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S. N. Pandey

Publications and source records attributed to S. N. Pandey.

16 recordsLinked to original sources
arXiv2017

Fractal analysis of BaF2 thin films deposited on different substrates

Barrium fluoride (BaF2) thin films were prepared by electron beam evaporation technique at room temperature, on glass, Silicon and Aluminum substrates having thickness of 20 nm each. Its structural property and surface morphology were studied using glancing angle X-ray diffraction (GAXRD) and atomic force microscopy (AFM) respectively. It was found that grain size, average surface roughness and interface width changes with different substrates. Higuchi algorithm is applied for the fractal measure on AFM images.It was observed found that the fractal dimension varied from substrate to substrate.

cond-mat.mtrl-sci↗
arXiv2016

Dzyaloshinskii-Moriya interaction as an agent to free the bound entangled states

In the present article we investigate the efficacy of Dzyaloshisnhkii-Moriya (DM) interaction to convert the bound entangled states into free entangled states. Here we consider the tripartite hybrid system as a pair of non interacting two qutrits initially prepared in bound entangled states and one auxiliary qubit. The auxiliary qubit interacts with any one of the qutrit of the pair through DM interaction. It has been found that the DM interaction free the bound entangled states as time advances. In the present work we consider two types of bound entangled states investigated by Horodecki. Further we find that the frequency of free entanglement conversion is same in both the states. We also investigate the phenomenon of entanglement and distillability sudden death and their possibilities. Here the realignment criteria and negativity have been used for detection and quantification of entanglement.

quant-ph↗
arXiv2016

Robustness of Greenberger-Horne-Zeilinger and W states against Dzyaloshinshkii-Moriya interaction

In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entanglement of the system. As a result we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand bipartite partitions and tripartite entanglement in GHZ states does not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work we consider generalised GHZ and W states and three $π$ is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place.

quant-ph↗
arXiv2016

The inverse problem of a mixed Liénard type nonlinear oscillator equation from symmetry perspective

In this paper, we discuss the inverse problem for a mixed Liénard type nonlinear oscillator equation $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$, where $f(x),\,g(x)$ and $h(x)$ are arbitrary functions of $x$. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle-Singer procedure we construct a time independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative non-standard Lagrangian and Hamiltonian functions. The classical dynamics of the nonlinear oscillator is also discussed and certain special properties including isochronous oscillations are brought out.

nlin.SI↗
arXiv2015

Dynamics of entanglement in qubit-qutrit with x component of DM interaction

In this present paper we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii-Moriya $(D_{x})$ by taking an auxiliary qubit C. Here we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction. We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and $D_{x}$ on entanglement. We find that the state (probability amplitude) of auxiliary qubit does not influence the entanglement, only $D_{x}$ influences the same. The phenomenon of entanglement sudden death (ESD) induced by $D_{x}$ has also been observed. We also present the affected and unaffected two parameter qubit-qutrit states by $D_{x}$.

quant-ph↗
arXiv2015

Influence of Dzyaloshinshkii-Moriya interaction on quantum correlations in two qubit Werner states and MEMS

In this paper we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quantum correlations in two qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubits pair and one auxiliary qubit which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two qubit Werner states. On the other hand the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state (i.e probability amplitude) of auxiliary qubit do not affect the quantum correlations in both the states, only DM interaction strength influences the quantum correlations. So one can avoid the intention to prepare the specific state of auxiliary qubit to manipulate the quantum correlations in both the states. We mention here that avoiding the preparation of state can contribute to cost reduction in quantum information processing. We also observe the phenomenon of entanglement sudden death in the present study.

quant-ph↗
arXiv2014

Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems

In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled quadratic and mixed Liénard type equations, which include various physical and mathematical models. The procedure is broadly divided into two parts. In the first part, we consider a general factorized form for the equation under consideration in terms of some unknown functions and identify the determining equations for them. In the second part, we systematically solve the determining equations and identify the compatible factorizing form for this class of equations. In addition, we also discuss the problem of identification of isochronous dynamical systems belonging to the above class of equations. In particular, we deduce an isochronocity condition for the coupled quadratic Liénard equation. We also present specific examples of physical interest.

nlin.SI↗
arXiv2014

On the complete Lie point symmetries classification of the mixed quadratic-linear Li$\acute{\textbf{e}}$nard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$

In this paper we develop a systematic and self consistent procedure based on a set of compatibility conditions for identifying all maximal (eight parameter) and non-maximal (one and two parameter) symmetry groups associated with the mixed quadratic-linear Li$\acute{e}$nard type equation, $\ddot {x} + f(x){\dot {x}}^{2} + g(x)\dot{x}+h(x)= 0$, where $f(x),\,g(x)$ and $h(x)$ are arbitrary functions of $x$. With the help of this procedure we show that a symmetry function $b(t)$ is zero for non-maximal cases whereas it is not so for the maximal case. On the basis of this result the symmetry analysis gets divided into two cases, $(i)$ the maximal symmetry group $(b\neq0)$ and $(ii)$ non-maximal symmetry groups $(b=0)$. We then identify the most general form of the mixed-quadratic linear Li$\acute{e}$nard type equation in each of these cases. In the case of eight parameter symmetry group, the identified general equation becomes linearizable. We present a specific example of physical interest. In the case of non-maximal symmetry groups the identified equations are all integrable. The integrability of all the equations is proved either by providing the general solution or by constructing time independent Hamiltonians. We also analyse the underlying equivalence transformations.

nlin.SI↗
arXiv2013

Classification of Lie point symmetries for quadratic Li$\acute{\textbf{e}}$nard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)=0$

In this paper we carry out a complete classification of the Lie point symmetry groups associated with the quadratic Li$\acute{e}$nard type equation, $\ddot {x} + f(x){\dot {x}}^{2} + g(x)= 0$, where $f(x)$ and $g(x)$ are arbitrary functions of $x$. The symmetry analysis gets divided into two cases, $(i)$ the maximal (eight parameter) symmetry group and $(ii)$ non-maximal (three, two and one parameter) symmetry groups. We identify the most general form of the quadratic Li$\acute{e}$nard equation in each of these cases. In the case of eight parameter symmetry group, the identified general equation becomes linearizable as well as isochronic. We present specific examples of physical interest. For the nonmaximal cases, the identified equations are all integrable and include several physically interesting examples such as the Mathews-Lakshmanan oscillator, particle on a rotating parabolic well, etc. We also analyse the underlying equivalence transformations.

nlin.SI↗
arXiv2011

Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift

We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation, governing the evolution of intensity in the femtosecond regime, is that of non-linear Schrodinger equation with a source. The exact localized solutions to this system can have both super and subluminal propagation belonging to two distinct class. A number of these solitons exhibit chirality, thereby showing preferential propagation behavior determined by group velocity dispersion. Both localized bright and dark solitons are found in complementary velocity and experimental parameter domains, which can exist for anomalous and normal dispersion regimes. It is found that, dark solitons in this system propagate with non-zero velocity, unlike their counterpart in nanosecond regime. Interestingly, subluminal propagation is observed for solitons having a nontrivial Pade type intensity profile.

nlin.PS↗
arXiv2009

On Basics of Cosmology

Some discussion of physical and geometrical interpretation of Einsteins theory of gravitation which is on basic of cosmology.

physics.gen-ph↗
arXiv2009

A Group Theoretical Identification of Integrable Cases of the Liénard Type Equation $\ddot{x}+f(x)\dot{x}+g(x) = 0$ : Part I: Equations having Non-maximal Number of Lie point Symmetries

We carry out a detailed Lie point symmetry group classification of the Liénard type equation, $\ddot{x}+f(x)\dot{x}+g(x) = 0$, where $f(x)$ and $g(x)$ are arbitrary smooth functions of $x$. We divide our analysis into two parts. In the present first part we isolate equations that admit lesser parameter Lie point symmetries, namely, one, two and three parameter symmetries, and in the second part we identify equations that admit maximal (eight) parameter Lie-point symmetries. In the former case the invariant equations form a family of integrable equations and in the latter case they form a class of linearizable equations (under point transformations). Further, we prove the integrability of all of the equations obtained in the present paper through equivalence transformations either by providing the general solution or by constructing time independent Hamiltonians. Several of these equations are being identified for the first time from the group theoretical analysis.

nlin.SI↗
arXiv2009

A Group Theoretical Identification of Integrable Equations in the Liénard Type Equation $\ddot{x}+f(x)\dot{x}+g(x) = 0$ : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Liénard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Liénard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.

nlin.SI↗
arXiv2006

An Electrical Spinning Particle In Einstein's Unified Field Theory

Previous work on exact solutions has been shown that sources need to be appended to the field equation of Einstein's unified field theory in order to achieve physically meaningful results,such sources can be included in a variational formulation by Borchsenius and moffat.The resulting field equations and conservation identities related to the theory that can be used to derive the equations of structure and motion of a pole-dipole particle according to an explicitly covariant approach by Dixon6.In this present paper it is shown that,under certain conditions for the energy tensor of the spinning particle,the equations of structure and motion in an electromagnetic field turn out to be formly identical to those occurring in Einstein-Maxwell theory.

gr-qc↗
arXiv2005

A Simple and Unified Approach to Identify Integrable Nonlinear Oscillators and Systems

In this paper, we consider a generalized second order nonlinear ordinary differential equation of the form $\ddot{x}+(k_1x^q+k_2)\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+λ_1x=0$, where $k_i$'s, $i=1,2,3,4$, $λ_1$ and $q$ are arbitrary parameters, which includes several physically important nonlinear oscillators such as the simple harmonic oscillator, anharmonic oscillator, force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden type equation and its hierarchy, generalized Duffing-van der Pol oscillator equation hierarchy and so on and investigate the integrability properties of this rather general equation. We identify several new integrable cases for arbitrary value of the exponent $q, q\in R$. The $q=1$ and $q=2$ cases are analyzed in detail and the results are generalized to arbitrary $q$. Our results show that many classical integrable nonlinear oscillators can be derived as sub-cases of our results and significantly enlarge the list of integrable equations that exist in the contemporary literature. To explore the above underlying results we use the recently introduced generalized extended Prelle-Singer procedure applicable to second order ODEs. As an added advantage of the method we not only identify integrable regimes but also construct integrating factors, integrals of motion and general solutions for the integrable cases, wherever possible, and bring out the mathematical structures associated with each of the integrable cases.

nlin.SI↗