arXiv subjects

Abhishek Dhar

Publications and source records attributed to Abhishek Dhar.

At least 145 records · Page 8Linked to original sources

arXiv2008

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.

cond-mat.dis-nn↗

arXiv2008

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.

cond-mat.mes-hall↗

arXiv2008

Scattering of electrons from an interacting region

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a single bond. We show that all the two-particle scattering states can be found exactly. Comparisons are made with numerical results on the time evolution of a two-particle wave packet and several interesting features are found for scattering. For N particles the scattering state is obtained by perturbation theory. For a dot connected to Fermi seas at different chemical potentials, we find an expression for the change in the Landauer current resulting from the interactions on the dot. We end with some comments on the case of spin-1/2 electrons.

cond-mat.mes-hall↗

arXiv2008

Heat conduction in the disordered Fermi-Pasta-Ulam chain

We address the question of the effect of disorder on heat conduction in an anharmonic chain with interactions given by the Fermi-Pasta-Ulam (FPU) potential. In contrast to the conclusions of an earlier paper [Phys. Rev. Lett. 86, 63 (2001)] which found that disorder could induce a finite thermal conductivity at low temperatures, we find no evidence of a finite temperature transition in conducting properties. Instead, we find that at low temperatures, small system size transport properties are dominated by disorder but the asymptotic system size dependence of current is given by the usual FPU result J ~ 1/N^{2/3}. We also present new interesting results on the binary-mass ordered FPU chain.

cond-mat.dis-nn↗

arXiv2008

Heat transport in ordered harmonic lattices

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N to infinity. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.

cond-mat.stat-mech↗

arXiv2008

Effect of phonon-phonon interactions on localization

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J~1/N dependence, implying diffusive transport of energy.

cond-mat.dis-nn↗

arXiv2008

Fluctuation theorem in quantum heat conduction

We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat, $Q$, flowing across the oscillator in a time interval $τ$ is a stochastic variable and we study the probability distribution function $P(Q)$. In the large $τ$ limit we use the formalism of full counting statistics (FCS) to compute the generating function of $P(Q)$ exactly. We show that $P(Q)$ satisfies the steady state fluctuation theorem (SSFT) regardless of the specifics of system, and it is nongaussian with clear exponential tails. The effect of finite $τ$ and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain predictions of universal heat current fluctuations at low temperatures in clean wires.

cond-mat.stat-mech↗

arXiv2007

Driving particle current through narrow channels using classical pump

We study a symmetric exclusion process in which the hopping rates at two chosen adjacent sites vary periodically in time and have a relative phase difference. This mimics a colloidal suspension subjected to external space and time dependent modulation of the diffusion constant. The two special sites act as a classical pump by generating an oscillatory current with a nonzero ${\cal DC}$ value whose direction depends on the applied phase difference. We analyze various features in this model through simulations and obtain an expression for the $\cal{DC}$ current via a novel perturbative treatment.

cond-mat.stat-mech↗

arXiv2007

Local Temperature and Universal Heat Conduction in FPU chains

It is shown numerically that for Fermi Pasta Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N^(1/3), relevant for the much debated question of the universality of one dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.

cond-mat.stat-mech↗

arXiv2007

Equilibration problem for the generalized Langevin equation

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions necessary for equilibration for the case when the system potential is harmonic. We then give an example with a particular bath where we show that, even for parameter values where the harmonic case always equilibrates, with any finite amount of nonlinearity the system does not equilibrate for arbitrary initial conditions. We understand this as a consequence of the formation of nonlinear localized excitations similar to the discrete breather modes in nonlinear lattices.

cond-mat.stat-mech↗

arXiv2007

Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs

We present an extension of the work of D'Amato and Pastawski on electron transport in a one-dimensional conductor modeled by the tight binding lattice Hamiltonian and in which inelastic scattering is incorporated by connecting each site of the lattice to one-dimensional leads. This model incorporates Büttiker's original idea of dephasing probes. Here we consider finite temperatures and study both electrical and heat transport across a chain with applied chemical potential and temperature gradients. Our approach involves quantum Langevin equations and nonequilibrium Green's functions. In the linear response limit we are able to solve the model exactly and obtain expressions for various transport coefficients. Standard linear response relations are shown to be valid. We also explicitly compute the heat dissipation and show that for wires of length $N >> \ell$, where $\ell$ is a coherence length scale, dissipation takes place uniformly along the wire. For $N << \ell$, when transport is ballistic, dissipation is mostly at the contacts. In the intermediate range between Ohmic and ballistic transport we find that the chemical potential profile is linear in the bulk with sharp jumps at the boundaries. These are explained using a simple model where the left and right moving electrons behave as persistent random walkers.

cond-mat.mes-hall↗

arXiv2007

Two simple models of classical heat pumps

Motivated by recent studies on models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.

cond-mat.stat-mech↗

arXiv2006

Non-equilibrium work fluctuations for oscillators in non-Markovian baths

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic oscillators indicate that the validity of these nonequilibrium theorems do not depend on the memory of the bath. We find that the JE and the CT are valid under many oscillator potentials and driving forces whereas the TFT fails when the driving force is asymmetric in time and the potential is asymmetric in position.

cond-mat.stat-mech↗

arXiv2006

Heat conduction in a confined solid strip: Response to external strain

We study heat conduction in a system of hard disks confined to a narrow two dimensional channel. The system is initially in a high density solid-like phase. We study, through nonequilibrium molecular dynamics simulations, the dependence of the heat current on an externally applied elongational strain. The strain leads to deformation and failure of the solid and we find that the changes in internal structure can lead to very sharp changes in the heat current. A simple free-volume type calculation of the heat current in a finite hard-disk system is proposed. This reproduces some qualitative features of the current-strain graph for small strains.

cond-mat.stat-mech↗

arXiv2006

Non-equilibrium Green's function formalism and the problem of bound states

The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density for the continuum states, we find that it does not lead, in the absence of any additional mechanisms for equilibration, to a unique expression for the density matrix of any bound states which may be present. Introducing some auxiliary reservoirs which are very weakly coupled to the system leads to a density matrix which is unique in the equilibrium situation, but which depends on the details of the auxiliary reservoirs in the non-equilibrium case.

cond-mat.mes-hall↗

arXiv2005

Work distribution functions for hysteresis loops in a single-spin system

We compute the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. Using Glauber dynamics we perform Monte-Carlo simulations to find the work distributions at different driving rates. We find that in general the work-distributions are broad with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates are studied analytically. We verify that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.

cond-mat.stat-mech↗

arXiv2005

Classical limit of master equation for harmonic oscillator coupled to oscillator bath with separable initial conditions

The equation for the Wigner function describing the reduced dynamics of a single harmonic oscillator, coupled to an oscillator bath, was obtained by Karrlein and Grabert [Phys. Rev. E, vol. 55, 153 (1997)]. It was shown that for some special correlated initial conditions the equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [J. Chem Phys., vol. 64, 124 (1976)]. However for separable initial conditions the Adelman equations were not recovered. We resolve this problem by showing that, for separable initial conditions, the classical Langevin equation obtained from the oscillator bath model is somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that it exactly matches the classical limit of the equation for the Wigner function obtained from the master equation for separable initial conditions. We also discuss why the special correlated initial conditions correspond to Adelman's solution.

cond-mat.stat-mech↗

arXiv2005

Heat Conduction in two-dimensional harmonic crystal with disorder

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size (L) dependence of the heat current (J). For white noise heat baths we find that J ~ 1/L^a with $ a \approx 0.59 $ while correlated noise heat baths gives $ a \approx 0.51 $. A special case with correlated disorder is studied analytically and gives a=3/2 which agrees also with results from exact numerics.

cond-mat.dis-nn↗