arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 37 records · Page 2Linked to original sources

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 $ϕ^4$ 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(ξ) $, the equation for $u(ξ)$ can be mapped to the equation for the static solutions of the 1+1 dimensional $ϕ^4$ 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 $Ψ(x,t) = Φ(x) e^{-i ωt}$ where the nonlinear interactions are a combination of vector-vector (V-V) and scalar-scalar (S-S) interactions with the interaction Lagrangian given by $L_I= \frac{g^2}{(κ+1)}(\barψ ψ)^{κ+1} -\frac{g^2}{p(κ+1)}[\barψ γ_μ ψ\barψ γ^μ ψ]^{(κ+1)/2}$. 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 $κ>0$ 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 $(κ,p)$ plane for $ω/m > 1/p^{1/(κ+1)} $, for frequency $ω$ and mass $m$. These solutions have the property that their energy divided by their charge is $\it {independent} $ of the coupling constant $g$. As $ω$ 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 $ω,p,κ$ 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 Schrödinger equation (NLSE) and discuss the stability of the solitary waves in the domain of validity of the modified NLSE.

nlin.PS↗

arXiv2025

Geometric transport signatures of strained multi-Weyl semimetals

The minimal coupling of strain to Dirac and Weyl semimetals, and its modeling as a pseudo-gauge field has been extensively studied, resulting in several proposed topological transport signatures. In this work, we study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudo-gauge field for any winding number larger than one. We focus on the double-Weyl semimetal as an illustrative example to show that the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Specifically, the Fermi surface of the double-Weyl semimetal acquires nematic order. By extending chiral kinetic theory for such nematic fields, we determine the effective gauge fields acting on the system and show how strain induces anisotropy and affects the geometry of the semi-classical phase space of the double-Weyl semimetal. Further, the strain-induced deformation of the Weyl nodes results in transport signatures related to the covariant coupling of the strain tensor to the geometric tensor associated with the Weyl nodes giving rise to strain-dependent dissipative corrections to the longitudinal as well as the Hall conductance. Thus, by extension, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures. Further, we highlight that the most general way to view strain is as a symmetry-breaking field rather than a pseudo-gauge field.

cond-mat.mes-hall↗

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 Schrödinger 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↗

arXiv2025

Multipolar multiferroics in $4d^2$/$5d^2$ Mott insulators

We extend the concept of conventional multiferroicity \ -- where ferroelectric and ferromagnetic orders coexist \ -- to include multipolar degrees of freedom. Specifically, we explore how this phenomenon emerges in $4d^2/5d^2$ Mott insulators with strong spin-orbit and Hund's couplings. Our study uncovers the origin of magnetic multipolar interactions in these systems and demonstrates that a combination of quadrupolar and octupolar magnetic order can simultaneously induce both electrical quadrupolar moments and ferroelectric polarization. By expanding the multiferroic framework to higher-order multipoles, we reveal the possibility of coexisting multipolar orders of different or same ranks, paving the way for new functional properties in a large class of strongly correlated materials.

cond-mat.str-el↗

arXiv2025

Spin-Triplet Excitonic Insulator in the Ultra-Quantum Limit of HfTe5

More than fifty years ago, excitonic insulators, formed by the pairing of electrons and holes due to Coulomb interactions, were first predicted. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moire superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet exciton insulator in the ultra-quantum limit of a three-dimensional topological material HfTe5. We observe that the spin-polarized zeroth Landau bands, dispersing along the field direction, cross each other beyond a characteristic magnetic field in HfTe5, forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 250 μeV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10 - 72 T). Our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

cond-mat.str-el↗

arXiv2025

Topological and nonlinearity-induced thermalization in a PT-symmetric split-Langevin bath

Open classical systems with balanced, separated gain and loss, called PT-symmetric systems, have been extensively studied over the past decade. Here, we investigate the properties of a uniform, harmonic chain with spatially separated viscous loss and stochastic gain that are only statistically balanced. We show that such a "split Langevin" bath leads to either the absence of thermalization or non-equilibrium steady states with inhomogeneous temperature profile, both of which are understood in terms of normal modes of the chain. With a Su-Schrieffer-Heeger (SSH) chain, a canonical model with topological edge modes, we show that the steady-state properties reflect the topological phase of the underlying chain. We also show that nonlinearity stabilizes the amplifying modes in a harmonic chain, thereby leading to thermalization irrespective of the gain and loss locations. Our results expand the pool of possible realizations of non-Hermitian models to the stochastic domain.

cond-mat.stat-mech↗

arXiv2024

Mass Oscillations in Superconducting Junctions for Gravitational Wave Emission and Detection

We revisit the nonlinear superconducting junction dynamics in order to provide evidence that the time-dependent current density in the junction is related to an oscillating charge and mass density in addition to a variable velocity. As a result, the superconducting tunnel junction emerges as a solid state device capable of producing rapid charge and mass oscillations inaccessible in classical contexts. Rapidity is required for gravitational wave emission when small masses are involved in the emission process. We provide designs for an emitting and a detecting device based on generating and capturing mass oscillations with a non-zero quadrupole moment component. Finally, we suggest that the smallness of the Einstein gravitational coupling constant can be fully compensated by the largeness of the quantum mechanical term $e^4 \hbar^{-6}$ manifested in the suggested set ups.

physics.gen-ph↗

arXiv2024

Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity

Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the coupled massive Thirring and the coupled Soler model to arbitrary nonlinear parameter $κ$ and obtain exact solitary wave solutions in both cases. Remarkably, it turns out that in both the models, because of the conservation laws of charge and energy, the exact solutions we find seem to not depend on how we parameterize them, and the charge density of these solutions is related to the charge density of the single field solutions found earlier by a subset of the present authors. In both the models, a nonrelativistic reduction of the equations leads to the same conclusion that the solutions are proportional to those found in the one component field case.

nlin.PS↗

arXiv2024

Quantum matter and gravitation: photons in a waveguide

The conditions required by quantum matter to modify space-time geometry are explored within the framework of the general theory of relativity. The required characteristics for space-time modification in solid state structures, are met in either (a) massive photon Bose-Einstein condensate in a waveguide, or (b) the massive photons in superconductor's bulk, or (c) the Bose-Einstein condensate of acoustic phonons, or (d) a metal-insulator-topological insulator heterostructure.

physics.gen-ph↗

arXiv2024

A Nonlinear Journey from Structural Phase Transitions to Quantum Annealing

Motivated by an exact mapping between equilibrium properties of a 1-dimensional chain of quantum Ising spins in a transverse field (the transverse field Ising (TFI) model) and a 2-dimensional classical array of particles in double-well potentials (the "$ϕ^4$ model") with weak inter-chain coupling, we explore connections between the driven variants of the two systems. We argue that coupling between the fundamental topological solitary waves in the form of kinks between neighboring chains in the classical $ϕ^4$ system is the analogue of the competing effect of the transverse field on spin flips in the quantum TFI model. As an example application, we mimic simplified measurement protocols in a closed quantum model system by studying the classical $ϕ^4$ model subjected to periodic perturbations. This reveals memory/loss of memory and coherence/decoherence regimes, whose quantum analogues are essential in annealing phenomena. In particular, we examine regimes where the topological excitations control the thermal equilibration following perturbations. This paves the way for further explorations of the analogy between lower-dimensional linear quantum and higher-dimensional classical nonlinear systems.

nlin.PS↗

arXiv2024

Twisted curve geometry underlying topological invariants

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the Gauss-Bonnet theorem shows that the Euler characteristic (a topological invariant) can be written as the integral of the Gaussian curvature (an intrinsic geometric quantity), the intriguing question of whether winding and linking numbers can also be expressed similarly as integrals of some intrinsic geometric quantities has not been addressed in the literature. In this paper we provide the answer by showing that for the winding number in two dimensions, these quantities are torsions of the two evolving space curves describing the manifold. On the other hand, in three dimensions we find that in addition to torsions, intrinsic twists of the space curves are necessary to obtain a nontrivial winding number and linking number. These new results arise from the hitherto unknown connections that we establish between these topological invariants and the corresponding appropriately normalized global anholonomies (i.e., geometric phases) associated with the unit vector fields on the respective manifolds. An application of our results to a 3D Heisenberg ferromagnetic model supporting a topological soliton is also presented.

nlin.PS↗

arXiv2023

Quantum dynamics of non-Hermitian many-body Landau-Zener systems

We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multi-state Landau-Zener models. The non-hermiticity is due to the anti-Hermitian couplings between the diabatic levels. We find that there exists a new conservation law, unique to this class of models, that describes the simultaneous growth of the unnormalized wavefunctions. These models have practical applications in Bose-Einstein condensates, and they can describe the dynamics of multi-species bosonic systems. The conservation law relates to a pair-production mechanism that explains the dissociation of diatomic molecules into atoms. We provide a general framework for both solvable and semiclassically solvable non-Hermitian Landau-Zener models. Our findings will open new avenues for a number of diverse emergent phenomena in explicitly time-dependent non-Hermitian quantum systems.

quant-ph↗

arXiv2023

Exact trapped $N$-soliton solutions of the nonlinear Schrödinger equation using the inverse problem method

In this work, we show the application of the ``inverse problem'' method to construct exact $N$ trapped soliton-like solutions of the nonlinear Schrödinger or Gross-Pitaevskii equation (NLSE and GPE, respectively) in one, two, and three spatial dimensions. This method is capable of finding the external (confining) potentials which render specific assumed waveforms exact solutions of the NLSE for both attractive ($g<0$) and repulsive ($g>0$) self-interactions. For both signs of $g$, we discuss the stability with respect to self-similar deformations and translations. For $g<0$, a critical mass $M_c$, or equivalently the number of particles, for instabilities to arise can often be found analytically. On the other hand, for the case with $g>0$ corresponding to repulsive self interactions which is often discussed in the atomic physics realm of Bose-Einstein condensates (BEC), the bound solutions are found to be always stable. For $g<0$, we also determine the critical mass numerically by using linear stability or Bogoliubov-de Gennes analysis, and compare these results with our analytic estimates. Various analytic forms for the trapped $N$-soliton solutions are discussed, including sums of Gaussians or higher-order eigenfunctions of the harmonic oscillator Hamiltonian.

nlin.PS↗

arXiv2023

New Solutions of Coupled Nonlocal NLS and Coupled Nonlocal mKdV Equations

We provide several novel solutions of the coupled Ablowitz-Musslimani (AM) version of the nonlocal nonlinear Schrödinger (NLS) equation and the coupled nonlocal modified Korteweg-de Vries (mKdV) equations. In each case we compare and contrast the corresponding solutions of the relevant coupled local equations. Further, we provide new solutions of the coupled local NLS and the coupled local mKdV equations which are not the solutions of the corresponding nonlocal equations.

nlin.SI↗

arXiv2023

Superposed periodic kink and pulse solutions of coupled nonlinear equations

We present novel previously unexplored periodic solutions, expressed in terms of Jacobi elliptic functions, for both a coupled $ϕ^4$ model and a coupled nonlinear Schrödinger equation (NLS) model. Remarkably, these solutions can be elegantly reformulated as a linear combination of periodic kinks and antikinks, or as a combination of two periodic kinks or two periodic pulse solutions. However, we also find that for $m=0$ and a specific value of the periodicity (or at a nonzero value of the elliptic modulus $m$) this superposition does not hold. These results demonstrate that the notion of superposed solutions extends to the coupled nonlinear equations as well.

nlin.SI↗

arXiv2023

New static solutions of symmetric $ϕ^4$ equation

In this paper, we provide new exact solutions of nonlinear Klein-Gordon ($ϕ^4$) equation in $1+1$-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric $ϕ^4$ equation has played an important role in several areas of physics. We obtain several novel non-singular solutions of the symmetric $ϕ^4$ model in terms of the Jacobi elliptic functions and compare them with the well-known solutions. Finally, we categorize these solutions in terms of the potential parameters.

nlin.SI↗

arXiv2023

New Solutions of Nonlocal NLS, mKdV and Hirota Equations

In this paper, we provide several novel solutions of the Ablowitz-Musslimani as well Yang's versions of the nonlocal nonlinear Schrödinger (NLS) equation, nonlocal modified Korteweg-de Vries (mKdV) as well as nonlocal Hirota equations. In each case we compare and contrast the corresponding solutions of the relevant local equation. Further, we provide new solutions of the local NLS, local mKdV and local Hirota equations which are not the solutions of the corresponding nonlocal equations.

nlin.SI↗