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A. Saxena

Publications and source records attributed to A. Saxena.

At least 127 records · Page 7Linked to original sources
arXiv2004

On Some Classes of mKdV Periodic Solutions

We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation.

nlin.PS↗
arXiv2004

Solitary Wave Interactions In Dispersive Equations Using Manton's Approach

We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schr{ö}dinger equation and kinks as well as breathers of the sine-Gordon equation.

nlin.PS↗
arXiv2004

Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

Exact solutions to a nonlinear Schr{ö}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable.

nlin.PS↗
arXiv2004

Simulations of Spinodal Nucleation in Systems with Elastic Interactions

Systems with long-range interactions quenched into a metastable state near the pseudospinodal exhibit nucleation that is qualitatively different than the classical nucleation observed near the coexistence curve. We have observed nucleation droplets in our Langevin simulations of a two-dimensional model of martensitic transformations and have determined that the structure of the nucleating droplet differs from the stable martensite structure. Our results, together with experimental measurements of the phonon dispersion curve, allow us to predict the nature of the droplet. These results have implications for nucleation in many solid-solid transitions and the structure of the final state.

cond-mat.stat-mech↗
arXiv2004

On adaptability and "intermediate phase" in randomly connected networks

We present a simple model that enables us to analytically characterize a floppy to rigid transition and an associated self-adaptive intermediate phase in a random bond network. In this intermediate phase, the network adapts itself to lower the stress due to constraints. Our simulations verify this picture. We use these insights to identify applications of these ideas in computational problems such as vertex cover and K-SAT.

cond-mat.stat-mech↗
arXiv2004

Persistent spin currents induced by a spatially-dependent magnetic field in a spin-1/2 Heisenberg antiferromagnetic ring

We show that a spatially-dependent magnetic field can induce a persistent spin current in a spin-1/2 Heisenberg antiferromagnetic ring, proportional to the solid angle subtended by the magnetic field on a unit sphere. The result is a direct consequence of Berry "parallel transport" in space. The magnitude of the spin current is determined by the ratio of longitudinal and transverse exchange interactions $J_\parallel/J_\perp$ and by the magnetic field. For large magnetic fields the Zeeman energy strongly renormalizes the Ising term giving rise to a maximum spin current. In the limit of $J_\parallel/J_\perp\ll1$ the amplitude of the current behaves like $1-(J_\parallel/J_\perp)^2$. In the opposite limit $πJ_\perp> J_\parallel>J_\perp$ the amplitude scales as $\sqrt{J_\parallel/ J_\perp}\exp{(-\sqrt{J_\parallel/J_\perp})}$.

cond-mat.mes-hall↗
arXiv2003

Adiabatic Heavy Ion Fusion Potentials for Fusion at Deep Sub-barrier Energies

The fusion cross sections from well above barrier to extreme sub-barrier energies have been analysed using the energy (E) and angular momentum (L) dependent barrier penetration model ({\small{ELDBPM}}). From this analysis, the adiabatic limits of fusion barriers have been determined for a wide range of heavy ion systems. The empirical prescription of Wilzynska and Wilzynski has been used with modified radius parameter and surface tension coefficient values consistent with the parameterization of the nuclear masses. The adiabatic fusion barriers calculated from this prescription are in good agreement with the adiabatic barriers deduced from {\small{ELDBPM}} fits to fusion data. The nuclear potential diffuseness is larger at adiabatic limit, resulting in a lower $\hbarω$ leading to increase of "logarithmic slope" observed at energies well below the barrier. The effective fusion barrier radius and curvature values are anomalously smaller than the predictions of known empirical prescriptions. A detailed comparison of the systematics of fusion barrier with and without L-dependence has been presented.

nucl-th↗
arXiv2003

Atomic scale lattice distortions and domain wall profiles

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained {\it atomic length} scale variations to {\it continuum} elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis, and find the elastic deformations and hierarchical atomic relaxations in the vicinity of a domain wall between two different homogeneous strain states. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Ginzburg-Landau theory, by showing that they are anisotropic.

cond-mat.mtrl-sci↗
arXiv2003

Breather lattice and its stabilization for the modified Korteweg-de Vries equation

We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However, such multi-breather structures can be stabilized through the concurrent application of ac driving and viscous damping terms.

nlin.PS↗
arXiv2003

Atomic scale elastic textures coupled to electrons in superconductors

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov-de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation-- the elasticity propagates the electronic response over long distances. In particular, it is possible for the trapping of low-lying quasiparticle states around the defects. These predictions could be directly tested by STM experiments in superconducting materials.

cond-mat.supr-con↗
arXiv2003

Energy minimization using Sobolev gradients: application to phase separation and ordering

A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.

physics.comp-ph↗
arXiv2003

Elasticity-driven Nanoscale Texturing in Complex Electronic Materials

Finescale probes of many complex electronic materials have revealed a non-uniform nanoworld of sign-varying textures in strain, charge and magnetization, forming meandering ribbons, stripe segments or droplets. We introduce and simulate a Ginzburg-Landau model for a structural transition, with strains coupling to charge and magnetization. Charge doping acts as a local stress that deforms surrounding unit cells without generating defects. This seemingly innocuous constraint of elastic `compatibility', in fact induces crucial anisotropic long-range forces of unit-cell discrete symmetry, that interweave opposite-sign competing strains to produce polaronic elasto-magnetic textures in the composite variables. Simulations with random local doping below the solid-solid transformation temperature reveal rich multiscale texturing from induced elastic fields: nanoscale phase separation, mesoscale intrinsic inhomogeneities, textural cross-coupling to external stress and magnetic field, and temperature-dependent percolation. We describe how this composite textured polaron concept can be valuable for doped manganites, cuprates and other complex electronic materials.

cond-mat.mtrl-sci↗
arXiv2002

Ferroelastic Dynamics and Strain Compatibility

We derive underdamped evolution equations for the order-parameter (OP) strains of a ferroelastic material undergoing a structural transition, using Lagrangian variations with Rayleigh dissipation, and a free energy as a polynomial expansion in the $N=n+N_{op}$ symmetry-adapted strains. The $N_{op}$ strain equations are structurally similar in form to the Lagrange-Rayleigh 1D strain dynamics of Bales and Gooding (BG), with `strain accelerations' proportional to a Laplacian acting on a sum of the free energy strain derivative and frictional strain force. The tensorial St. Venant's elastic compatibility constraints that forbid defects, are used to determine the n non-order-parameter strains in terms of the OP strains, generating anisotropic and long-range OP contributions to the free energy, friction and noise. The {\it same} OP equations are obtained by either varying the displacement vector components, or by varying the N strains subject to the $N_c$ compatibility constraints. A Fokker-Planck equation, based on the BG dynamics with noise terms, is set up. The BG dynamics corresponds to a set of nonidentical nonlinear (strain) oscillators labeled by wavevector $\vec{k}$, with competing short- and long-range couplings. The oscillators have different `strain-mass' densities $ρ(k) \sim 1/k^2$ and dampings $\sim 1/ρ(k) \sim k^2$, so the lighter large-k oscillators equilibrate first, corresponding to earlier formation of smaller-scale oriented textures. This produces a sequential-scale scenario for post-quench nucleation, elastic patterning, and hierarchical growth. (Continued ...)

cond-mat.mtrl-sci↗
arXiv2002

Polarized Magnetic Wire Induced by Tunneling Through a Magnetic Impurity

Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $α(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance while the other is off-resonance causing a strong asymmetry between the spin-up and spin-down conductances.

cond-mat.str-el↗
arXiv2002

Mechanism for BCC to HCP Transformation: Generalization of the Burgers Model

Many structural transformations involve a group-nonsubgroup relationship between the initial and transformed phases, and hence are beyond the purview of conventional Landau theory. We utilize a systematic and robust methodology to describe such reconstructive martensitic transformations by coupling group-theoretical arguments to first-principles calculations. In this context we (i) use a symmetry-based algorithm to enumerate transformation paths, (ii) evaluate the energy barriers along these transformation paths using all-electron first principles calculations, (iii) deduce the full set of primary and secondary order parameters for each path to establish the appropriate Ginzburg-Landau free-energy functionals, and (iv) for each path, identify special points of the primary order parameter, as a function of local distortions, corresponding to the end product phase. We apply this method to the study of a pressure driven body-centered cubic (bcc) to hexagonal close-packed (hcp) transformation in titanium. We find a generalization of the Burgers mechanism, and also find that there is no energy barrier to this transformation. In fact, surprisingly, we also find a region of volumes in which the intermediate path becomes more stable than either of the end-points (bcc or hcp). We therefore predict a new orthorhombic phase for Ti between 51 and 62 GPa.

cond-mat.mtrl-sci↗
arXiv2002

Ground state properties of ferromagnetic metal/conjugated polymer interfaces

We theoretically investigate the ground state properties of ferromagnetic metal/conjugated polymer interfaces. The work is partially motivated by recent experiments in which injection of spin polarized electrons from ferromagnetic contacts into thin films of conjugated polymers was reported. We use a one-dimensional nondegenerate Su-Schrieffer-Heeger (SSH) Hamiltonian to describe the conjugated polymer and one-dimensional tight-binding models to describe the ferromagnetic metal. We consider both a model for a conventional ferromagnetic metal, in which there are no explicit structural degrees of freedom, and a model for a half-metallic ferromagnetic colossal magnetoresistance (CMR) oxide which has explicit structural degrees of freedom. The Fermi energy of the magnetic metallic contact is adjusted to control the degree of electron transfer into the polymer. We investigate electron charge and spin transfer from the ferromagnetic metal to the organic polymer, and structural relaxation near the interface. Bipolarons are the lowest energy charge state in the bulk polymer for the nondegenerate SSH model Hamiltonian. As a result electrons (or holes) transferred into the bulk of the polymer form spinless bipolarons. However, there can be spin density in the polymer localized near the interface.

cond-mat.mtrl-sci↗
arXiv2002

A new paradigm for modulated phases in multi-stage structural transformations

For multi-stage, displacive structural transitions we present a general framework that accounts for various intermediate modulated phases, elastic constant, phonon and related thermodynamic anomalies. Based on the presence or absence of modulated phases we classify these transformations in four categories and apply this approach to four different representative materials: Ni-Mn-Ga, NiTi(Fe),Ni-Al, Cu-Zn-Al and alpha-U. We suggest that the anomalous increase in elastic constant(s) and phonon frequency observed when approaching the martensitic transition from above is a signature of the conmensurate modulated phase.

cond-mat.mtrl-sci↗