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Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 181 records · Page 10Linked to original sources
arXiv2007

Exact Static Solutions of a Generalized Discrete ϕ^4 Model Including Short-Periodic Solutions

For a five-parameter discrete $ϕ^4$ model, we derive various exact static solutions, including the staggered ones, in the form of the basic Jacobi elliptic functions $\sn$, $\cn$, and $\dn$, and also in the form of their hyperbolic function limits such as kink ($\tanh$) and single-humped pulse ($\sech$) solutions. Such solutions are admitted by the considered model in seven cases, two of which have been discussed in the literature, and the remaining five cases are addressed here. We also obtain $\sin$e, staggered $\sin$e as well as a large number of short-periodic static solutions of the generalized 5-parameter model. All the Jacobi elliptic, hyperbolic and trigonometric function solutions (including the staggered ones) are translationally invariant (TI), i.e., they can be shifted along the lattice by an arbitrary $x_0$, but among the short-periodic solutions there are both TI and non-TI solutions. The stability of these solutions is also investigated. Finally, the constructed Jacobi elliptic function solutions reveal four new types of cubic nonlinearity with the TI property.

nlin.SI↗
arXiv2007

Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schrödinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving pulse solution. We also address the problem of finding exact stationary solutions and, for a particular case of the model when stationary solutions can be expressed through the Jacobi elliptic functions, we present a two-point map from which all possible stationary solutions can be found. Numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long-term dynamics.

nlin.PS↗
arXiv2007

Effect of Intra-molecular Disorder and Inter-molecular Electronic Interactions on the Electronic Structure of Poly-p-Phenylene Vinylene (PPV)

We investigate the role of intra-molecular conformational disorder and inter-molecular electronic interactions on the electronic structure of disorder clusters of poly-p-phenylene vinylene (PPV) oligomers. Classical molecular dynamics is used to determine probable molecular geometries, and first-principle density functional theory (DFT) calculations are used to determine electronic structure. Intra-molecular and inter-molecular effects are disentangled by contrasting results for densely packed oligomer clusters with those for ensembles of isolated oligomers with the same intra-molecular geometries. We find that electron trap states are induced primarily by intra-molecular configuration disorder, while the hole trap states are generated primarily from inter-molecular electronic interactions.

cond-mat.soft↗
arXiv2007

Exact static solutions to a translationally invariant discrete $ϕ^4$ model

For a discrete, translationally-invariant $ϕ^4$ model introduced by Barashenkov {\it et al.} [Phys. Rev. E {\bf 72}, 35602R (2005)], we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a Jacobi elliptic function (JEF) solution. The first integral can be written in the form of a nonlinear map from which {\it any} static solution supported by the model can be constructed. A set of JEF solutions, including the staggered ones, is derived. We also report on the stability analysis for the static bounded solutions and exemplify the dynamical behavior of the unstable solutions. This work provides a road-map, through this illustrative example, on how to fully analyze translationally-invariant models in terms of their static problem, its first integral, their full-set of static solutions and associated conservation laws.

nlin.SI↗
arXiv2006

Domain Wall and Periodic Solutions of Coupled Asymmetric Double Well Models

Coupled asymmetric double well ($aϕ^2-bϕ^3+cϕ^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of such a coupled asymmetric model in terms of elliptic functions (domain wall arrays) and obtain single domain wall solutions in specific limits. We also calculate the energy and interaction between solitons for various solutions. Both topological (kink-like at $T=T_c$) and nontopological (pulse-like for $T\ne T_c$) domain wall solutions are obtained. We relate some of these solutions to domain walls in hydrogen bonded materials and also in the field theory context. As a byproduct, we also obtain a new one parameter family of kink solutions of the uncoupled asymmetric double well model.

nlin.PS↗
arXiv2006

Domain Wall and Periodic Solutions of a Coupled phi6 Model

Coupled triple well (phi6) one-dimensional potentials occur in both condensed matter physics and field theory. Here we provide a set of exact periodic solutions in terms of elliptic functions (domain wall arrays) and obtain single domain wall solutions in specific limits. Both topological, nontopological (e.g. some pulse-like solutions) as well as mixed domain walls are obtained. We relate these solutions to structural phase transitions in materials with polarization, shuffle modes and strain. We calculate the energy and the asymptotic interaction between solitons for various solutions. We also consider the discrete analog of these coupled models and obtain several single and periodic domain wall exact solutions.

nlin.SI↗
arXiv2006

Domain Wall and Periodic Solutions of Coupled phi4 Models in an External Field

Coupled double well (phi4) one-dimensional potentials abound in both condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of a coupled $ϕ^4$ model in an external field in terms of elliptic functions (domain wall arrays) and obtain single domain wall solutions in specific limits. We also calculate the energy and interaction between solitons for various solutions. Both topological and nontopological (e.g. some pulse-like solutions in the presence of a conjugate field) domain walls are obtained. We relate some of these solutions to the recently observed magnetic domain walls in certain multiferroic materials and also in the field theory context wherever possible. Discrete analogs of these coupled models, relevant for structural transitions on a lattice, are also considered.

nlin.SI↗
arXiv2006

Comparative Study of Different Discretizations of the $ϕ^4$ Model

We examine various recently proposed discretizations of the well-known $ϕ^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral properties of the linearization around such waves. We study these features as a function of the lattice spacing $h$, as one deviates from the continuum limit of $h \to 0$. We then proceed to a more ``stringent'' comparison of the models, by discussing the scattering properties of a kink-antikink pair for the different discretizations. These collisions are well-known to possess properties that quite sensitively depend on the initial speed even at the continuum limit. We examine how typical model behaviors are modified in the presence (and as a function) of discreteness and attempt to extract qualitative trends and issue pertinent warnings about some of the surprising resulting properties.

nlin.PS↗
arXiv2006

Statistical Mechanics of Lamé Solitons

We study the exact statistical mechanics of Lamé solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schrödinger equation with the periodic Lamé potential. Since the latter is a quasi-exactly solvable system, an analytical evaluation of the partition function can be done only for a few temperatures. We also study approximately the finite temperature thermodynamics using the ideal kink gas phenomenology. The zero-temperature "thermodynamics" of the soliton lattice solutions is also addressed. Moreover, in appropriate limits our results reduce to that of the sine-Gordon problem.

cond-mat.stat-mech↗
arXiv2006

Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities

A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers and moving solutions, are investigated.

nlin.PS↗
arXiv2005

Spectral correlations of individual quantum graphs

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $σ$--model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner--Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

nlin.CD↗
arXiv2005

Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: lithium niobate and lithium tantalate

A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial, trigonal ferroelectrics lithium niobate and lithium tantalate. The contributions to the domain wall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed which are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y-walls are preferred over x-walls in both materials. This agrees well with experimental observation of domain geometries in stoichiometric composition crystals.

cond-mat.mtrl-sci↗
arXiv2005

Exact solitary wave solutions for a discrete $λϕ^4$ field theory in 1+1 dimensions

We have found exact, periodic, time-dependent solitary wave solutions of a discrete $ϕ^4$ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi elliptic functions $\sn(x,m)$ (which reduce to the kink function $\tanh(x)$ for $m\to 1$), or they are $\dn(x,m)$ and $\cn(x,m)$ (which reduce to the pulse function $\sech(x)$ for $m\to 1$). We have studied the stability of these solutions numerically, and we find that our solutions are linearly stable in most cases. We show that this model is a Hamiltonian system, and that the effective Peierls-Nabarro barrier due to discreteness is zero not only for the two localized modes but even for all three periodic solutions. We also present results of numerical simulations of scattering of kink--anti-kink and pulse--anti-pulse solitary wave solutions.

nlin.SI↗
arXiv2005

Semiclassical kinetic theory of electron spin relaxation in semiconductors

We develop a semiclassical kinetic theory for electron spin relaxation in semiconductors. Our approach accounts for elastic as well as inelastic scattering and treats Elliott-Yafet and motional-narrowing processes, such as D'yakonov-Perel' and variable g-factor processes, on an equal footing. Focusing on small spin polarizations and small momentum transfer scattering, we derive, starting from the full quantum kinetic equations, a Fokker-Planck equation for the electron spin polarization. We then construct, using a rigorous multiple time scale approach, a Bloch equation for the macroscopic ($\vec{k}$-averaged) spin polarization on the long time scale, where the spin polarization decays. Spin-conserving energy relaxation and diffusion, which occur on a fast time scale, after the initial spin polarization has been injected, are incorporated and shown to give rise to a weight function which defines the energy averages required for the calculation of the spin relaxation tensor in the Bloch equation. Our approach provides an intuitive way to conceptualize the dynamics of the spin polarization in terms of a ``test'' spin polarization which scatters off ``field'' particles (electrons, impurities, phonons). To illustrate our approach, we calculate for a quantum well the spin lifetime at temperatures and densities where electron-electron and electron-impurity scattering dominate. The spin lifetimes are non-monotonic functions of temperature and density. Our results show that at electron densities and temperatures, where the cross-over from the non-degenerate to the degenerate regime occurs, spin lifetimes are particularly long.

cond-mat.mtrl-sci↗
arXiv2004

Domain Size Dependence of Piezoelectric Properties of Ferroelectrics

The domain size dependence of piezoelectric properties of ferroelectrics is investigated using a continuum Ginzburg-Landau model that incorporates the long-range elastic and electrostatic interactions. Microstructures with desired domain sizes are created by quenching from the paraelectric phase by biasing the initial conditions. Three different two-dimensional microstructures with different sizes of the $90^{o}$ domains are simulated. An electric field is applied along the polar as well as non-polar directions and the piezoelectric response is simulated as a function of domain size for both cases. The simulations show that the piezoelectric coefficients are enhanced by reducing the domain size, consistent with recent experimental results of Wada and Tsurumi (Brit. Ceram. Trans. {\bf 103}, 93, 2004) on domain engineered $BaTiO_{3} $

cond-mat.mtrl-sci↗
arXiv2004

Spatial Structures in a Generalized Ginzburg-Landau Free Energy

Searching for characteristic signatures of a higher order phase transition (specifically of order three or four), we have calculated the spatial profiles and the energies of a spatially varying order parameter in one dimension. In the case of a $p^{th}$ order phase transition to a superconducting ground state, the free energy density depends on temperature as $a^p$, where $a = a_o(1-T/T_c)$ is the reduced temperature. The energy of a domain wall between two degenerate ground states is $ε_p \simeq a^{p-1/2}$. We have also investigated the effects of a supercurrent in a narrow wire. These effects are limited by a critical current which has a temperature dependence $J_c(T) \simeq a^{(2p-1)/2}$. The phase slip center profiles and their energies are also calculated. Given the suggestion that the superconducting transtion in \bkbox, for $x = 0.4$, may be of order four, these predictions have relevance for future experiments.

cond-mat.stat-mech↗
arXiv2004

Soliton Lattice and Single Soliton Solutions of the Associated Lamé and Lamé Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lamé equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lamé equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lamé equation, and also the sine-Gordon soliton solution.

nlin.PS↗