arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 145 records · Page 8Linked to original sources

arXiv2013

Nonlinear Dirac equation solitary waves in external fields

We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{κ+1} ({\bPsi} Ψ)^{κ+1}$ in the presence of various external electromagnetic fields. Starting from the exact solutions for the unforced problem we study the behavior of solitary wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width and phase of these waves to vary in time. We find that in this approximation the position $q(t)$ of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time independent external fields we find that the energy of the solitary wave is conserved but not the momentum which becomes a function of time. We postulate that similar to the nonlinear Schr{ö}dinger equation (NLSE) that a sufficient dynamical condition for instability to arise is that $ dP(t)/d \dq(t) < 0$. Here $P(t)$ is the momentum of the solitary wave, and $\dq$ is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials we always have $ dP(t)/d \dq(t) > 0$ so when instabilities do occur they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations.

nlin.PS↗

arXiv2013

Particle model for skyrmions in metallic chiral magnets: dynamics, pinning and creep

Recently spin textures called skyrmions have been discovered in certain chiral magnetic materials without spatial inversion symmetry, and have attracted enormous attention due to their promising application in spintronics since only a low applied current is necessary to drive their motion. When a conduction electron moves around the skyrmion, its spin is fully polarized by the spin texture and acquires a quantized phase; thus, the skyrmion yields an emergent electrodynamics that in turn determines skyrmion motion and gives rise to a finite Hall angle. While Skyrmions behave as particles, no particle level description of their dynamics exists to date. Such a model would have tremendous impact on understanding skyrmion dynamics by theoretical analysis and computational modeling. Here we derive the equation of motion from a microscopic continuum model and obtain the short-range interaction between skyrmions, and the interaction between skyrmions and defects. Skyrmions also experience a Magnus force perpendicular to their velocity due to the underlying emergent electromagnetic field. We validate the equation of motion by studying the depinning transition using both the particle and the continuum models. By using the particle description, we explain the recent experimental observations of the rotation of a skyrmion lattice in the presence of a temperature gradient. We also predict quantum and thermal creep motion of skyrmions in the pinning potential.

cond-mat.str-el↗

arXiv2013

Manipulation of skyrmions in nanodisks with a current pulse and skyrmion rectifier

A skyrmion in a nanosized disk of a chiral magnet can be used as a bit of information. To this end, it is desirable to control the creation and removal of a skyrmion only by currents without using external magnetic fields. Here we propose to create a skyrmion by applying a current pulse to a nanodisk. The skyrmion can be removed from the disk by applying a dc current. We show that the dynamics of the created skyrmion can lead to a rectification effect, in which a dc voltage is generated by the motion of skyrmion in the presence of an ac current.

cond-mat.mes-hall↗

arXiv2013

Driven skyrmions and dynamical transitions in chiral magnets

We study the dynamics of skyrmions in chiral magnets in the presence of a spin polarized current. The motion of skyrmions in the ferromagnetic background excites spin waves and contributes to additional damping. At a large current, the spin wave spectrum becomes gapless and skyrmions are created dynamically from the ferromagnetic state. At an even higher current, these skyrmions are strongly deformed due to the damping and become unstable at a threshold current, leading to a chiral liquid. We show how skyrmions can be created by increasing the current in the magnetic spiral state. We then construct a dynamic phase diagram for a chiral magnet with a current. The instability transitions between different states can be observed as experimentally clear signatures in the transport measurements, such as jumps and hysteresis.

cond-mat.str-el↗

arXiv2013

Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is non-trivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS in fact becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.

nlin.PS↗

arXiv2013

Linear Superposition for a Large Number of Nonlinear Equations

We demonstrate a kind of linear superposition for a large number of nonlinear equations, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$, then it also admits solutions in terms of their sum as well as difference, i.e. $\dn(x,m) \pm \sqrt{m}\, \cn(x,m)$. Further, we also show that whenever a nonlinear equation admits a solution in terms of $\dn^2(x,m)$, it also has solutions in terms of $\dn^2(x,m) \pm \sqrt{m}\, \cn(x,m)\, \dn(x,m)$ even though $\cn(x,m)\, \dn(x,m)$ is not a solution of that nonlinear equation. Finally, we obtain similar superposed solutions in coupled theories.

nlin.SI↗

arXiv2012

Thermodynamics of Ferrotoroidic Materials: Toroidocaloric Effect

The three primary ferroics, namely ferromagnets, ferroelectrics and ferroelastics exhibit corresponding large (or even giant) magnetocaloric,electrocaloric and elastocaloric effects when a phase transition is induced by the application of an appropriate external field. Recently the suite of primary ferroics has been extended to include ferrotoroidic materials in which there is an ordering of toroidic moments in the form of magnetic vortex-like structures, examples being LiCo(PO_4)_3 and Ba_2CoGe_2O_7. In the present work we formulate the thermodynamics of ferrotoroidic materials. Within a Landau free energy framework we calculate the toroidocaloric effect by quantifying isothermal entropy change (or adiabatic temperature change) in the presence of an applied toroidic field when usual magnetization and polarization may also be present simultaneously. We also obtain a nonlinear Clausius-Clapeyron relation for phase coexistence.

cond-mat.mtrl-sci↗

arXiv2012

Direct observation of magnetic phase coexistence and magnetization reversal in a Gd$_{0.67}$Ca$_{0.33}$MnO$_{3}$ thin film

We have investigated the ferrimagnetic domain structure in a Gd$_{0.67}$Ca$_{0.33}$MnO$_{3}$ thin film using magnetic force microscopy. We observe clear signs of phase separation, with magnetic islands embedded in a non-magnetic matrix. We also directly visualize the reversal of magnetization of ferrimagnetic domains as a function of temperature and attribute it to a change in the balance of magnetization of anti-aligned Mn and Gd sublattices.

cond-mat.str-el↗

arXiv2011

Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Arbitrary Order

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lamé polynomials of arbitrary order. The models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled $ϕ^4$ model, and (iv) coupled $ϕ^6$ model. In all these cases we show that the coefficients of the Lamé polynomials are such that the Lamé polynomials can be reexpressed in terms of Chebyshev polynomials of the relevant Jacobi elliptic function.

math-ph↗

arXiv2011

Forced Nonlinear Schroedinger Equation with Arbitrary Nonlinearity

We consider the nonlinear Schr{ö}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{κ+1} (ψ^\star ψ)^{κ+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx + θ)} -δψ$. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where $v_k=2 k$. These new exact solutions reduce to the constant phase solutions of the unforced problem when $r \rightarrow 0.$ In particular we study the behavior of solitary wave solutions in the presence of these external forces in a variational approximation which allows the position, momentum, width and phase of these waves to vary in time. We show that the stationary solutions of the variational equations include a solution close to the exact one and we study small oscillations around all the stationary solutions. We postulate that the dynamical condition for instability is that $ dp(t)/d \dot{q} (t) < 0$, where $p(t)$ is the normalized canonical momentum $p(t) = \frac{1}{M(t)} \frac {\partial L}{\partial {\dot q}}$, and $\dot{q}(t)$ is the solitary wave velocity. Here $M(t) = \int dx ψ^\star(x,t) ψ(x,t)$. Stability is also studied using a "phase portrait" of the soliton, where its dynamics is represented by two-dimensional projections of its trajectory in the four-dimensional space of collective coordinates. The criterion for stability of a soliton is that its trajectory is a closed single curve with a positive sense of rotation around a fixed point. We investigate the accuracy of our variational approximation and these criteria using numerical simulations of the NLSE.

nlin.PS↗

arXiv2011

Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lame polynomials of order one and two. Some of the models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled saturated discrete nonlinear Schrodinger equation, (iv) coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.

nlin.PS↗

arXiv2011

On the properties of compacton-anticompacton collisions

We study the properties of compacton-anticompacton collision processes. We compare and con- trast results for the case of compacton-anticompacton solutions of the K(l, p) Rosenau-Hyman (RH) equation for l = p = 2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard- Sodano (CSS) equation for p = 1 and l = 3. This study is performed using a Padé discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton- anticompacton scattering. For the CSS equation, the scattering can be interpreted as "annihila- tion" as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision which eventually lead to "blowup" of the resulting waveform.

nlin.PS↗

arXiv2011

The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart

We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics which may be explored in coupled waveguides.

quant-ph↗

arXiv2011

Electronic properties of corrugated graphene, the Heisenberg principle and wormhole geometry in solid state

Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts and in the process the embedding of this surface into the three dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the Mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or "straintronics" is clearly an important field of study in graphene. This opens a venue to producing electronic devices, MEMS and NEMS where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks like in the curved space-time of general relativity. In this context, we explore a two-dimensional cross-section of the wormhole geometry realized with graphene as a solid state thought experiment.

cond-mat.mes-hall↗

arXiv2011

Mapping Between Generalized Nonlinear Schroedinger Equations and Neutral Scalar Field Theories and New Solutions of the Cubic-Quintic NLS Equation

We highlight an interesting mapping between the moving breather solutions of the generalized Nonlinear Schrodinger (NLS) equations and the static solutions of neutral scalar field theories. Using this connection, we then obtain several new moving breather solutions of the cubic-quintic NLS equation both with and without uniform phase in space. The stability of some stationary solutions is investigated numerically and the results confirmed via dynamical evolution.

nlin.PS↗

arXiv2010

Stability and dynamical properties of Cooper-Shepard-Sodano compactons

Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons reemerge with same coherent shape when scattered. The time evolution of the small-amplitude ripple resulting after scattering depends on the values of the parameters $l$ and $p$ characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability, than in the case of RH compactons propagation.

nlin.PS↗

arXiv2010

Staggered and short period solutions of the Saturable Discrete Nonlinear Schrödinger Equation

We point out that the nonlinear Schr{ö}dinger lattice with a saturable nonlinearity also admits staggered periodic as well as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as well as the short period solutions are stable in most cases. We also show that the effective Peierls-Nabarro barrier for the pulse-like soliton solutions is zero.

nlin.SI↗

arXiv2010

Exact Solutions of the Two-Dimensional Discrete Nonlinear Schrödinger Equation with Saturable Nonlinearity

We show that the two-dimensional, nonlinear Schrödinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.

nlin.SI↗