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Bijan Bagchi

Publications and source records attributed to Bijan Bagchi.

At least 19 recordsLinked to original sources
arXiv2026

Entropy bounds, Geroch process, and the sign of deformation parameter

Based on Geroch's process of dropping a system into a black hole from the vicinity of the horizon, we investigate in this paper the influence of deformation on the Bekenstein entropy bound both for (3+1) and (2+1) dimensions in the context of a generalized uncertainty principle (GUP). While providing a coherent framework that sets an upper limit on the entropy across dimensions we show, within a semiclassical treatment, that while a negative GUP deformation yields a universal relaxation of the bound, a positive deformation tightens it. Our results may be interpreted as a response to Planck-scale modifications of the near-horizon redshift.

hep-th↗
arXiv2026

Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model

A fermionic three-site generalization of the popular bosonic Swanson model is studied as providing an exactly solvable five-parametric example of the quantum-mechanical unitary-evolution process leading to an ultimate loss of the observability and fall in an exceptional-point singularity (EP3). The instant of degeneracy is found to have an explicit one-parametric form. Its unitarity-compatible vicinity (i.e., the corridor of access to EP3) is also specified in closed form. The exact, numerical-error-independent solvability is found essential due to another, avoided, false energy-level crossing which is found to occur not too far from the true EP3 singularity.

quant-ph↗
arXiv2026

Generalized quantum theory for accessing nonlinear systems: the case of Liénard and Levinson-Smith equations

We show that a recently introduced generalized scheme of quantum mechanics has connections to Liénard and Levinson-Smith classes of nonlinear systems. For the Liénard type, which has coefficients of odd and odd symmetry, we demonstrate that closed form solutions exist on conversion to the Abel form. For the Levinson-Smith equations, we find their relevance to position-dependent mass systems, with an interesting off-shoot that solitonic-like solutions emerge from the condition of the level surface in the system.

quant-ph↗
arXiv2026

Dynamical symmetries of the anisotropic oscillator

It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. Consequently, the anisotropic oscillator is found to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too (commensurate case). The first integrals are explicitly calculated in the case of a two-dimensional anisotropic oscillator and remarkably, they admit closed-form expressions.

math-ph↗
arXiv2025

Quasi-harmonic spectra from branched Hamiltonians

We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + ω^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Liénard-Kukles equation. While its classical isochronicity and canonical quantization, leading to polynomial solutions with an exactly-equispaced spectrum have been discussed earlier, including in the recent paper [Int. J. Theor. Phys. 64, 212 (2025)], the present study focuses on the quantization of its branched Hamiltonians. For small $k$, we show numerically that the resulting energy spectrum is no longer perfectly harmonic but only approximately equispaced, exhibiting quasi-harmonic behavior characterized by deviations from uniform spacing. Our numerical results are precisely validated by analytical calculations based on perturbation theory.

quant-ph↗
arXiv2025

Painlev\'{e}-Gullstrand coordinates for Kiselev black holes

We investigate the implications provided by the modified Painlev\'{e}-Gullstrand coordinates in the context of quintessence for the Kiselev black hole. In this regard, we set up a fully static line element in terms of lapse and shift functions, apart from including the deformation parameter signaling deviation from the standard Painlev\'{e}-Gullstrand metric. We address two specific issues pertaining to the problems of radiation and dust furnished by the corresponding barotropic index parameter and study the related consequences by performing a range of analyses to explore the influence imposed by quintessence. We also discuss the thermodynamical consequences by evaluating the expressions of the Hawking temperature and the entropy function in closed forms.

gr-qc↗
arXiv2025

Generalized Liénard systems and isochronous connections

In this paper, we explore some classical and quantum aspects of the nonlinear Liénard equation $\ddot{x} + k x \dot{x} + ω^2 x + (k^2/9) x^3 = 0$, where $x=x(t)$ is a real variable and $k, ω\in \mathbb{R}$. We demonstrate that such an equation could be derived from an equation of the Levinson-Smith kind which is of the form $\ddot{z} + J(z) \dot{z}^2 + F(z) \dot{z} + G(z) = 0$, where $z=z(t)$ is a real variable and $\{J(z), F(z), G(z)\}$ are suitable functions to be specified. It can further be mapped to the harmonic oscillator by making use of a nonlocal transformation, establishing its isochronicity. Computations employing the Jacobi last multiplier reveal that the system exhibits a bi-Hamiltonian character, i.e., there are two distinct types of Hamiltonians describing the system. For each of these, we perform a canonical quantization in the momentum representation and explore the possibility of bound states. While one of the Hamiltonians is seen to exhibit an equispaced spectrum with an infinite tower of states, the other one exhibits branching but can be solved exactly in closed form for certain choices of the parameters.

quant-ph↗
arXiv2025

Isochronous oscillator with a singular position-dependent mass and its quantization

In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 ω^2 x - 1/8x = 0$, where $ω> 0$ and $x = x(t)$ is a real-valued variable. We first discuss the appearance of this equation from a position-dependent-mass scenario in which the mass profile goes inversely with $x$, admitting a singularity at $x = 0$. The associated potential is also singular at $x = 0$, splitting the real axis into two halves, i.e., $x > 0$ and $x < 0$. The dynamics is exactly solvable for both the branches and so for definiteness, we stick to the $x > 0$ branch. Performing a canonical quantization in the position representation and upon employing the ordering strategy of the kinetic-energy operator due to von Roos, we show that the problem is isospectral to the isotonic oscillator. Thus, the quantum spectrum consists of an infinite number of equispaced levels. The spacing between the energy levels is found to be insensitive to the specific choices of the ambiguity parameters that are employed for ordering the kinetic-energy operator à la von Roos.

quant-ph↗
arXiv2025

Quantized Area of the Schwarzschild Black Hole: A non-Hermitian Perspective

In this work, our aim is to link Bekenstein's quantized form of the area of the event horizon to the Hamiltonian of the non-Hermitian Swanson oscillator which is known to be $\mathbb{PT}$-symmetric. We achieve this by employing a similarity transformation that maps the non-Hermitian quantum system to a scaled harmonic oscillator. Our procedure is standard and well known. We, first of all, consider the unconstrained reduced Hamiltonian which is directly expressed in terms of the Schwarzschild mass and implies a periodic character for the conjugate momentum (which represents the asymptotic time coordinate), the period being the inverse Hawking temperature. This leads to the quantization of the event-horizon area in terms of the harmonic-oscillator levels. Within the framework of the Swanson oscillator, we proceed to derive novel expressions for the Hawking temperature and the black hole entropy. Notably, the logarithmic area-correction term -(1/2)$\ln$(area) is consistent with our results whereas -(3/2) $\ln$(area) is not.

gr-qc↗
arXiv2025

First integrals of some two-dimensional integrable Hamiltonian systems

In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following this, we discuss the computation of first integrals for integrable two-dimensional systems using the framework of the Jacobi last multiplier. Using the latter, we describe some novel physical examples, namely, the classical Landau problem with a scalar-potential-induced hyperbolic mode, the two-dimensional Kepler problem, and a problem involving a linear curl force.

nlin.SI↗
arXiv2024

Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model

Motivated by recent interest in the search for generating potentials for which the underlying Schrödinger equation is solvable, we report in the recent work several situations when a zero-energy state becomes bound depending on certain restrictions on the coupling constants that define the potential. In this regard, we present evidence of the existence of regular zero-energy normalizable solutions for a system of quasi-exactly solvable (QES) potentials that correspond to the rationally extended many-body truncated Calogero-Sutherland (TCS) model. Our procedure is based upon the use of the standard potential group approach with an underlying $so(2, 1)$ structure that utilizes a point canonical transformation with three distinct types of potentials emerging having the same eigenvalues while their common properties are subjected to the evaluation of the relevant wave functions. These cases are treated individually by suitably restricting the coupling parameters.

quant-ph↗
arXiv2024

Landauer's principle and black hole area quantization

This article assesses Landauer's principle from information theory in the context of area quantization of the Schwarzschild black hole. Within a quantum-mechanical perspective where Hawking evaporation can be interpreted in terms of transitions between the discrete states of the area (or mass) spectrum, we justify that Landauer's principle holds consistently in the saturated form when the number of microstates of the black hole goes as $2^n$, where $n$ is a large positive integer labeling the levels of the area/mass spectrum in the semiclassical regime. This is equivalent to the area spacing $ΔA = αl_P^2$ (in natural units), where $α= 4 \ln 2$ for which the entropy spacing between consecutive levels in Boltzmann units coincides exactly with one bit of information. We also comment on the situation for other values of $α$ prevalent in the literature.

gr-qc↗
arXiv2024

Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases.

quant-ph↗
arXiv2024

Dynamical symmetries of supersymmetric oscillators

In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical counterpart to commutators and anticommutators. In one dimension, i.e., in the presence of one bosonic and one fermionic coordinate, the Hamiltonian admits a $U(1,1)$ symmetry for which we explicitly compute the first integrals. It is found that suitable forms of the supercharges emerge in a natural way as fermionic conserved quantities. Following this, we describe classical supercharge operators based on the generalized Poisson bracket and subsequently define supersymmetry transformations. We perform a straightforward generalization to two spatial dimensions where the Hamiltonian has an overall $U(2,2)$ symmetry. We comment on plausible supersymmetric generalizations of the Pais-Uhlenbeck and isotonic oscillators, and also present the possibility of defining a generalized Nambu bracket within the classical formalism.

math-ph↗
arXiv2024

A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including specifically the types of the Liénard class; for another, very often the problem of their quantization opens up multiple branches of the corresponding Hamiltonians, ending up with the presence of singularities in the associated eigenfunctions. In this article, we furnish a brief review of the classical theory of such Lagrangians and the associated branched Hamiltonians, starting with the example of Liénard-type systems. We then take up other cases where the Lagrangians depend upon the velocity with powers greater than two while still having a tractable mathematical structure, while also describing the associated branched Hamiltonians for such systems. For various examples, we emphasize upon the emergence of the notion of momentum-dependent mass in the theory of branched Hamiltonians.

math-ph↗
arXiv2024

Refractive index profiles for a $\mathcal{PT}$-symmetric optical structure

By mapping the scalar Helmholtz equation (SHE) to the Schrodinger form we investigate the behaviour of $\mathcal{PT}$ optical structure when the refractive index distribution $n$ admits variation in the longitudinal direction only. Interpreting the Schrodinger equation in terms of a superpotential we determine the supersymmetric partners for $n$. We also obtain new analytical solutions for the refractive index profiles and provide graphical illustrations for them.

quant-ph↗
arXiv2023

Analogue Hawking radiation as a tunneling in a two-level $\mathcal{PT}$-symmetric system

In the light of a general scenario of a two-level non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. It is done by making use of the conventional null-geodesic approach wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian.

gr-qc↗