arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 127 records · Page 7Linked to original sources

arXiv2015

Non-circular skyrmion and its anisotropic response in thin films of chiral magnets under tilted magnetic field

We study the equilibrium and dynamical properties of skyrmions in thin films of chiral magnets with oblique magnetic field. The shape of an individual skyrmion is non-circular and the skyrmion density decreases with the tilt angle from the normal of films. As a result, the interaction between two skyrmions depends on the relative angle between them in addition to their separation. The triangular lattice of skyrmions under a perpendicular magnetic field is distorted into a centered rectangular lattice for a tilted magnetic field. For a low skyrmion density, skyrmions form a chain like structure. The dynamical response of the non-circular skyrmions depends on the direction of external currents.

cond-mat.mtrl-sci↗

arXiv2015

Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy

We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy $A$. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic field evolves continuously as a function of increasing $A$ into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value $Q=1$ and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" $Q_A \ll 1$ that grows as a function of increasing $A$. The system undergoes a first order phase transition into a square vortex-antivortex lattice at a critical value of $A$. Finally, a canted ferromagnetic state becomes stable through another first order transition for a large enough anisotropy $A$. Interestingly enough, this first order transition is accompanied by {\it metastable} meron solutions.

cond-mat.mtrl-sci↗

arXiv2015

Recent Progress in the thermodynamics of ferrotoroidic materials

Recent theoretical and experimental progress on the study of ferrotoroidic materials is reviewed. The basic field equations are first described and then the expressions for magnetic toroidal moment and toroidization are derived. Relevant materials and experimental observation of magnetic toroidal moment and toroidal domains are summarized next. The thermodynamics of such magnetic materials is discussed in detail with examples of ferrorotoidic phase transition studied using Landau modelling. Specifically, an example of application of Landau modelling to the study of toroidocaloric effect is also provided. Recent results of polar nanostructures with electrical toroidal moment are finally reviewed.

cond-mat.mtrl-sci↗

arXiv2015

Jarzynski equality in $\mathcal{PT}$-symmetric quantum mechanics

We show that the quantum Jarzynski equality generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$-symmetry. In the regime of broken $\mathcal{PT}$-symmetry the Jarzynski equality does not hold as also the $\mathcal{CPT}$-norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system -- two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken $\mathcal{PT}$-symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

cond-mat.stat-mech↗

arXiv2015

Nonlinear Dirac equation solitary waves in the presence of external driving forces

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $ f(x,t) - i μγ^0 Ψ$, where both $f$ and $Ψ$ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. This approach predicts intrinsic oscillations of the solitary waves, i.e. the amplitude, width and phase all oscillate with the same frequency. The translational motion is also affected, because the soliton position oscillates around a mean trajectory. We then compare the results of the variational approximation with numerical simulations of the NLD equation, and find a good agreement, if we take into account a certain linear excitation with specific wavenumber that is excited together with the intrinsic oscillations such that the momentum in a transformed NLD equation is conserved. We also solve explicitly the CC equations of the variational approximation in the non-relativistic regime for a homogeneous external force and obtain excellent agreement with the numerical solution of the CC equations.

nlin.PS↗

arXiv2014

Quasi-One-Dimensional Thermal Breakage

Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced breakage at the nano-scale for one-dimensional systems. We test it on a simple approximation and find that the probability of breakage controls distinct regimes, characterized by sharp crossovers and narrow peaks in the thermal fluctuations and specific heat. Our work provides predictions on clustering of new phases, of relevance in nano-fabrication.

cond-mat.stat-mech↗

arXiv2014

PT-symmetry breaking with divergent potentials: lattice and continuum cases

We investigate the parity- and time-reversal ($\mathcal{PT}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\mathcal{PT}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_α(x)\propto i |x|^α\mathrm{sign}(x)$ have a positive $\mathcal{PT}$-breaking threshold for $α>-2$, and a zero threshold for $α\leq -2$. When $α<0$ localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of $\mathcal{PT}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the $\mathcal{PT}$-symmetry broken region.

quant-ph↗

arXiv2014

Successive phase transitions and kink solutions in $ϕ^{8}$, $ϕ^{10}$, and $ϕ^{12}$ field theories

We obtain exact solutions for kinks in $ϕ^{8}$, $ϕ^{10}$ and $ϕ^{12}$ field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order $ϕ^4$ and $ϕ^6$ theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a $ϕ^{12}$ potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the $ϕ^{10}$ field theory, which is a quasi-exactly solvable (QES) model akin to $ϕ^6$, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

math-ph↗

arXiv2014

Bent waveguides for matter-waves: supersymmetric potentials and reflectionless geometries

Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found whose geometry-induced potentials share the same scattering properties. As a result, reflectionless waveguides, dual to the straight waveguide, are identified. Strictly isospectral waveguides are also found by modulating the depth of the trapping potential. Numerical simulations are used to demonstrate the efficiency of these approaches in tailoring and controlling curvature-induced quantum-mechanical effects.

quant-ph↗

arXiv2014

Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity

We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction $ \frac{g^2}{κ+1} ({\bar Ψ} Ψ)^{κ+1}$ and with mass $m$. Using the exact analytic form for rest frame solitary waves of the form $Ψ(x,t) = ψ(x) e^{-i ωt}$ for arbitrary $ κ$, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem, the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed 4th-order operator splitting integration method. For different ranges of $κ$ we map out the stability regimes in $ω$. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time $t_c$, it takes for the instability to set in, is an exponentially increasing function of $ω$ and $t_c$ decreases monotonically with increasing $κ$.

nlin.PS↗

arXiv2014

Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations

For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrödinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL and coupled nonlocal, saturable DNLSE, we obtain periodic solutions in terms of Jacobi elliptic functions as well as the corresponding hyperbolic soliton solutions. Remarkably, in all the six cases, we find that unlike the corresponding local cases, all the nonlocal models simultaneously admit both the bright and the dark soliton solutions. Further, in all the six cases, not only $\dn(x,m)$ and $\cn(x,m)$ but even their linear superposition is shown to be an exact solution. Finally, we show that the coupled nonlocal NLSE not only admits solutions in terms of Lamé polynomials of order 1, but it also admits solutions in terms of Lamé polynomials of order 2, even though they are not the solutions of the uncoupled nonlocal problem. We also remark on the possible integrability in certain cases.

nlin.PS↗

arXiv2014

AC current generation in chiral magnetic insulators and skyrmion motion induced by the spin Seebeck effect

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of skyrmion motion on the ac current generation and demonstrate that skyrmions in insulators are a promising route for spin caloritronics applications.

cond-mat.mtrl-sci↗

arXiv2014

Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$ with modulus $m$, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, $λϕ^4$, the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of $\dn^2(x,m)$, it also admits 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 these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.

math-ph↗

arXiv2014

Intrinsic Localized Modes of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain

We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of Jacobian elliptic functions. These include one, two and three spin excitations. All these solutions have smooth anticontinuum limits. Their linear stability and semiclassical quantization are also discussed briefly.

nlin.PS↗

arXiv2014

Internal modes of a skyrmion in the ferromagnetic background in chiral magnets

A spin texture called skyrmion has been recently observed in certain chiral magnets without inversion symmetry. The observed skyrmions are extended objects with typical linear sizes of 10 nm to 100 nm that contain $10^3$ to $10^5$ spins and can be deformed in response to external perturbations. Weak deformations are characterized by the internal modes which are localized around the skyrmion center. Knowledge of internal modes is crucial to assess the stability and rigidity of these topological textures. Here we compute the internal modes of a skyrmion in the ferromagnetic background state by numerical diagonalization of the dynamical matrix. We find several internal modes below the magnon continuum, such as the mode corresponding to the translational motion, and different kinds of breathing modes. The number of internal modes is larger for lower magnetic fields. Indeed, several modes become gapless in the low field region indicating that the single skyrmion solution becomes unstable, although a skyrmion lattice is thermodynamically stable. On the other hand, at high fields only three internal modes exist and the skyrmion is stable even at higher fields when the ferromagnetic state is thermodynamically stable. We also show that the presence of out-of-plane easy-axis anisotropy stabilizes the single skyrmion solution. Finally, we discuss the effects of damping and possible experimental observations of these internal modes.

cond-mat.str-el↗

arXiv2014

Dynamics of skyrmions in chiral magnets: dynamic phase transitions and equation of motion

We study the dynamics of skyrmions in a metallic chiral magnet. First we show that skyrmions can be created dynamically by destabilizing the ferromagnetic background state through a spin polarized current. We then treat skyrmions as rigid particles and derive the corresponding equation of motion. The dynamics of skyrmions is dominated by the Magnus force, which accounts for the weak pinning of skyrmions observed in experiments. Finally we discuss the quantum motion of skyrmions.

cond-mat.mtrl-sci↗

arXiv2013

Higher Order Spin Noise Statistics

The optical spin noise spectroscopy (SNS) is a minimally invasive route towards obtaining dynamical information about electrons and atomic gases by measuring mesoscopic time-dependent spin fluctuations. Recent improvements of the sensitivity of SNS should make it possible to observe higher order spin correlators at thermodynamic equilibrium. We develop theoretical methods to explore higher order (3rd and 4th) cumulants of the spin noise in the frequency domain. We make predictions for the possible functional form of these correlators in single quantum dot experiments and then apply the method of the stochastic path integral to estimate effects of many-body interactions.

cond-mat.mes-hall↗

arXiv2013

Spin noise spectroscopy of quantum dot molecules

We discuss advantages and limitations of the spin noise spectroscopy for characterization of interacting quantum dot systems on specific examples of individual singly and doubly charged quantum dot molecules (QDMs). It is shown that all the relevant parameters of the QDMs including tunneling amplitudes with spin-conserving and spin-non-conserving interactions, decoherence rates, Coulomb repulsions, anisotropic g-factors and the distance between the dots can be determined by measuring properties of the spin noise power spectrum.

cond-mat.mes-hall↗