arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 55 records · Page 3Linked to original sources

arXiv2023

Exact Hopfion Vortices in a 3D Heisenberg Ferromagnet

We find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers $n$ and $m$. It is a (modified) skyrmion in the $z=0$ plane with winding number $n$, which twists out of the plane $m$ times in the $z$-direction to become a 3D soliton. Here $m$ arises due to the periodic boundary condition at the $z$-boundaries. We use Whitehead's integral expression to find that the Hopf invariant of the soliton is an integer $H =nm$. It represents a hopfion vortex. Plots of the preimages of this topological soliton show that they are either unknots or nontrivial knots, depending on $n$ and $m$. Any pair of preimage curves links $H$ times, corroborating the interpretation of $H$ as a linking number. We also calculate the exact energy of the hopfion vortex, and show that its topological lower bound has a sublinear dependence on $H$. Using Derrick's scaling analysis, we demonstrate that the presence of a spatial inhomogeneity in the anisotropic interaction, which in turn introduces a characteristic length scale in the system, leads to the stability of the hopfion vortex.

nlin.SI↗

arXiv2023

Uniform Bose-Einstein Condensates as Kovaton solutions of the Gross-Pitaevskii Equation through a Reverse-Engineered Potential

In this work, we consider a ``reverse-engineering'' approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schrödinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to $\pm g ψ^{\ast}ψ$ gets added to the confining potential and $\pm g M$, where $M$ is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of $M$ (related to the number of particles in the BEC). Comparing the stability criteria from Derrick's theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass $M$ for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry $x\rightarrow-x$ assumed by Derrick's theorem.

nlin.PS↗

arXiv2023

Stability of time-periodic $\mathcal{PT}$ and anti-$\mathcal{PT}$-symmetric Hamiltonians with different periodicities

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time-periodicity offers avenues to engineer the landscape of Floquet quasi-energies across the complex plane. We investigate two-level non-Hermitian Hamiltonians with coefficients that have different periodicities using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasi-energies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany the cyclic changes. Our results demonstrate that time-periodic, non-Hermitian Hamiltonians generate a rich landscape of stable and unstable regions.

quant-ph↗

arXiv2022

Nonlocal Superposed Solutions II: Coupled Nonlinear Equations

We obtain novel periodic as well as hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schrödinger equation (NLS) as well as a coupled nonlocal modified Korteweg-de Vries (mKdV) equation which can be re-expressed as a linear superposition of the sum or the difference of two hyperbolic or two periodic kink or pulse solutions. Besides, we also discuss some of the other solutions admitted by these coupled equations. These results demonstrate that the notion of the superposed solutions extends to the coupled nonlocal nonlinear equations as well.

nlin.PS↗

arXiv2022

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

quant-ph↗

arXiv2022

Kink Solutions With Power Law Tails

We present a comprehensive review about the various facets of kink solutions with a power law tail which have received considerable attention during the last few years. This area of research is in its early stages and while several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off while the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off. We note that in all the polynomial models while the potential $V(ϕ)$ is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink-kink and the kink-antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink-antikink collisions at finite velocity and present some open questions.

nlin.PS↗

arXiv2022

Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations

We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schröd-inger (NLS) equation, nonlocal modified Korteweg de Vries (mKdV) equation as well as the nonlocal Hirota equation admit novel kinklike and pulselike superposed periodic solutions. Further, we show that the nonlocal mKdV equation, in addition also admits the superposed (hyperbolic) kink-antikink solution. Besides, we show that while the nonlocal Ablowitz-Musslimani variant of the NLS admits complex (parity-time reversal or) PT-invariant kink and pulse solutions, neither the local NLS nor the Yang variant of the nonlocal NLS admits such solutions. Finally, except for the Yang variant of the nonlocal NLS, we show that the other three nonlocal equations admit both the kink and pulse solutions in the same model.

nlin.PS↗

arXiv2022

Stability of exact solutions of the $(2+1)$-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter $κ$

In this work, we consider the nonlinear Schrödinger equation (NLSE) in $2+1$ dimensions with arbitrary nonlinearity exponent $κ$ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability over their "mass" (i.e., the $L^2$ norm) and the parameter $κ$ is explored. We observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all $κ$ as long as their mass is less than a critical value $M^{\ast}(κ)$. Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve $M^{\ast}(κ)$ vs. $κ$ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, $κ=1$ demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for $κ<1$, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the "frustrated" blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension $d$.

nlin.PS↗

arXiv2022

Superposed Hyperbolic Kink and Pulse Solutions of Coupled $ϕ^4$, NLS and MKdV Equations

We obtain novel solutions of a coupled $ϕ^4$, a coupled nonlinear Schrödinger (NLS) and a coupled modified Korteweg de Vries (MKdV) model which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic kink or two hyperbolic pulse solutions. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.

nlin.PS↗

arXiv2022

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

We show that a number of nonlinear equations including symmetric as well as asymmetric $ϕ^4$, modified Korteweg de Vries (MKdV), mixed KdV-MKdV, nonlinear Schrödinger (NLS), quadratic-cubic NLS as well as higher order neutral scalar field theories, higher order KdV-MKdV and higher order quadratic-cubic NLS admit superposed periodic kink and pulse solutions and some of them also admit superposed hyperbolic kink solutions.

nlin.PS↗

arXiv2021

Spin-transfer torque driven intrinsic localized spin excitations in the presence of field-like torque

We study the existence of intrinsic localized one-spin excitation in the Heisenberg one-dimensional ferromagnetic spin chain in the presence of perpendicular and parallel external magnetic fields and current with spin-transfer torque and field-like torque. The Landau-Lifshitz-Gilbert-Slonczewski(LLGS) equation is exactly solved for the one spin excitation in the absence of onsite anisotropy for the excitations of spin with fields perpendicular and parallel to the chain. We show the removal of damping in the spin excitations by appropriately introducing current and also the enhancement of angular frequency of the oscillations due to field-like torque in the case of both perpendicular and parallel field. The exactness of the analytical results is verified by matching with numerical counterparts. Further, we numerically confirm the existence of in-phase and anti-phase stable synchronized oscillations for two spin-excitations in the presence of current with perpendicular field and field-like torque.

cond-mat.mes-hall↗

arXiv2021

Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators

The recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and theoretical investigations in two-dimensional transition metal dichalcogenides and Weyl semimetals. The origin of this type of second order effect has been attributed to the emergence of a Berry curvature dipole, which requires a low-symmetry environment. Here, we propose a mechanism for generating such a second order nonlinear Hall effect in Kane-Mele two-dimensional topological insulators due to spatial and time reversal symmetry breaking in the presence of Zeeman and Rashba couplings. By actively tuning the energy gaps with external electromagnetic fields we also demonstrate that the nonlinear Hall effect shows remarkable signatures of topological phase transitions existing in the considered two-dimensional systems.

cond-mat.mes-hall↗

arXiv2021

Spin-transfer torque driven localized spin excitations in the presence of field-like torque

We study the existence of localized one-spin excitation in the Heisenberg one-dimensional ferromagnetic spin chain in the presence of perpendicular and parallel external magnetic fields and current with spin-transfer torque and field-like torque. The Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation is exactly solved for the one spin excitation in the absence of onsite anisotropy for the excitations of spin with fields perpendicular and parallel to the chain. We show the removal of damping in the spin excitations by appropriately introducing current and also the enhancement of angular frequency of the oscillations due to field-like torque in the case of both perpendicular and parallel field. The exactness of the analytical results is verified by matching with numerical counterparts. Further, we numerically confirm the existence of in-phase and anti-phase stable synchronized oscillations for two spin-excitations in the presence of current with perpendicular field and field-like torque. We also show that the one-spin excitation is stable against thermal noise and gets only slightly modified against thermal fluctuations.

cond-mat.stat-mech↗

arXiv2021

Novel Deformation Function Creating or Destroying any Number of Even Kink Solutions

We present a one-parameter family of deformation functions $f(ϕ)$ which have novel properties. Firstly, the deformation function is its own inverse. We show that a class of potentials remains invariant under this deformation. Further, when applied to a certain class of kink bearing potentials, one obtains potentials which are not bounded from below. Besides, we show that there is a wide class of potentials having power law kink tails which are connected by this deformation but the corresponding kink tails of the two potentials have different asymptotic behavior. Finally, we show that when this deformation function is applied to an appropriate one-parameter family of potentials having two kink solutions, it creates new potentials with an arbitrary even number ($2n$) of kink solutions. Conversely, by starting from this potential with $2n$ kink solutions the deformation function annihilates $2n-2$ kinks and we get back the potential which we started with having only two kink solutions.

nlin.PS↗

arXiv2021

Higher Chern numbers in multilayer ($\mathcal{N} \ge 2$) Lieb lattices: Topological transitions and quadratic band crossing lines

We consider a hitherto unexplored setting of stacked multilayer ($\mathcal{N}$) Lieb lattice which undergoes an unusual topological transition in the presence of intra-layer spin-orbit coupling (SOC). The specific stacking configuration induces an effective non-symmorphic 2D lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent non-symmorphicity leads to multiple doubly-degenerate bands extending over the edge of the Brillouin zone (i.e. Quadratic Band Crossing Lines). In the presence of intra-layer SOC, these doubly-degenerate bands typically form three $\mathcal{N}$-band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multi-band subspaces, using specially devised Wilson loop operators to compute non-abelian Berry phases, in order to show that they carry a higher Chern number $\mathcal{N}$.

cond-mat.str-el↗

arXiv2021

From Crystal Color Symmetry to Quantum Spacetime

This perspective article elucidates both the importance and the implications of relativistic spacetime crystals as well as the renormalized blended coordinates transformation. It alludes to possible applications in materials science, condensed matter physics and quantum gravity.

physics.pop-ph↗

arXiv2021

Stability of exact solutions of a nonlocal and nonlinear Schrödinger equation with arbitrary nonlinearity

This work focuses on the study of solitary wave solutions to a nonlocal, nonlinear Schrödinger system in $1$+$1$ dimensions with arbitrary nonlinearity parameter $κ$. Although the system we study here was first reported by Yang (Phys. Rev. E, 98 (2018), 042202) for the fully integrable case $κ=1$, we extend its considerations and offer criteria for soliton stability and instability as a function of $κ$. In particular, we show that for $κ<2$ the solutions are stable whereas for $κ>2$ they are subject to collapse or blowup. At the critical point of $κ=2$, there is a critical mass necessary for blowup or collapse. Furthermore, we show there is a simple one-component nonlocal Lagrangian governing the dynamics of the system which is amenable to a collective coordinate approximation. To that end, we introduce a trial wave function with two collective coordinates to study the small oscillations around the exact solution. We obtain analytical expressions for the small oscillation frequency for the width parameter in the collective coordinate approximation. We also discuss a four collective coordinate approximation which in turn breaks the symmetry of the exact solution by allowing for translational motion. The ensuing oscillations found in the latter case capture the response of the soliton to a small translation. Finally, our results are compared with numerical simulations of the system.

nlin.PS↗

arXiv2021

Valley filtering in strain-induced $α$-$\mathcal{T}_3$ quantum dots

We test the valley-filtering capabilities of a quantum dot inscribed by locally straining an $α$-$\mathcal{T}_3$ lattice. Specifically, we consider an out-of-plane Gaussian bump in the center of a four-terminal configuration and calculate the generated pseudomagnetic field having an opposite direction for electrons originating from different valleys, the resulting valley-polarized currents, and the conductance between the injector and collector situated opposite one another. Depending on the quantum dot's width and width-to-height ratio, we detect different transport regimes with and without valley filtering for both the $α$-$\mathcal{T}_3$ and dice lattice structures. In addition, we analyze the essence of the conductance resonances with a high valley polarization in terms of related (pseudo-) Landau levels, the spatial distribution of the local density of states, and the local current densities. The observed local charge and current density patterns reflect the local inversion symmetry breaking by the strain, besides the global inversion symmetry breaking due to the scaling parameter $α$. By this way we can also filter out different sublattices.

cond-mat.mes-hall↗