arXiv subjects

Aradhya Shukla

Publications and source records attributed to Aradhya Shukla.

10 recordsLinked to original sources

arXiv2025

Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection

We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation. We demonstrate that the Fokker-Planck equation reduces to a simplified form equivalent to a scaled quantum mechanical problem with a harmonic oscillator potential. In this framework, we highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker-Planck dynamics associated with the Schwarzschild metric. Utilizing the isospectral deformation, an intrinsic feature of SUSY QM, we derive a family of one-parameter isospectral potentials. Notably, this new class of potentials exhibits the same energy spectrum as the original harmonic oscillator potential, but with distinct wavefunctions.

hep-th↗

arXiv2024

(Anti-)BRST Symmetries in FLRW Model: Supervariable Approach

Friedmann-Lemaitre-Robertson-Walker (FLRW) model, representing the isotropic and homogeneous Universe, has an inherent diffeomorphism (or reparametrization) invariance. For a given local time-reparametrization symmetry transformation of (0+1)-dimensional (1D) diffeomorphism invariant FLRW model, we derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations in a consistent manner. The supervariable approach to BRST formalism is used as a guiding tool in finding the proper (anti-)BRST transformations. An application of (super-)diffeomorphism invariance, in the context of superspace formalism, yields horizontality conditions. Moreover, the celebrated CF-type condition which is universal for 1D diffeomorphism invariant theories, emerges as an off-shoot of the horizontality condition and provides the absolute anticommutativity of the (anti-)BRST transformations. In addition, this CF-type condition leads to the derivation of coupled (but equivalent) (anti-)BRST invariant quantum Lagrangians for FLRW model. We also capture the geometrical interpretation of the (anti-)BRST transformations and their properties in terms of the Grassmannian translational generators and supervariables.

hep-th↗

arXiv2023

Exact Solutions of Augmented GP Equation: Solitons, Droplets and Supersolid

The augmented nonlinear Schrödinger equation (ANLSE), describing BEC, with the Lee-Huang-Yang (LHY) correction has exhibited a quantum droplet state, which has found experimental verification. In addition to the droplet, exact kink-antikink and supersolid phases have been recently obtained in different parameter domains. Interestingly, these solutions are associated with a constant background, unlike the form of BEC in quasi-one dimension, where dark, bright, and grey solitons have been experimentally obtained. Here, we connect a wide class of solutions of the ANLSE with the Jacobi elliptic functions using a fractional transformation method in a general scenario. The conserved energy and momentum are obtained in this general setting which differentiates and characterizes the different phases of the solution space. We then concentrate on the Jacobi-elliptic $dn(x, m^2)$ function, as the same is characterized by a non-vanishing background as compared to the other $cn$ and $sn$ functions.

nlin.PS↗

arXiv2023

Free Particle to Complex KdV breathers through Isospectral Deformation

The free particle in quantum mechanics in real space is endowed with supersymmetry, which enables a natural extension to complex spectra with a built-in parity (P) and time reversal (T) symmetry. It also explains the origin of unbroken and broken phases of the PT-symmetry and their relationship with the real and complex eigenvalues respectively, the latter further displaying zero-width resonances. This is possible as the extension of the eigenvalue problem to the complex plane enables the incorporation of bound and decaying states in the enlarged Hilbert space. The inherent freedom of modification of the potential without changing the spectra in supersymmetry naturally explains the connection of complex breather solutions of KdV with PT-symmetry and the free particle on the complex plane. Further, non-trivial zero-width resonances in the broken PT phase mandate a generalization that is directly connected to the sl(2, R) potential algebra.

math-ph↗

arXiv2022

Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings

We construct an exact black hole solution for the Einstein gravity coupled with the nonlinear electrodynamics (which corresponds to the Maxwell electrodynamics in the weak field limit) in the presence of a cloud of strings as the source. We study the thermodynamical properties of the black hole solutions and derive the corrected first-law of thermodynamics. The presence of a cloud of strings does not affect the stability of the present black hole. However, a second-order phase transition exists for this system at a critical horizon radius. Furthermore, we study the quasinormal modes and their shadow radius. In addition, we find that, upon variation, the parameters of the theory show different aspects of the optical characteristics of the black hole solutions.

gr-qc↗

arXiv2021

PT-Symmetry and Supersymmetry: Interconnection of Broken and Unbroken Phases

The broken and unbroken phases of PT and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of PT-symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in PT-symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scarf potential, in PT-symmetric phase, a connection between complex isospectral superpotentials and modified KdV equation occurs, only with certain restrictive parametric conditions. In the broken PT-symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

quant-ph↗

arXiv2021

Kink-like Solitons in Quantum Droplet

Solitonic excitations of the one-dimensional quantum droplets are obtained, which smoothly connect vacuum with the flat-top droplet, akin to compactons in classical liquids. These solitons are of the kink type, necessarily residing on a constant pedestal, determined by the mean-field repulsion and beyond mean field quantum correction and having exactly one-third of the uniform condensate amplitude. Akin to the kinks, the propagating modes occur in pairs and are phase-locked with the background. The lowest chemical potential and condensate amplitude at the flat-top boundary matches with the self-trapped quantum droplet. More general excitations of analogous kind are obtained through the Möbius transform, which connect the required solutions to elliptic functions in general.

cond-mat.quant-gas↗

arXiv2019

Chiral Kinetic Theory from Effective Field Theory Revisited

We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/μ)$ expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.

hep-ph↗

arXiv2017

A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach

By exploiting the supersymmetric invariant restrictions on the chiral and anti-chiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (θ, \barθ). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N = 2 SUSY quantum mechanical model is a model for Hodge theory.

hep-th↗

arXiv2016

Conservation Law for Massive Scale-Invariant Photons in Weyl-Invariant Gravity

It is demonstrated that a Stueckelberg-type gauge theory, coupled to the scalar-tensor theory of gravity, is invariant under both gauge and Weyl transformations. Unlike the pure Stueckelberg theory, this coupled Lagrangian has a genuine Weyl symmetry, with a non-vanishing current. The above is true in the Jordan frame, whereas in the Einstein frame, the same theory manifests as Proca theory in presence of pure gravity. It is found that broken scale invariance leads to simultaneous spontaneous breaking of the gauge symmetry.

hep-th↗