A first course on quantum mechanics mainly focuses on quantum systems that are isolated from the rest of the universe, leading to unitary time evolution that preserves coherence. Relalistic systems, however, interact with the environment, leading to the notion of a ‘dissipative’ or ‘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. Dissipation in quantum mechanics is also relevant in quantum optics, solid-state physics, etc.
One of my primary avenues of research is to develop an understanding of dissipative quantum systems aided by theoretical tools and techniques from statistical mechanics. As one might guess, the study of dissipative quantum systems is quite challenging, although, there has been significant progress over the past several decades -- that is to say, I stand on the shoulder of giants.
As a theoretical physicist, my primary goal is to understand the phenomena of quantum dissipation by analyzing paradigmatic models which often allow an exact analytic treatment. A model that is really useful is the quantum (harmonic) oscillator coupled to a heat bath which is in turn itself composed of a collection of quantum oscillators. The resulting dissipative quantum oscillator can be treated by a variety of methods, namely, the Heisenberg-picture formalism which uses Langevin-type equations (the same kind of equations one gets in the problem of Brownian motion), the master-equation formalism in which one is able to analyze the equation of motion of the reduced density operator under certain approximations, and also the path-integral formulation that is based on computing Feynman's influence functional. These seemingly-distinct approaches, however, often cross each other's path.
In collaboration with the statistical mechanics group at IIT Bhubaneswar, I worked on problems leading to the understanding of the notion of thermally-averaged energy of a dissipative quantum oscillator and its variants such as a two/three-dimensional dissipative quantum oscillator in a uniform magnetic field, a problem greatly relevant from the point of view of dissipative Landau diamagnetism. Amongst the results we found was a quantum generalization of the energy equipartition theorem [1,2] (see references therein) which has the correct classical limit in which Boltzmann's equipartition theorem is recovered! Our results are true in the strong-coupling regime as well as in the weak-coupling limit. Such results, as we showed, could be generalized to electronic (fermionic) systems relevant in mesoscopic physics such as quantum dots connected to metallic leads [3]. As a matter of fact, guided by the quantum counterpart of energy equipartition theorem, we observed that the quantum thermodynamic functions (such as free energy, entropy, specific heat) of the dissipative quantum oscillator could be endowed with a similar interpretation [4,5] and that in the classical limit, all the above-mentioned results reduce to the well-known ones for the classical oscillator in the canonical ensemble. Moreover, for the dissipative quantum oscillator, a novel virial theorem was formulated [6] which departs significantly from its classical counterpart.
Subsequent publications have explored the weak-coupling regime of the dissipative quantum oscillator [7] and the formulation of a quantum heat engine where the working substance is a dissipative quantum oscillator in two dimensions with a transverse magnetic field acting upon it [8].
Some of our recent results and also the generic approach towards attacking the dissipative quantum oscillator using quantum Langevin equations have been summarized in the review article [9].
Collaborators:
1) Malay Bandyopadhyay (IIT-BBS)
2) Jasleen Kaur (IIT-BBS)
3) Sushanta Dattagupta (Sister Nivedita University)
4) Shamik Gupta (TIFR)
5) Subhash Chaturvedi (IISER Bhopal)
Related publications:
[1] J. Kaur, A. Ghosh, and M. Bandyopadhyay, Phys. Rev. E 104, 064112 (2021) [arXiv].
[2] J. Kaur, A. Ghosh, and M. Bandyopadhyay, Physica A 625, 128993 (2023) [arXiv].
[3] J. Kaur, A. Ghosh, and M. Bandyopadhyay, J. Stat. Mech. 2022, 053105 (2022) [arXiv].
[4] J. Kaur, A. Ghosh, and M. Bandyopadhyay, Physica A 599, 127466 (2022) [arXiv].
[5] A. Ghosh, J. Kaur, and M. Bandyopadhyay, Physica A 643, 129782 (2024) [arXiv].
[6] A. Ghosh and M. Bandyopadhyay, Physica A 625, 128999 (2023) [arXiv].
[7] A. Ghosh and S. Dattagupta, Physica A 648, 129926 (2024) [arXiv].
[8] J. Kaur, A. Ghosh, S. Dattagupta, S. Chaturvedi, and M. Bandyopadhyay, Physica A 660, 130327 (2025) [arXiv].
[9] A. Ghosh, M. Bandyopadhyay, S. Dattagupta, and S. Gupta, J. Stat. Mech. 2024, 074002 (2024) [arXiv].