Current Research Interests:
1. Heat transport in low dimensional macroscopic systems: A surprising result that has emerged from many studies over the last few decades is that Fourier's law of heat conduction is not valid in a large class of one-dimensional systems. Some questions I think are interesting: (a) finding the equation that should replace the heat diffusion equation in such systems, (b) extending the results, mostly studied currently in the context of toy models, to more realistic systems and looking for more experimental verifications.
2. Quantum transport: Understanding the effect of nonequilibrium driving in quantum systems is a difficult problem. The theoretical framework is that of open quantum systems and some approaches include quantum Langevin equations (QLE) method, master equation methods and path integral methods. The QLE approach is one of the simplest one when one is dealing with systems described by quadratic Hamiltonians. Some questions of my present interest: (a) What is the best approach for interacting systems, even say a single anharmonic oscillator or a spin-1/2 system, connected to multiple reservoirs ? (b) extending the QLE approach to models such as the Kitaev chain (still described by quadratic Hamiltonians).
3. Measurement problem in quantum systems: Imagine relaeasing a particle from a closed box and waiting for it to get detected by a detector. Recently I have got interested in the question "what is the probability that the particle is detected in the time interval t - t+dt?" This turns out to be a subtle question and I am trying to understand this and also exploring the possibility of relating to recent experiments using non-demolition measurements and detecting quantum trajectories.
4. Models of active matter: It is believed that the dynamics of so called active particles is well described by Langevin-type stochastic equations, which differ from that of passive Brownian particles in that they have "active" components that do not satisfy the detailed balance condition. The removal of the detailed balance condition leads to many interesting features in the behaviour of these systems. Some problems that I am interested in are: (a) even for a single particle, the solution of the Fokker-Planck equation is nontrivial and is an interesting mathematical problem -- interesting properties include the form of the steady state, relaxation and questions related to first passsage times, (b) properties of many particle dynamics --- form of static and dynamical correlation functions.
- Heat transport in low-dimensional systems, A. Dhar, Adv. Phys. 57, 457 (2008).
- Heat conduction and phonon localization in disordered harmonic crystals, A. Kundu, A. Chaudhuri, D. Roy, A. Dhar, J. L. Lebowitz, H. Spohn, Europhys. Lett. 90, 40001 (2010).
- Generating Function Formula of Heat Transfer in Harmonic Networks, K. Saito and A. Dhar, Phys. Rev. Lett. 107, 250601 (2011).
- Large deviations of heat flow in harmonic chains, A. Kundu, S. Sabhapandit and A. Dhar, J. Stat. Mech. P03007 (2011).
- Nonequilibrium density matrix description of steady state quantum transport, A. Dhar, K. Saito and P. Hanggi, Phys. Rev. E 85, 011126 (2012).
- Exact solution of a Levy walk model for anomalous heat transport, A. Dhar, K. Saito and B. Derrida, Phys. Rev. E 87, 010103(R) (2013).
- Numerical test of hydrodynamic uctuation theory in the Fermi-Pasta-Ulam chain, S. G. Das, A. Dhar, K. Saito, C. B. Mendl and H. Spohn, Phys. Rev. E 90, 012124 (2014).
- Detection of a quantum particle on a lattice under repeated projective measurements, S. Dhar, S. Dasgupta, A. Dhar, D. Sen, Phys. Rev. A 91, 062115 (2015).
- Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results, A. Purkayastha, A. Dhar, M. Kulkarni, Phys. Rev. A 93, 062114 (2016).
- Waiting for rare entropic fluctuations, K.Saito and A. Dhar, Euro Phys Lett., 114, 50004 (2016).
- Exact Extremal Statistics in the Classical 1D Coulomb Gas, A. Dhar, A. Kundu, S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. Lett. 119, 060601 (2017).
- Light-cone spreading of perturbations and the butterfly effect in a classical spin chain, A Das, S Chakrabarty, A Dhar, A Kundu, DA Huse, R Moessner, SS Ray, and S. Bhattacharjee, Phys. Rev. Lett. 121, 024101 (2018).
- Anomalous heat equation in a system connected to thermal reservoirs, Priyanka, A. Kundu, A. Dhar, A. Kundu, Phys. Rev. E 98, 042105 (2018).
- Fractional equation description of an open anomalous heat conduction set-up, A. Kundu, C. Bernardin, K. Saito, A. Kundu, A. Dhar, J. Stat. Mech. 013205 (2019).
|Full list of Publications --- from google scholar|
|Selected Talks||Lecture Notes|
|Puzzles in the theory of heat conduction - Kottayam 2019||On random walks and polymers.|
|Large deviations and fluctuation theorems in heat conduction||On random walk with absorbing and reflecting barriers, first passage problem.|
|Green-Kubo formula for open systems||On Kramer's escape rate problem.|
|Heat conduction in disordered harmonic lattices with energy conserving noise||Lectures on Random Walks - I , II|
|Phononic heat conduction in disordered crystals||Statistical physics course (Aug-Dec 2012)|
|Scattering of electrons from an interacting region||Lecture notes on large deviations in heat transport (2013) 1, 2, 3|
|Light cone spreading of perturbations - Rutgers 2018|
|Understanding anomalous transport through hydrodynamics - Nanjing 2018|
|Quasi-zeno dynamics of a quantum particle - Bad Honnef 2018|