Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs

Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from before whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. Essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.Comment: 4 pages, 2 figur

Role of pinning potentials in heat transport through disordered harmonic chain

The role of quadratic onsite pinning potentials on determining the size (N) dependence of the disorder averaged steady state heat current , in a isotopically disordered harmonic chain connected to stochastic heat baths, is investigated. For two models of heat baths, namely white noise baths and Rubin's model of baths, we find that the N dependence of is the same and depends on the number of pinning centers present in the chain. In the absence of pinning, ~ 1/N^{1/2} while in presence of one or two pins ~ 1/N^{3/2}. For a finite (n) number of pinning centers with 2 <= n << N, we provide heuristic arguments and numerical evidence to show that ~ 1/N^{n-1/2}. We discuss the relevance of our results in the context of recent experiments.Comment: 5 pages, 2 figures, quantum case is added in modified versio

Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless/Ehrenfest time which scales with the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or absence of $U(1)$ symmetry, respectively. Using random phase assumption which essentially requires long-range nature of interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian.Comment: 6 pages, 1 figur

Heat transport in harmonic lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green's function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.Comment: One misprint and one error have been corrected; 22 pages, 2 figure

Correlated few-photon transport in one-dimensional waveguides: linear and nonlinear dispersions

We address correlated few-photon transport in one-dimensional waveguides coupled to a two-level system (TLS), such as an atom or a quantum dot. We derive exactly the single-photon and two-photon current (transmission) for linear and nonlinear (tight-binding sinusoidal) energy-momentum dispersion relations of photons in the waveguides and compare the results for the different dispersions. A large enhancement of the two-photon current for the sinusoidal dispersion has been seen at a certain transition energy of the TLS away from the single-photon resonances.Comment: 6 pages, 5 figures, revised version, to appear in Phys. Rev.