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Introduction
I am a graduate student at the Indian Institute of Technology Bhubaneswar, India working on some aspects of theoretical and mathematical physics. My primary research interest is centered around studying the thermodynamics of black holes in various theories of gravity. I am also actively working on certain aspects of mathematical physics, including contact geometry, mathematical formulation of thermodynamics, and quantum dissipation.
Additional affiliations
July 2018 - June 2020
Education
July 2018 - July 2020
July 2015 - June 2018
Publications
Publications (74)
In this paper we discuss a formulation of extended phase space thermodynamics of black holes in anti–de
Sitter (AdS) spacetimes from the contact geometry point of view. Thermodynamics of black holes can be
understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian
functions on equilibrium submanifolds in...
In this paper, we study the thermodynamic geometry of charged Gauss-Bonnet black holes (and Reissner-Nordström black holes, for the sake of comparison) in anti–de Sitter spacetimes in both (T, V) and (S, P) planes. The thermodynamic phase space is known to have an underlying contact and metric structure; Ruppeiner geometry then naturally arises in...
For a thermodynamic system, apart from thermal fluctuations, there are also fluctuations in thermodynamic volume when the system is in contact with a volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the effect of thermal fluctuations on the entropy is well studied. The aim of this work is to compute novel logarithmic corr...
In this paper, we consider general statistical ensembles and compute logarithmic corrections to the microcanonical entropy resulting due to thermodynamic fluctuations which are controlled by the boundary conditions , i.e. due to choice of ensemble. The framework is applied to the case of non-extremal black holes to give certain logarithmic correcti...
We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling in a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for...
Hamiltonian dynamics describing conservative systems naturally preserves the standard notion of phase-space volume, a result known as the Liouville's theorem which is central to the formulation of classical statistical mechanics. In this paper, we obtain explicit expressions for invariant phase-space measures for certain (generally dissipative) mec...
In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 \omega^2 x - 1/8x = 0$, where $\omega > 0$ 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 $x = 0$. Th...
In this paper, we explore some classical and quantum aspects of the nonlinear Li\'enard equation $\ddot{x} + k x \dot{x} + \omega^2 x + (k^2/9) x^3 = 0$, where $x=x(t)$ is a real variable and $k, \omega \in \mathbb{R}$. We demonstrate that such an equation could be derived from an equation of the Levinson-Smith kind which is of the form $\ddot{z} +...
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...
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 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. T...
In this work, we study an Ericsson cycle whose working substance is a charged (quantum) oscillator in a magnetic field that is coupled to a heat bath. The resulting quantum Langevin equations with built-in noise terms encapsulate a thermodynamic structure and allow for the computation of the efficiency of the cycle. We numerically compute the effic...
Hamiltonian dynamics describing conservative systems naturally preserves the standard notion of phase-space volume, a result known as the Liouville's theorem which is central to the formulation of classical statistical mechanics. In this paper, we obtain explicit expressions for invariant phase-space measures for certain dissipative systems, namely...
We describe a symplectic approach to thermodynamics in which thermodynamic transformations are described by Hamiltonian dynamics on thermodynamic spaces. By identifying the spaces of equilibrium states with Lagrangian submanifolds of a symplectic manifold, we construct a Hamiltonian description of thermodynamic processes where the space of equilibr...
In this paper, we discuss some results on integrable Hamiltonian systems with two coordinate variables. 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 th...
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 co...
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 num...
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 co...
The Swanson oscillator forms a prototypical example of a $\mathcal{PT}$-symmetric and non-Hermitian system with a quadratic Hamiltonian. The system is described by the generic quadratic Hamiltonian $\hat{H}_{\rm Swanson} = \hbar \Omega_0 \big( \hat{a}^\dagger \hat{a} + \frac{1}{2}\big) + \alpha \hat{a}^2 + \beta ({\hat{a}^\dagger})^2$, where $\Omeg...
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 fermioni...
In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., H = H 1 + H 2 , where H 1 and H 2 are the Hamiltonians of two one-dimensional unit-mass oscillators. It is shown that there exist...
This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, th...
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 parity-time-symmetric. We achieve this by employing a similarity transformation that maps the non-Hermitian quantum system to a scaled harmonics oscillator. To this end, we cons...
Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have received 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 ope...
The quantum Langevin equation as obtained from the independent-oscillator model describes a strong-coupling situation, devoid of the Born-Markov approximation that is employed in the context of the Gorini-Kossakowski-Sudarshan-Lindblad equation. The question we address is what happens when we implement such 'Born-Markov'-like approximations at the...
Time and again, non-conventional forms of Lagrangians 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 correspondin...
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 n...
In this paper, we discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap, also known as the dissipative quantum oscillator. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy that can be ascribed to the oscillator. These energy functions, respectively d...
It is well known that the Hamiltonian an $n$-dimensional isotropic oscillator admits of 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 th...
In this paper, we consider general statistical ensembles and compute logarithmic corrections to the microcanonical entropy resulting due to thermodynamic fluctuations which are controlled by the boundary conditions, i.e. due to choice of ensemble. The framework is applied to the case of non-extremal black holes to give certain logarithmic correctio...
In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit mass oscillators admitting a separable Hamiltonian description, i.e. $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit mass oscillators, and subsequently show th...
We review in a pedagogic manner the topic of quantum Brownian motion, with an emphasis on its thermodynamic aspects. For the sake of completeness, we begin with the classical treatment of one-dimensional Brownian motion, discussing correlation functions and fluctuation-dissipation relations. The equation-of-motion approach, based on the Langevin eq...
In this brief note, we demonstrate a generalised energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admit...
It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits of 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...
In this note, we study some classical aspects of supersymmetric oscillators, in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket, which emerges as a classical counterpart to commutators and anticommutators from supersymmetric quantum mechanics. In one dimension, i.e. in presence of one bosonic and one f...
In this note, we formulate and study a Hamilton–Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton–Jacobi theory consistently...
In this short note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the virial theorem. Subsequently, we derive a generalized virial theorem for a dissipative quantum oscillator,...
We review recent studies of contact and thermodynamic geometry for black holes in AdS space-times in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure P = −Λ/8π and, subsequently a conjugate volume V , thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we rev...
We review recent studies of contact and thermodynamic geometry for black holes in AdS spacetimes in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure P = −Λ/8π and, subsequently a conjugate volume V, thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we revie...
We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling in a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for...
In this brief note, we demonstrate a generalized energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admit...
In this paper, we demonstrate a remarkable connection between the recently proposed quantum energy equipartition theorem and dissipative diamagnetism exhibited by a charged particle moving in a two dimensional harmonic potential in the presence of a uniform external magnetic field. The system is coupled to a quantum heat bath through coordinate var...
An 'open' or (µ, P, T)-ensemble describes equilibrium systems whose control parameters are chemical potential µ, pressure P and temperature T. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler relation. How...
We compute logarithmic corrections to the black hole entropy S bh in a holographic set up where the cosmological constant Λ and Newton's constant GD are taken to be thermodynamic parameters, related to variations in bulk pressure P and central charge c. In the bulk, the logarithmic corrections are of the form: S = S bh − k ln S bh + · · · arising d...
In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected...
Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate...
In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton-Jacobi theory self consiste...
Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate...
In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected...
In this paper, we formulate and study the quantum counterpart of the energy equipartition theorem for a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a passive quantum heat bath through coordinate variables. The bath is modeled as a collection of independent quan...
We develop a geometric formalism suited for describing the quantum thermodynamics of certain class of nanoscale systems (whose density matrix is expressible in the McLennan-Zubarev form) at any arbitrary nonequilibrium steady state. It is shown that the non-equilibrium steady states are points on control parameter spaces which are in a sense genera...
In this paper, we formulate and study the quantum counterpart of the energy equipartition theorem for a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a passive quantum heat bath through coordinate variables. The bath is modelled as a collection of independent qua...
An `open' or $(\mu,P,T)$-ensemble describes equilibrium systems whose control parameters are chemical potential $\mu$, pressure $P$ and temperature $T$. Such an unconstrained ensemble is seldom used for applications to standard thermodynamic systems due to the fact that the corresponding free energy identically vanishes as a result of the Euler rel...
Within the framework of extended thermodynamics, black hole entropy is expected to receive corrections from thermal fluctuations as well as fluctuations of its thermodynamic volume around equilibrium. Working in the isothermal-isobaric ensemble with the cosmological constant playing the role of a barostat, we find the general form of these correcti...
In this paper, we study the effect of dark energy on the extended thermodynamic structure and interacting microstructures of black holes in AdS, through an analysis of thermodynamic geometry. Considering various limiting cases of the novel equation of state obtained in charged rotating black holes with quintessence, and taking enthalpy H as the key...
In the AdS/CFT correspondence, a dynamical cosmological constant $\Lambda$ in
the bulk corresponds to varying the number of colors $N$ in the boundary gauge
theory with a chemical potential $\mu$ as its thermodynamic conjugate. In this
work, within the context of Schwarzschild black holes in $AdS_5 \times S^5$ and
its dual finite temperature $\math...
In the AdS/CFT correspondence, a variable cosmological constant $\Lambda$ in
the bulk corresponds to varying the number of colors $N$ in the boundary gauge
theory, with chemical potential $\mu$ as its thermodynamic conjugate. In this work, within the context of $AdS_5 \times S^5$ and its dual $\mathcal{N}=4$ SUSY Yang-Mills theory at large $N$, we...
In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the BTZ black holes. Even though BTZ black holes without any angular momentum or electric charge thermodynamically behave as an ideal gas, i.e. with non-interacting microstructures; in the presence of electric charge or angular mo...
In this paper, we study the effect of dark energy on the extended thermodynamic structure and interacting microstructures of black holes in AdS, through an analysis of thermodynamic geometry. Considering various limiting cases of the novel equation of state obtained in charged rotating black holes with quintessence, and taking enthalpy $H$ as the k...
In this paper a general geometric formalism of thermodynamic non-equilibrium steady states is developed within the framework of contact geometry. We show that the non-equilibrium steady states are points on Legendre submanifolds generated by the Massieu potential of the system. These submanifolds correspond to control parameter spaces of the system...
In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the BTZ black holes. Even though BTZ black holes without any rotation or electric charge thermodynamically behave as an ideal gas, i.e. with non-interacting microstructures; in the presence of electric charge and/or rotation, BTZ...
In this paper, we study the thermodynamic geometry of charged Gauss-Bonnet black holes (and Reissner-Nordstr\"{o}m black holes, for the sake of comparison) in AdS: in both (T,V)- and (S,P)-planes. The thermodynamic phase space is known to have an underlying contact and metric structure; Ruppeiner geometry then naturally arises in this framework. Si...
In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) spacetimes from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in...
In this letter, we study the purely nonlinear oscillator by the method of action-angle variables of Hamiltonian systems. The frequency of the non-isochronous system is obtained, which agrees well with the previously known result. Exact analytic solutions of the system involving generalized trigonometric functions are presented. We also present
argu...
In this letter, we study the purely nonlinear oscillator by the method of action-angle
variables of Hamiltonian systems. The frequency of the non-isochronous system is ob-
tained, which agrees well with the previously known result. Exact analytic solutions of
the system involving generalized trigonometric functions are presented. We also present
ar...
In this paper we consider a nonlinear generalization of the isotonic oscillator in the same spirit as one considers the generalization of the harmonic oscillator with a truly nonlinear restoring force. The corresponding potential being asymmetric we invoke the symmetrization principle and construct a symmetric potential in which the period function...
In this paper we consider a nonlinear generalization of the isotonic oscillator in the same spirit as one considers the generalization of the harmonic oscillator with a truly nonlinear restoring force. The corresponding potential being asymmetric we invoke the symmetrization principle and construct a symmetric potential in which the period function...
