Research

My research interests are quite diverse and I love spending my time on research. Given below are brief descriptions summarizing my recent interests.
I am very grateful to the Ministry of Education, Government of India, for funding my PhD and to the people of India, for their support towards research in basic sciences. 

My list of publications and preprints can be found here. 

Black hole chemistry:

As many of us are aware, black holes are rather exotic thermodynamic systems where the entropy scales with the area, rather than volume. This brings in interesting features, such as non-extensivity, i.e. the black hole entropy does not scale linearly with the energy content of the spacetime. Thermodynamic features become all the more interesting when variations of the cosmological constant are taken into account, in a framework dubbed `black hole chemistry' suited for black holes in asymptotically AdS spacetimes. 

I have been interested in understanding the fluctuation properties of black holes, within the framework of black hole chemistry and have coauthored several papers on thermodynamic geometries described by Hessian metrics on the spaces of equilibrium states [arXiv:1911.06280; 2001.10510; 2002.08787; 2006.02943]. These geometries are believed to encode some empirical information about the nature of microscopic interactions of the system, and therefore may reveal early insights into the microscopics of black holes. 

For my PhD thesis, I have computed logarithmic corrections to the black hole entropy due to thermodynamic fluctuations in fixed pressure ensembles, where the pressure of the black hole solution is dictated by the background cosmological constant. In my coauthored papers [arXiv:2104.05388; 2104.12720], we have reported corrections to the microcanonical entropy of black holes due to fluctuations of energy & volume, and energy, volume, & electric charge/angular momentum, respectively. As a further development [arXiv:2307.00832], I have presented a comprehensive discussion on obtaining logarithmic corrections in black hole chemistry and also in frameworks where the cosmological constant is not treated as a thermodynamic variable, while demonstrating a match between corrections obtained in the bulk and the boundary via the AdS/CFT correspondence. In another coauthored paper [arXiv:2207.02820] (yet to appear in final published form), we discussed logarithmic corrections in holographic black hole chemistry. In the near future, I plan to study the implications of having a variable Newton's constant in black hole thermodynamics, and possibly discuss its origin from scalar-tensor theories of gravity. 

Open quantum systems and quantum thermodynamics:

An introductory textbook treatment of quantum mechanics mainly focusses on quantum systems that are completely isolated from the rest of the universe. In real life however, this is rarely true and a quantum system interacts with the environment, leading to the notion of an ‘open quantum system’. Examples include situations encountered in cold-atom experiments, wherein an atom or an ion interacts with an environment, while possibly also interacting with other fields like a magnetic field, or electrical (optical) pulses. I am greatly interested in the theoretical study of such systems via paradigmatic models such as quantum Brownian motion.

In collaboration with the statistical mechanics group at IIT Bhubaneswar, I have performed investigations on the energetics of quantum Brownian motion, in situations where external fields or biases are present. In particular, in [arXiv:2106.07509; 2201.07721; 2202.02504], we have studied the quantum counterpart of energy equipartition theorem for such systems, where a single quantum particle/quantum dot interacts with a heat bath (modeled as a collections of oscillators). Generalization to linear electrical circuits is presented in [arXiv:2212.07024]. Dissipative diamagnetism and its connection with the quantum counterpart of the energy equipartition theorem was recently obtained in [arXiv:2208.00161]. In the paper [arXiv:2302.12008], we have also obtained a generalized virial theorem for strongly-coupled Brownian oscillators and have studied its limiting cases, while in a recent paper [arXiv:2310.03595], we have revisited studies on the energetics of the dissipative quantum oscillator, carefully analyzing the notions of internal energy and mean energy, highlighting the important differences in their definitions.

I have also coauthored a review paper on the subject of quantum Brownian motion, wherein we discuss the formulation of the problem, followed by a detailed description of the thermodynamic aspects, tied together with important topics such as dissipative diamagnetism, anomalous dissipation, Brownian heat engines, and fluctuation theorems [arXiv:2306.02665].

Current projects (in collaboration) include the computation and analysis of efficiency of the Ericsson cycle for the dissipative oscillator in a magnetic field. I have recently become interested in non-hermitian quantum systems [arXiv:2401.17189], and plan to explore about non-hermitian descriptions of open quantum systems in the near future.

Analytical mechanics:

Since my undergraduate days, I have had a keen interest in classical mechanics, and have coauthored two papers [arXiv:1906.10387; 1905.08062] on (strongly) nonlinear oscillators, i.e. second order differential equations with nonlinear restoring forces that cannot be linearized, i.e. such forces are ‘strong’.

Recently, I have become interested in various generalizations of the harmonic oscillator problem and its symmetries. In particular, in a coauthored paper [arXiv:2304.14306], we have demon- strated that there exists a canonical transformation between the anisotropic oscillator and the isotropic oscillator, thereby allowing the anisotropic oscillator to possess the same number of con- served quantities as its isotropic counterpart, where the conserved quantities are dictated by sym- metry under U(n) transformations in n spatial dimensions.

I am also interested in describing classical oscillators with fermionic (Grassmann) variables. In the preprint [arXiv:2304.04747], we present (classical) supersymmetric versions of two-dimensional oscillators and describe supersymmetry transformations between them, while also studying their dynamical symmetries and conserved quantities.

I have also been interested in integrable systems and in the preprint [arXiv:2306.08837], we have shown the role of the Jacobi last multiplier in the context of superintegrable oscillators in two spatial dimensions. Interestingly, we demonstrate that the Bateman pair is a superintegrable system although energy conservation cannot be observed directly. In the near future, I plan to work on problems on integrable systems, in particular, on the role of Nambu-bracket-like structures.

Recently, I have coauthored a review on nonstandard Lagrangians and branched Hamiltonians [arXiv:2403.18801].

Contact geometry and physics:

Contact geometry is like the odd dimensional cousin of symplectic geometry which is commonly encountered in Hamiltonian dynamics. In standard Hamiltonian dynamics, given any function H, one can determine the equations of motion via differentiation (dH) whose solutions satisfy the integral curves of the Hamiltonian vector field (X). In other words, there is a bijective map which takes every dH (corresponding to some Hamiltonian function H) to a vector field X whose integral curves are the solutions to the Hamilton's equations of motion. Symplectic geometry provides the natural setting for this kind of bijective maps better known as vector-bundle isomorphisms.

Similarly, in contact geometry one finds maps (but not vector-bundle isomorphisms) allowing one to associated with a differentiable function, the notion of a dynamical (contact) vector field. Both symplectic and contact geometries admit different versions of Darboux's theorem making them locally equivalent to their simplest counterparts in the same number of dimensions. It turns out that contact geometry finds applications in various disciplines including classical mechanics, thermostat problems as well as reversible and irreversible thermodynamics. 

My work has involved studying thermodynamics from a geometric viewpoint, from representing thermodynamic processes as contact Hamiltonian flows [arXiv:1909.11506], to describing an as- sociated Hamilton-Jacobi formulation [arXiv:2203.03473], in both equilibrium and also certain special non-equilibrium situations [arXiv:2002.06338].  I have also worked towards formulating a geometric version of the virial theorem for contact Hamiltonian systems [arXiv:2301.09355].

The contact structure naturally leads to a compatible metric on thermodynamic phase spaces providing deep connections with thermodynamic fluctuation theory. One may utilize tools of thermodynamic fluctuation theory to develop a better understanding of the thermodynamic structure of various systems, including asymptotically AdS black holes. I have been involved in the analysis of the thermodynamic curvature (which refers to the Ricci scalar summarizing the curvature properties of spaces of thermodynamic equilibrium states) for various black holes. It has been emprically demonstrated that the sign of the thermodynamic curvature carriers useful information about the nature of microscopic interactions underlying the thermodynamic system. Therefore, we hope that the analysis of the thermodynamic curvature for black holes may reveal novel insights into their microscopic degrees of freedom. At present, we are exploring such connections in rigourous detail and have published a detailed review of recent developments [arXiv:2302.04467].