Anupam Kundu

Role of light and heavy embedded nanoparticles on the thermal conductivity of SiGe alloys

We have used an atomistic {\it ab initio} approach with no adjustable parameters to compute the lattice thermal conductivity of Si

Heat transport and phonon localization in mass-disordered harmonic crystals

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Large deviations of heat flow in harmonic chains

Ge

Exact distributions of the number of distinct and common sites visited by N independent random walkers.

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Heat conduction and phonon localization in disordered harmonic crystals

with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact Greens function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in

The Green-Kubo formula for heat conduction in open systems

\text{Si}_{0.5}\text{Ge}_{0.5}

Energy versus Information Based Estimations of Dissipation Using a Pair of Magnetic Colloidal Particles

provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation which predicts an equal amount of reduction for the two cases, irrespective of the sign of the mass difference. Despite these differences, we find that the Born approximation still performs remarkably well, and it permits investigation of larger nanoparticle sizes, up to 60 nm in diameter, not feasible with the exact approach.

Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions

We investigate the steady-state heat current in two- and three-dimensional disordered harmonic crystals in a slab geometry connected at the boundaries to stochastic white-noise heat baths at different temperatures. The disorder causes short-wavelength phonon modes to be localized so the heat current in this system is carried by the extended phonon modes which can be either diffusive or ballistic. Using ideas both from localization theory and from kinetic theory we estimate the contribution of various modes to the heat current and from this we obtain the asymptotic system size dependence of the current. These estimates are compared with results obtained from a numerical evaluation of an exact formula for the current, given in terms of a frequency-transmission function, as well as from direct nonequilibrium simulations. These yield a strong dependence of the heat flux on boundary conditions. Our analytical arguments show that for realistic boundary conditions the conductivity is finite in three dimensions but we are not able to verify this numerically, except in the case where the system is subjected to an external pinning potential. This case is closely related to the problem of localization of electrons in a random potential and here we numerically verify that the pinned three-dimensional system satisfies Fouriers law while the two-dimensional system is a heat insulator. We also investigate the inverse participation ratio of different normal modes.

Application of importance sampling to the computation of large deviations in nonequilibrium processes.

We consider heat transport across a harmonic chain connected at its two ends to white-noise Langevin reservoirs at different temperatures. In the steady state of this system the heat Q flowing from one reservoir into the system in a finite time τ has a distribution P(Q, τ). We study the large time form of the corresponding moment generating function e − λQ ~ g(λ)eτμ(λ). Exact formal expressions, in terms of phonon Greens functions, are obtained for both μ(λ) and also the lowest order correction g(λ). We point out that, in general, a knowledge of both μ(λ) and g(λ) is required for finding the large deviation function associated with P(Q, τ). The function μ(λ) is known to be the largest eigenvector of an appropriate Fokker–Planck type operator and our method also gives the corresponding eigenvector exactly.

Exact Extremal Statistics in the Classical 1D Coulomb Gas

We study the number of distinct sites S(N)(t) and common sites W(N)(t) visited by N independent one dimensional random walkers, all starting at the origin, after t time steps. We show that these two random variables can be mapped onto extreme value quantities associated with N independent random walkers. Using this mapping, we compute exactly their probability distributions P(N)(d)(S,t) and P(N)(c)(W,t) for any value of N in the limit of large time t, where the random walkers can be described by Brownian motions. In the large N limit one finds that S(N)(t)/√t∝2√(log N)+s/(2√(log N)) and W(N)(t)/√t∝w/N where s and w are random variables whose probability density functions are computed exactly and are found to be nontrivial. We verify our results through direct numerical simulations.