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Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 91 records · Page 5Linked to original sources
arXiv2019

Kelvin modes of a skyrmion line in chiral magnets and the associated magnon transport

Magnetic skyrmions in bulk crystals are line-like topologically protected spin textures. They allow for the propagation of magnons along the skyrmion line but are localized inside the skyrmion line. Analogous to the vortex line, these propagating modes are the Kelvin modes of a skyrmion line. In crystals without an inversion center, it is known that the magnon dispersion in the ferromagnetic state is asymmetric in the wavevector. It is natural to expect that the dispersion of the Kelvin modes is also asymmetric with respect to the wavevector. We study the Kelvin modes of a skyrmion line in the ferromagnetic background. In contrast, we find that the lowest Kelvin mode is symmetric in the wavevector in the low energy region despite the inversion symmetry breaking. Other Kelvin modes below the magnon continuum are asymmetric, and most of them have a positive group velocity. Our results suggest that a skyrmion line can function as a one-way waveguide for magnons.

cond-mat.mtrl-sci↗
arXiv2019

Kink-kink and kink-antikink interactions with long-range tails

In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $φ^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of $n=2$ ($φ^8$ model), $n=3$ ($φ^{10}$ model) and $n=4$ ($φ^{12}$ model).

hep-th↗
arXiv2018

Noise-Assisted Quantum Exciton and Electron Transfer in Bio-Complexes with Finite Donor and Acceptor Bandwidths

We present an analytic and numerical study of noise-assisted quantum exciton (electron) transfer (ET) in a bio-complex, consisting of an electron donor and acceptor (a dimer), modeled by interacting continuous electron bands of finite widths. The interaction with the protein-solvent environment is modeled by a stationary stochastic process (noise) acting on all the donor and acceptor energy levels. We start with discrete energy levels for both bands. Then, by using a continuous {limit} for the electron spectra, we derive integro-differential equations for ET dynamics between two bands. Finally, we derive from these equations rate-type differential equations for ET dynamics. We formulate the conditions of validity of the rate-type equations. We consider different regions of parameters characterizing the widths of the donor and acceptor bands and the strength of the dimer-noise interaction. For a simplified model with a single energy level donor and a continuous acceptor band, we derive a generalized analytic expression and provide numerical simulations for the ET rate. They are consistent with Wigner-Weisskopf, Förster-type, and Marcus-type expressions, in their corresponding regime of parameters.Our analytic results are confirmed by numerical simulations. We demonstrate how our theoretical results are modified {when both the donor and the acceptor are described by finite bands}. We also show that, for a relatively wide acceptor band, the efficiency of the ET from donor to acceptor can be close to 100% for a broad range of noise amplitudes, for both "downhill" and "uphill" ET, for sharp and flat redox potentials, and for reasonably short times. We discuss possible experimental implementations of our approach with application to bio-complexes.

physics.bio-ph↗
arXiv2018

Higher-order field theories: $ϕ^6$, $ϕ^8$ and beyond

The $ϕ^4$ model has been the "workhorse" of the classical Ginzburg--Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical developments in nonlinear science. However, the $ϕ^4$ model, in its usual variant (symmetric double-well potential), can only possess two equilibria. Many complex physical systems possess more than two equilibria and, furthermore, the number of equilibria can change as a system parameter (e.g., the temperature in condensed matter physics) is varied. Thus, "higher-order field theories" come into play. This chapter discusses recent developments of higher-order field theories, specifically the $ϕ^6$, $ϕ^8$ models and beyond. We first establish their context in the Ginzburg--Landau theory of successive phase transitions, including a detailed discussion of the symmetric triple well $ϕ^6$ potential and its properties. We also note connections between field theories in high-energy physics (e.g., "bag models" of quarks within hadrons) and parametric (deformed) $ϕ^6$ models. We briefly mention a few salient points about even-higher-order field theories of the $ϕ^8$, $ϕ^{10}$, etc.\ varieties, including the existence of kinks with power-law tail asymptotics that give rise to long-range interactions. Finally, we conclude with a set of open problems in the context of higher-order scalar fields theories.

hep-th↗
arXiv2018

Magnetization induced shape transformations in flexible ferromagnetic rings

Flexible ferromagnetic rings are spin-chain magnets, in which the magnetic and mechanical subsystems are coupled. The coupling is achieved through the tangentially oriented anisotropy axis. The possibility to operate the mechanics of the nanomagnets by controlling their magnetization is an important issue for the nanorobotics applications. A minimal model for the deformable curved anisotropic Heisenberg ferromagnetic wire is proposed. An equilibrium phase diagram is constructed for the closed loop geometry: (i) A vortex state with vanishing total magnetic moment is typical for relatively large systems; in this case the wire has the form of a regular circle. (ii) A topologically trivial onion state with the planar magnetization distribution is realized in small enough systems; magnetic loop is elliptically deformed. By varying geometrical and elastic parameters a phase transition between the vortex and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by numerical simulations.

cond-mat.mes-hall↗
arXiv2018

Engineered Chiral Skyrmion and Skyrmionium States by the Gradient of Curvature

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose a new mechanism to stabilize chiral Néel skyrmion states relying on the \textit{gradient} of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers $\pm 1$ and a skyrmionium state with a winding number $0$. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii--Moriya interaction. The latter emerges due to the gradient of the local curvature at a bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables one to reduce a magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii--Moriya interaction.

cond-mat.mes-hall↗
arXiv2018

Localization of magnon modes in a curved magnetic nanowire

Spin waves in magnetic nanowires can be bound by a local bending of the wire. The eigenfrequency of a truly local magnon mode is determined by the curvature: a general analytical expression is established for any infinitesimally weak localized curvature of the wire. The interaction of the local mode with spin waves, propagating through the bend, results in scattering features, which is well confirmed by spin-lattice simulations.

cond-mat.mes-hall↗
arXiv2018

Exact Intrinsic Localized Excitation of an Anisotropic Ferromagnetic Spin Chain in External Magnetic Field with Gilbert Damping, Spin Current and PT-Symmetry

We obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT-symmetric magnetic nanostructure. We also briefly consider more general spin excitations.

cond-mat.mes-hall↗
arXiv2018

Tunneling Current Measurement Scheme to Detect Majorana Zero Mode Induced Crossed Andreev Reflection

We propose a scheme to detect the Majorana-zero-mode-induced crossed Andreev reflection by measuring tunneling current directly. In this scheme a metallic ring structure is utilized to separate electron and hole signals. Since tunneling electrons and holes have different propagating wave vectors, the conditions for them to be constructively coherent in the ring differ. We find that when the magnetic flux threading the ring varies, it is possible to observe adjacent positive and negative current peaks of almost equal amplitudes.

cond-mat.mes-hall↗
arXiv2018

Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

Quantum walks often provide telling insights about the structure of the system on which they are performed. In PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today's experimental systems.

quant-ph↗
arXiv2017

Comparing skyrmions and merons in chiral liquid crystals and magnets

When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have 180° double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have 90° double twist going outward from the center; packing such merons requires singularities in the orientational order. In the liquid crystal context, a lattice of merons is regarded as a blue phase. Here, we perform theoretical and computational studies of skyrmions and merons in chiral liquid crystals and magnets. Through these studies, we calculate the phase diagrams for liquid crystals and magnets in terms of dimensionless ratios of energetic parameters. We also predict the range of metastability for liquid crystal skyrmions, and show that these skyrmions can move and interact as effective particles. The results show how the properties of skyrmions and merons depend on the vector or tensor nature of the order parameter.

cond-mat.soft↗
arXiv2017

Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry

We discuss the effect of small perturbation on nodeless solutions of the nonlinear \Schrodinger\ equation in 1+1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier [Phys.~Rev.~E 92, 042901 (2015)]. In particular we consider the nonlinear partial differential equation $\{ \, \rmi \, \partial_t + \partial_x^2 + g |ψ(x,t)|^2 - V^{+}(x) \, \} \, ψ(x,t) = 0$, where $V^{+}(x) = \qty( -b^2 - m^2 + 1/4 ) \, \sech^2(x) - 2 i \, m \, b \, \sech(x) \, \tanh(x)$ represents the complex potential. Here we study the perturbations as a function of $b$ and $m$ using a variational approximation based on a dissipation functional formalism. We compare the result of this variational approach with direct numerical simulation of the equations. We find that the variational approximation works quite well at small and moderate values of the parameter $b m$ which controls the strength of the imaginary part of the potential. We also show that the dissipation functional formalism is equivalent to the generalized traveling wave method for this type of dissipation.

nlin.PS↗
arXiv2017

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential

We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\barΨ Ψ)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find that, for all three cases, after a short transit time, the initial pulse breaks into two pulses which are solutions of the massless linear Dirac equation traveling in opposite directions with the speed of light. During this splitting the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation.

nlin.PS↗
arXiv2017

Stability of new exact solutions of the nonlinear Schrodinger equation in a Poschl-Teller external potential

We discuss the stability properties of the solutions of the general nonlinear \Schrodinger\ equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time ($\PT$) symmetric superpotential $W(x)$ that we considered earlier \cite{PhysRevE.92.042901}. In particular we consider the nonlinear partial differential equation $ \{ i \, \partial_t + \partial_x^2 - V(x) + g | ψ(x,t) |^{2κ} \} \, ψ(x,t) = 0 \>, $ for arbitrary nonlinearity parameter $κ$, where $g= \pm1$ and $V$ is the well known P{ö}schl-Teller potential which we allow to be repulsive as well as attractive. Using energy landscape methods, linear stability analysis as well as a time dependent variational approximation, we derive consistent analytic results for the domains of instability of these new exact solutions as a function of the strength of the external potential and $κ$. For the repulsive potential (and $g=+1$) we show that there is a translational instability which can be understood in terms of the energy landscape as a function of a stretching parameter and a translation parameter being a saddle near the exact solution. In this case, numerical simulations show that if we start with the exact solution, the initial wave function breaks into two pieces traveling in opposite directions. If we explore the slightly perturbed solution situations, a 1\% change in initial conditions can change significantly the details of how the wave function breaks into two separate pieces. For the attractive potential (and $g=+1$), changing the initial conditions by 1 \% modifies the domain of stability only slightly. For the case of the attractive potential and negative $g$ perturbed solutions merely oscillate with the oscillation frequencies predicted by the variational approximation.

nlin.PS↗
arXiv2017

Fluctuations and Noise Signatures of Driven Magnetic Skyrmions

Magnetic skyrmions are particle-like objects with topologically-protected stability which can be set into motion with an applied current. Using a particle-based model we simulate current-driven magnetic skyrmions interacting with random quenched disorder and examine the skyrmion velocity fluctuations parallel and perpendicular to the direction of motion as a function of increasing drive. We show that the Magnus force contribution to skyrmion dynamics combined with the random pinning produces an isotropic effective shaking temperature. As a result, the skyrmions form a moving crystal at large drives instead of the moving smectic state observed in systems with a negligible Magnus force where the effective shaking temperature is anisotropic. We demonstrate that spectral analysis of the velocity noise fluctuations can be used to identify dynamical phase transitions and to extract information about the different dynamic phases, and show how the velocity noise fluctuations are correlated with changes in the skyrmion Hall angle, transport features, and skyrmion lattice structure.

cond-mat.str-el↗
arXiv2017

Nearly-optimal quantum control: analytical approach

We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for optimization. This optimization strategy can be preferred in practice because it is physically transparent and does not lead to combinatorial complexity in multistate problems. For demonstration, we design optimized control protocols that achieve switching between orthogonal states of a naturally biased quantum two-level system.

quant-ph↗
arXiv2016

Peakompactons: Peaked compact nonlinear waves

This article is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of non-standard solitary waves termed \emph{peakompactons}. These peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg--de Vries-type models. Peakompactons, like the now-well-know compactons and unlike the soliton solutions of the Korteweg--de Vries equation, have finite support, {\it i.e.}, they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, {\it i.e.}, a higher spatial derivative suffers a jump discontinuity at the wave's crest. Here, we construct such solutions exactly by reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. A simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called $K^\#(n,m)$ hierarchy of nonlinearly dispersive Korteweg--de Vries-type models are discussed as well.

nlin.PS↗