard wall boundary conditions, is also solved exactly by numerical integration. It is observed that the agreement between the two energy values is quite good, suggesting that the WKB approximation works well for such a confined quantum system as well. This may provide motivation to extend this to more realistic confined potentials.

quant-ph↗

arXiv2002

PT-invariant one-dimensional Coulomb problem

The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) = {alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of PT-symmetry. The PT-invariant exactly solvable model so formed, is found to admit a double set of real and discrete energies, numbered by a quasi-parity q = +/- 1.

quant-ph↗

arXiv2002

Isospectral partners for a complex PT-invariant potential

We construct isospectral partner potentials of a complex PT-invariant potential, viz., V(x) = V_1 sech ^2 x - i V_2 sech x tanh x using Darboux's method. Oneset of isospectral potentials are obatined which can be termed 'Satellite potentials', in the sense that they are pf the same form as the original potential. In a particular case, the supersymmetric partner potential has the same spectrum, including the zero energy ground state, a fact which cannot occur in conventional supersymmetric quantum mechanics with real potential. An explicit example of a non-trivial set of isospectral potential is also obtained.

quant-ph↗

arXiv1999

SWKB Quantization Rules for Bound States in Quantum Wells

In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix formulation of the Bohr-Sommerfield quantization rule has been applied to the study of bound states in one dimension quantum wells. Here we study these potentials in the frame work of supersymmetric WKB (SWKB) quantization approximation and find that SWKB quantization rule is superior to the modified Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.

quant-ph↗