arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 19 recordsLinked to original sources

arXiv2026

Dirac Equations With All Possible Combinations of Scalar-Scalar, Vector-Vector and Pseudoscalar-Pseudoscalar Interactions

We obtain exact solutions of the nonlinear Dirac (NLD) equation in $1+1$ dimensions of the form $ψ(x,t) = e^{-iωt} ψ(x)$ for all possible combinations of scalar-scalar (SS), vector-vector (VV) and pseudoscalar-pseudoscalar (PP) interactions at nonlinearity parameter $κ= 1$, which corresponds to the most general 4-Fermion interactions. We look for solutions where $0 < ω< m$ where $ω, m$ are frequency and mass respectively. Remarkably, we show that at $κ= 1$, all the NLD models with SS, VV and PP interactions can be reduced to suitable combinations of SS and VV interactions and hence all solitary waves in these models must also be bound states. We show that two of the ten possible combinations are equivalent to $SS -(1/p) VV$ interactions while two other combinations are equivalent to $VV -(1/q) SS$ interactions for which we already know the results. For the remaining six combinations of SS, VV and PP, we show that depending on the parameters, whereas in some cases entire range of $0 < ω< m$ is allowed, in some other cases $ω$ is restricted to a smaller range $ω_{min} < ω< m$. Further, depending on the parameters, while the solitary waves in some cases have only one hump, in other cases the solitary waves have both single and double hump depending on the value of $ω$. We compute the charge $Q$ and the energy $E$ for each of the solitary wave solutions and show that while $E$ and $Q$ depend on coupling constant $g$, their ratio $E/Q$ is independent of $g$. When $κ= 1$, all the NLD models with SS, VV and PP interactions can be reduced to suitable combinations of SS and VV interactions. As a result all solitary waves in these models are bound states with $E/Q<m$.

nlin.PS↗

arXiv2026

Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence

By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric $ϕ^4$-like coupled equations in $x$ and $t$, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) $\mathcal{PT}$-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.

nlin.PS↗

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 Schrödinger (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

Hyperbolic, Trigonometric and Periodic Solutions of Local and Nonlocal Fokas-Lennels Equations

We obtain a large number of exact hyperbolic, trigonometric, and periodic solutions in terms of Jacobi elliptic functions as well as algebraic solutions with a power law tail of the integrable local Fokas-Lennels equation and integrable nonlocal Fokas-Lennels equation. Further, we consider a one-parameter family of generalized Fokas-Lenells equations and obtain a few of their exact solutions.

nlin.PS↗

arXiv2026

Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions

We obtain exact solutions of the nonlinear Dirac equation in $1+1$ dimensions of the form $ψ(x,t) = e^{-iωt} ψ(x)$ for scalar-scalar (SS) plus vector-vector (VV) interaction with interaction Lagrangian given by $$L_{I} = \frac{g^2}{κ+1}[(\barψ ψ)^{κ+1} +\frac{1}{p} (\barψ γ_μψ\barψ γ^μ ψ)^{κ+1}]$$ where $p > 0$ but arbitrary otherwise. We look for solutions with $0 < ω< m$ where $ω, m$ are frequency and mass, respectively. We find solutions for all values of $ω$ in this range. We compute the charge $Q$ and the energy $E$ for each of the solitary wave solutions and explore the region in the ($p, κ$) parameter space in which solitary wave bound states exist (i.e., for which $E/Q < m$). We show that for all the cases while both $E$ and $Q$ depend on the coupling constant $g$, their ratio $E/Q$ is independent of $g$. We further find that in case $pκ\le 1$, the charge density for all the solitary waves have only single hump while for $p κ> 1$ there is a transition from double to single hump and we determine it as a function of $ω/m$. We notice that for all $p$ there is a transition at $κ=2$ in the behavior of $E/Q$ as a function of $ω$ which we speculate is related to the onset of instability of the solutions at $κ=2$. We obtain the nonrelativistic reduction of the two-parameter family to a non-relativistic modified nonlinear Schrödinger equation (NLSE) and discuss the stability of the single hump olitary waves in the domain of validity of the modified NLSE.

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

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 Néel 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 Schrödinger 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 Schrödinger 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 $π$-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 $π$-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

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 Schrödinger equation.

nlin.SI↗

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↗

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↗

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 $-{\rm sn}(θ,m)/{\rm dn}(θ,m)$ 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), $ϕ^3$ and a few other nonlinear equations.

nlin.SI↗

arXiv2025

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

We derive the Schrödinger 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 $ϕ^4$-$ϕ^2 |ϕ|$-$ϕ^2$ Triple Well Model

A symmetric $ϕ^4$-$ϕ^2 |ϕ|$-$ϕ^2$ 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 $ϕ^{4n}$-$ϕ^{2n}|ϕ|$-$ϕ^2$ 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↗