Quantum Langevin equations and Green’s function (LEGF) method

Schematic of a semiconductor-superconductor hybrid structure connected to leads (metallic baths) at its two ends as it is modeled and studied in Phys. Rev. B 88, 020502 (RC) (2013)

During my Ph.D. at RRI, we have developed a theoretical tool based on quantum Langevin equations and Green’s function to study nonequilibrium quantum transport across a system connected to baths at the boundaries. Our method is a generalization of the Heisenberg-Langevin equation approach to nonequilibrium when the baths at the boundaries of the system are kept at different temperatures or chemical potentials or magnetizations. Quantum LEGF method leads to NEGF-like expressions for transport coefficients. It also reproduces the results of the Landauer-Buttiker formalism in particular limits. We have applied quantum LEGF method for investigating nonequilibrium transport in various noninteracting and interacting open quantum systems of electrons, phonons, and photons as listed below. Currently, we are trying to further extend the applicability of LEGF method in interacting models.

(a) Electrical & thermal transport in metals:

D. Roy and A. Dhar, Phys. Rev. B 75, 195110 (2007)

R. Bag and D. Roy, Phys. Rev. B 111, 064309 (2025)

(b) Electrical transport in superconductors:

D. Roy, C. J. Bolech, and N. Shah, Phys. Rev. B 86, 094503 (2012)

D. Roy, N. Bondyopadhaya, and S. Tewari, Phys. Rev. B 88, 020502 (R) (2013)

N. Bondyopadhaya and D. Roy, J. Stat. Phys. 187, 11 (2022)

(c) Heat transport in lattices:

A. Dhar and D. Roy, J. Stat. Phys. 125, 801 (2006)

D. Roy and A. Dhar, J. Stat. Phys. 131, 535 (2008)

T. R. Vishnu and D. Roy,  J. Stat. Phys. 191, 123 (2024)

(d) Light propagation in nonlinear medium:

D. Roy, Phys. Rev A 96, 033838 (2017)

P. Manasi and D. Roy, Phys. Rev. A 98, 023802 (2018)