arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 19 recordsLinked to original sources

arXiv2026

Planar Interfaces for Transmission of Chiral Spin Textures

Lateral magnetic interfaces provide a direct way to test whether skyrmions remain robust when driven across abrupt changes in material parameters and magnetic order. Here we study skyrmion transmission across planar ferromagnet-ferromagnet (FM-FM), antiferromagnet-antiferromagnet (AFM-AFM), ferromagnet-antiferromagnet (FM-AFM), and antiferromagnet-ferromagnet (AFM-FM) interfaces using micromagnetic simulations and analytic reduced-coordinate criteria. The outcomes are organized into phase diagrams according to the morphology formed in the receiving region, distinguishing compact transmission from deformed skyrmions, stripe-domain states, amorphous textures, and relaxation into the background. Same-order FM-FM and AFM-AFM skyrmion transmission is captured by an analytically defined range of the reduced Dzyaloshinskii-Moriya interaction, identifying the wall-softening regime that supports compact transmission without stripe formation. Mixed-order FM-AFM and AFM-FM interfaces are directionally distinct, requiring conversion between ferromagnetic magnetization and antiferromagnetic N\'eel textures. These results show that planar interfaces act as active transport elements and provide reduced design criteria for heterogeneous skyrmion tracks.

cond-mat.mes-hall↗

arXiv2026

Quantum geometric potential induced conformational transitions in elastic helical nanoribbons

We consider an {\em elastic} helical nanoribbon that can take on various conformations, and study the effect of placing a quantum particle on its curved surface. Using a modified Canham-Helfrich model for the elastic energy, we write down the local elastic potential for the ribbon in terms of its bending rigidity, mean curvature $M$ and Gaussian curvature $K$. The Schr\"odinger equation of a particle confined to a {\em rigid} curved surface is found using da Costa's formulation. It has a purely quantum geometric potential which depends on $M$ and $K$. The Schr\"odinger equation of a particle on an {\em elastic } curved surface will therefore have a total potential comprising quantum and elastic potentials. We compute $M$ and $K$ for a helical ribbon and derive the total potential which depends on the conformation and is thus geometric in nature. Defining a dimensionless quantity $R_H$, we study the behavior of the total geometric potential as $R_H$ is varied. In the absence of an electron, the elastic potential is positive and has a single positive maximum for all conformations. Further, a binormal helical ribbon conformation has the lowest potential, while the normal ribbon has the highest, with those of the intermediate ribbons lying in between these. Intriguingly, when a quantum particle is placed on the elastic ribbon, above a certain critical value of $R_H$, the presence of the quantum geometric potential {\em reverses} this order. But localized states for the particle are not supported. Only above a second critical value of $R_H$, localized states appear for all conformations. The injection of an electron on {\it any} given conformation of the elastic ribbon will induce a conformational transition to the normal ribbon conformation.

quant-ph↗

arXiv2026

Geometry contribution to sound attenuation in double-Weyl semimetals

The axial coupling of strain to the nodes of the simple Weyl semimetals leads to anomalous contributions to sound attenuation in such materials. However, in double Weyl semimetals, there is no such axial coupling. Strain instead couples as a symmetry-breaking director field that deforms the Fermi surface around each Weyl node. In this work, we show that absence of axial coupling in double Weyl semimetals implies a very different mechanism of relaxation due to sound. The deformed geometry of the Fermi surface is the only source of sound attenuation under these conditions. Thus, we identify a geometric contribution to sound attenuation in double Weyl semimetals that is entirely absent in simple Weyl semimetals.

cond-mat.mes-hall↗

arXiv2026

Helically Enhanced Chiroptical Response and Symmetry Breaking in Conjugated Polymers

Chiral $\pi$-conjugated polymers are an attractive material platform for spin polarized carrier-transport and spectroscopy, but fundamental considerations for how torsional disorder influences the response properties of the material have not been considered. Here we combine atomistic electronic structure modeling with with experimental spectroscopic measurements to examine symmetry breaking in the prototypical $\pi$-conjugated polymer polyacetylene, (CH)$_x$. Chiral (CH)$_x$ oligomers are generated in distinct conformations which differ in their out-of-plane tonsorial ordering. We find that a \textit{helical }conformation introduces orders of magnitude enhanced chiroptical activity due to a solenoid effect. This effect is visualized by the Transition Chiral Tensor analysis which shows signatures of domain ordering which eliminates destructive interference between electric and magnetic contributions. These findings highlight the capability to develop a hierarchical interpretation relating local, fragment symmetry breaking to global, nonlocal interactions governing chiroptical response in emerging chiral materials.

cond-mat.mtrl-sci↗

arXiv2026

Nonlinear Localized States on a Pyrochlore Lattice

In the present work we explore a prototypical three-dimensional (3d) lattice possessing a flat band in the form of a pyrochlore lattice in the context of a dispersive nonlinear dynamical model, namely the discrete nonlinear Schr\"odinger (DNLS) equation. We set up the corresponding steady state and dynamical problems and discuss the linear spectrum of the relevant model before delving into a more detailed analysis of the nonlinear equilibria of the system. For the latter, we analyze the more well-established -- at the DNLS level -- fundamental discrete soliton states, as well as vortex structures. For the fundamental solitary waves, we connect their existence and stability with how they approach the linear bands. In the vortex case, we identify their stability features for vortices of topological charge $S=1$ and $S=2$ with those of the honeycomb and triangular lattices. An arguably even more intriguing feature of the pyrochlore lattice concerns the compactly supported nonlinear eigenstates stemming from the flat band of the linear spectrum. These compact localized modes are found to possess oscillatory instabilities for a range of propagation constants in the focusing case, although they can be stable in the latter, while they are found to be subject to symmetry-breaking instabilities in the defocusing nonlinearity case. These results offer a glimpse at the nexus of topology, flat band systems and dispersive nonlinear lattices in three spatial dimensions and as such may be a starting point toward a deeper exploration of such an intriguing interplay.

nlin.PS↗

arXiv2026

Collective dynamics in a one-dimensional Heisenberg ferromagnetic spin chain

We investigate the different oscillatory modes, namely, complete synchronization, inphase synchronization, antiphase synchronization and desynchronization in a one-dimensional anisotropic Heisenberg ferromagnetic spin chain consisting of a large number of spins. By solving the associated Landau-Lifshitz-Gilbert-Slonczewski equation for the spins we show the simultaneous existence of the above mentioned oscillatory modes in the spins. We observe that when the number of the spins is large the synchronization is lost between the spins; however, we identify that the field-like torque is able to induce synchronous oscillations of the spins in the chain again. We also confirm the agreement of the numerically obtained values of the frequency of the inphase synchronized oscillations with the analytically obtained values.

nlin.PS↗

arXiv2026

Integrable motion of curves associated with the Fokas-Lenells equation and related spin system

In this article, we study the gauge equivalence between the integrable Fokas- Lenells equation (FLE) and an associated spin equation through a gauge transformation and the zero curvature condition. We also construct the Lax pair for the generalized spin equation to confirm its integrability. Further, by mapping a generalized spin system on a moving space curve in R3, we show its geometrical equivalence with the FLE. In particular, the associated evolution equations for the curvature and torsion of the space curve are shown to be equivalent to the FLE through a complicated complex transformation unlike the case of the well known Heisenberg spin equation and the nonlinear Schr\"odinger equation.

nlin.SI↗

arXiv2026

One-Parameter Family of Elliptic Sine-Gordon Equations

We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus $0 \le m \le 1$ of Jacobi elliptic functions and analyze some of its properties and obtain its kink solution for various values of modulus $m$. These elliptic SGE have the novel property that while in the limit $m = 0$ they go over to the integrable sine-Gordon equation, in the $m = 1$ limit they go over to the integrable sine hyperbolic-Gordon equations (SHGE).

nlin.PS↗

arXiv2026

Bayesian post-correction of non-Markovian errors in bosonic lattice gravimetry

We study gravimetry with bosonic trapped atoms in the presence of random spatial inhomogeneity. The errors resulting from a random, shot-to-shot fluctuating spatial inhomogeneity are quantum non-Markovian. We show that in a system with $L>2$ modes (i.e., trapping sites), these errors can be post-corrected using a Bayesian inference. The post-correction is done via in situ measurements of the errors and refining the data-processing according to the measured error. We define an effective Fisher information $F_{\text{eff}}$ for such measurements with a Bayesian post-correction and show that the Cramer-Rao bound for the final precision is $\frac{1}{\sqrt{F_{\text{eff}}}}$. Exploring the scaling of the effective Fisher information with the number of atoms $N$, we show that it saturates to a constant when there are too many sources of error and too few modes. That is, with $\ell$ independent sources of error, we show that the effective Fisher information scales as $F_{\text{eff}} \sim \frac{N^2}{a+bN^2}$ for constants $a, b>0$ when the number of modes is small: $L<\ell+2$, even after maximization over the Hilbert space. With larger number of modes, $L\geq \ell+2$, we show that the effective Fisher information has a Heisenberg scaling $F_{\text{eff}}= O(N^2)$ when optimized over the Hilbert space. Finally, we study the density of the effective Fisher information in the Hilbert space and show that when $L\geq \ell+2$, almost any Haar random state has a Heisenberg scaling, i.e., $F_{\text{eff}}=O(N^2)$. Based on these results, we develop a Loschmidt echo-like experimental sequence for error mitigated gravimetry and gradiometry and discuss potential implementations. Finally, we argue that the effective Fisher information can be interpreted as the Fisher information corresponding to an equivalent non-Hertimitian evolution.

quant-ph↗

arXiv2025

Some Novel Aspects of the Plane Pendulum in Classical Mechanics

We obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of the sine-Gordon and the sine hyperbolic-Gordon equations and obtain a few exact solutions of the above mentioned equations. Besides, we consider the plane pendulum equation in the first anharmonic approximation and obtain its large number of exact periodic as well as hyperbolic solutions.In addition, we obtain two exact solutions of the plane pendulum equation in the second anharmonic approximation. Further, we introduce an elliptic plane pendulum equation in terms of the Jacobi elliptic functions $-{\rm sn}(\theta,m)/{\rm dn}(\theta,m)$ which smoothly goes over to the the plane pendulum equation in the $m=0$ limit and the hyperbolic plane pendulum equation in the $m = 1$ limit where $m$ is the modulus of the Jacobi elliptic functions. We show that in the harmonic approximation, the elliptic pendulum problem represents a one-parameter family of isochronous system. Further, for the special case of $m = 1/2$, we show that one has an isochronous system even in the first anharmonic approximation. Finally, we also briefly discuss the hyperbolic plane pendulum and obtain a few of its exact solutions in the harmonic as well as the first anharmonic approximation.

nlin.PS↗

arXiv2025

Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation

We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions involving Jacobi elliptic functions of the form ${\rm dn}^2(x,m)$, ${\rm cn}(x,m){\rm dn}(x,m)$, ${\rm sn}(x,m) {\rm cn}(x,m)$ and ${\rm sn}(x,m){\rm dn}(x,m)$. These results must be contrasted with only partial superposition of such functions in Korteweg-de Vries (KdV), $\phi^3$ and a few other nonlinear equations.

nlin.SI↗

arXiv2025

Particle localization on helical nanoribbons: Quantum analog of the Coriolis effect

We derive the Schr\"odinger equation for a particle confined to the surface of a normal and a binormal helical nanoribbon, obtain the quantum potentials induced by their respective curved surface geometries, and study the localized states of the particle for each ribbon. When the particle momentum satisfies a certain geometric condition, the particle localizes near the inner edge for a normal ribbon, and on the central helix for a binormal ribbon. This result suggests the presence of a pseudo-force that pushes the particle transversely along the width of the ribbon. We show that this phenomenon can be interpreted as a quantum analog of the Coriolis effect, which causes a transverse deflection of a classical particle moving in a rotating frame. We invoke Ehrenfest's theorem applicable to localized states and identify the quantized angular velocities of the rotating frames for the two ribbons. If the particle is an electron, its localization at a specific width gives rise to a Hall-like voltage difference across the ribbon's width. However, unlike in the Hall effect, its origin is not an applied magnetic field, but the ribbon's curved surface geometry. When a normal helical ribbon is mechanically flipped to a binormal configuration in a periodic fashion, it results in a periodic electron transport from the inner edge to the center, giving rise to a quantum AC voltage. This can be used for designing nanoscale electromechanical devices. Quantum transport on a helical nanoribbon can be controlled by tuning the bends and twists of its surface, suggesting diverse applications in biopolymers and nanotechnology.

cond-mat.mes-hall↗

arXiv2025

Solitons of the Symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ Triple Well Model

A symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model for the entire range of parameters and obtain its kink and pulse solutions. For completeness, we also present several periodic solutions of this model. Furthermore, we present a generalized symmetric $\phi^{4n}$-$\phi^{2n}|\phi|$-$\phi^2$ model where $n = 1, 2, 3, ...$ and obtain its kink and pulse solutions for arbitrary $n$.

nlin.PS↗

arXiv2025

Programmable Exploration of Magnetic States in Lieb-Kagome Interpolated Lattices

We investigate a hybrid modeling framework in which a quantum annealer is used to simulate magnetic interactions in molecular qubit lattices inspired by experimentally realizable systems. Using phthalocyanine assemblies as a structurally constrained prototype, we model a continuous deformation from a Lieb to a kagome lattice, revealing frustration-driven disorder and magnetic field-induced reordering in the spin structure. The annealer provides access to observables such as the static structure factor and magnetization over a wide parameter space, enabling the characterization of magnetic arrangements beyond the reach of current molecular architectures. This surrogate modeling approach supports a feedback loop between experiment and programmable quantum hardware, offering a pathway to explore and iteratively design tunable magnetic states in synthetic quantum materials. The synthetic design, structural characterization, and quantum simulation framework established here defines a modular and scalable paradigm for probing the limits of engineered quantum matter across chemistry, condensed matter, and quantum information science.

quant-ph↗

arXiv2025

Solitary waves in the complementary generalized ABS model

We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $ \Psi(x,t) =\Phi(x) \rme^{-\rmi \omega t}$ where the nonlinear interactions are a combination of vector-vector and scalar-scalar interactions with the interaction Lagrangian given by $L_I = \frac{g^2}{(\kappa+1)}[\bar{\psi} \gamma_{\mu}\psi \bar{\psi} \gamma^{\mu} \psi]^{(\kappa+1)/2} - \frac{g^2}{q(\kappa+1)}(\bar{\psi} \psi)^{\kappa+1}$, where $\kappa>0$ and $q>1$. This is the complement of the generalization of the ABS model \cite{abs} that we recently studied \cite{ak} and denoted as the gABS model. We show that like the gABS model, in the complementary gABS models the solitary wave solutions also exist in the entire $(\kappa, q)$ plane and further in both models energy of the solitary wave divided by its charge is {\it independent} of the coupling constant $g$. However, unlike the gABS model here all the solitary waves are single humped, any value of $0 < \omega < m$ is allowed and further unlike the gABS model, for this complementary gABS model the solitary wave bound states exist only in case $\kappa \le \kappa_c$, where $\kappa_c$ depends on the value of $q$. Here $\omega$ and $m$ denote frequency and mass, respectively. We discuss the regions of stability of these solutions as a function of $\omega,q,\kappa$ using the Vakhitov-Kolokolov criterion. Finally we discuss the non-relativistic reduction of the two-parameter family of this complementary generalized ABS model to a modified nonlinear Schr\"odinger equation (NLSE) and discuss the stability of the solitary waves in the domain of validity of the modified NLSE.

nlin.PS↗

arXiv2025

Connection Between the Exact Moving Solutions of the Negative Korteweg-de Vries (nKdV) Equation and the Negative Modified Korteweg-de Vries (nmKdV) Equation and the Static Solutions of 1+1 Dimensional $\phi^4$ Field Theory

The negative order KdV (nKdV) and the modified KdV (nmKdV) equations have two different formulations based on different hierarchy operators. Both equations can be written in terms of a nonlinear differential equation for a field $u(x,t)$ which we call the ``Lou form" of the equation. We find that for moving solutions of the nKdV equation and the nmKdV equation written in the ``Lou form" with $u(x,t) \rightarrow u (x-ct)= u(\xi) $, the equation for $u(\xi)$ can be mapped to the equation for the static solutions of the 1+1 dimensional $\phi^4$ field theory. Using this mapping we obtain a large number of solutions of the nKdV and the nmKdV equation, most of which are new. We also show that the nKdV equation can be derived from an Action Principle for both of its formulations. Furthermore, for both forms of the nmKdV equations as well as for both focusing and defocusing cases, we show that with a suitable ansatz one can decouple the $x$ and $t$ dependence of the nmKdV field $u(x,t)$ and obtain novel solutions in all the cases. We also obtain novel rational solutions of both the nKdV and the nmKdV equations.

nlin.SI↗

arXiv2025

Solitary waves in a Two Parameter Family of Generalized Nonlinear Dirac Equations in $1+1$ Dimensions

We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $\Psi(x,t) = \Phi(x) e^{-i \omega t}$ where the nonlinear interactions are a combination of vector-vector (V-V) and scalar-scalar (S-S) interactions with the interaction Lagrangian given by $L_I= \frac{g^2}{(\kappa+1)}(\bar{\psi} \psi)^{\kappa+1} -\frac{g^2}{p(\kappa+1)}[\bar{\psi} \gamma_{\mu} \psi \bar{\psi} \gamma^{\mu} \psi]^{(\kappa+1)/2}$. This generalizes the model of ABS (N.V. Alexeeva, I.V. Barashenkov and A. Saxena, Annals Phys. {\bf 403}, 198, (2019)) by having the arbitrary nonlinearity parameter $\kappa>0$ and by replacing the coefficient of the V-V interaction by the arbitrary positive parameter $p>1$ which alters the relative weights of the vector-vector and the scalar-scalar interactions. We show that the solitary wave solutions exist in the entire allowed $(\kappa,p)$ plane for $\omega/m > 1/p^{1/(\kappa+1)} $, for frequency $\omega$ and mass $m$. These solutions have the property that their energy divided by their charge is $\it {independent} $ of the coupling constant $g$. As $\omega$ increases, there is a transition from the double humped to the single humped solitons. We discuss the regions of stability of these solutions as a function of $\omega,p,\kappa$ using the Vakhitov-Kolokolov criterion. Finally we discuss the non-relativistic reduction of the 2-parameter family of generalized ABS models to a modified nonlinear Schr\"odinger equation (NLSE) and discuss the stability of the solitary waves in the domain of validity of the modified NLSE.

nlin.PS↗

arXiv2025

Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection

We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where the effective mass of the field is associated with the material and the dark energy content via the cosmological term. We solve the equation in the case of a Schwarzschild black hole and show that it can be cast into an effective Schr\"odinger form with an effective geometric potential which binds the zero angular momentum states. The non-zero angular momentum states experience a positive potential peak before the event horizon pointing to gravitational waves scattering. Black holes scatter gravitational waves and thus we provide an unambiguous testable prediction of black hole existence. The Newtonian limit for this equation points to the possibility of reflecting gravitational waves at interfaces with sharp density boundary, thus opening up gravitational wave propulsion physics. We discuss this type of propulsion in the light of Newton's third law of Mechanics. Compelling questions such as the existence of quanta of this field which may account for the dark matter content are also addressed.

physics.gen-ph↗