My interests are in the theory and applications of nonequilibrium statistical mechanics. The following are some problems that I am currently working on.
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 probably not valid in low-dimensional systems. An open question is to find the correct macroscopic description of heat transport in such systems.
2. Heat and electron transport across small systems: Here one would like to see the effects of nonequilibrium driving in small interacting systems. The theoretical framework is that of open quantum systems.
3. Nonequilibrium fluctuation theorems: There have been recent attempts to extend the results of linear response theory to systems far from equilibrium. The full implications and generality of these results is not yet known and we are looking at some aspects of these.
4. Tagged particle diffusion: We are trying to compute the effective random motion (usually referred to as Brownian motion) of a single tagged particle in a many particle system with specified microscopic dynamics.
- 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).