arXiv subjects

Dibyendu Roy

Publications and source records attributed to Dibyendu Roy.

69 records · Page 4Linked to original sources

arXiv2010

Symmetric and asymmetric charge transport in interacting asymmetric quantum impurities

We study steady-state charge transfer across an interacting resonance-level model connected asymmetrically to two leads. For a linear energy dispersion relation of the leads, we calculate current-voltage characteristics of the model exactly employing the scattering Bethe-Ansatz of Mehta-Andrei and find symmetric transport showing the absence of diode effect. Next we study a lattice version of this model with a nonlinear dispersion for the leads using the Lippmann-Schwinger scattering theory. We find that the inclusion of nonlinearity in the leads' dispersion causes rectification for asymmetric junctions but does not rectify for asymmetric interactions and perfect junctions. The model in the latter case can be mapped into a model of a single noninteracting electron in higher dimensions.

cond-mat.mes-hall↗

arXiv2009

Thermoelectric phenomena in disordered open quantum systems

Using a stochastic quantum approach, we study thermoelectric transport phenomena at low temperatures in disordered electrical systems connected to external baths. We discuss three different models of one-dimensional disordered electrons, namely the Anderson model of random on-site energies, the random-dimer model and the random-hopping model - also relevant for random-spin models. We find that although the asymptotic behavior of transport in open systems is closely related to that in closed systems for these noninteracting models, the magnitude of thermoelectric transport strongly depends on the boundary conditions and the baths spectral properties. This shows the importance of employing theories of open quantum systems in the study of energy transport.

cond-mat.dis-nn↗

arXiv2009

Heat transport and phonon localization in mass-disordered harmonic crystals

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 Fourier's law while the two dimensional system is a heat insulator. We also investigate the inverse participation ratio of different normal modes.

cond-mat.dis-nn↗

arXiv2009

Two mesoscopic models of two interacting electrons

We study two simple mesoscopic models of interacting two electrons; first one consists of two quantum coherent parallel conductors with long-range Coulomb interaction in some localized region and the other is of an interacting quantum dot (QD) side-coupled to a noninteracting quantum wire. We evaluate exact two-particle scattering matrix as well as two-particle current which are relevant in a two-particle scattering experiment in these models. Finally we show that the on-site repulsive interaction in the QD filters out the spin-singlet two-electron state from the mixed two-electron input states in the side-coupled QD model.

quant-ph↗

arXiv2009

Nonequilibrium charge transport in an interacting open system: two-particle resonance and current asymmetry

We use Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry we find that the two-particle current is quite different depending on whether the electrons are incident from the left lead or the right lead.

cond-mat.mes-hall↗

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

Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations

Based on the classical Langevin equation, we have re-visited the problem of orbital motion of a charged particle in two dimensions for a normal magnetic field crossed with or without an in-plane electric bias. We are led to two interesting fluctuation effects: First, we obtain not only a longitudinal "work-fluctuation" relation as expected for a barotropic type system, but also a transverse work-fluctuation relation perpendicular to the electric bias. This "Hall fluctuation" involves the product of the electric and the magnetic fields. And second, for the case of harmonic confinement without bias, the calculated probability density for the orbital magnetic moment gives non-zero even moments, not derivable as field derivatives of the classical free energy.

cond-mat.mes-hall↗

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 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

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.

cond-mat.stat-mech↗

arXiv2008

Decohering d-dimensional quantum resistance

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a 1-dimensional disordered conductor, where decoherence is introduced at par with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent re-injection into the conductor. This is essentially in the spirit of B{ü}ttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the 4-probe resistance in the presence of decoherence is then generalised from the 1-dimensional to the d-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitatively new result is that arbitrarily small decoherence reduces the localisation-delocalisation transition to a crossover making resistance moments of all orders finite.

cond-mat.mes-hall↗

arXiv2007

Electron transport in an open mesoscopic metallic ring

We study electron transport in a normal-metal ring modeled by the tight binding lattice Hamiltonian, coupled to two electron reservoirs. First, Buttiker's model of incorporating inelastic scattering, hence decoherence and dissipation, has been extended by connecting each site of the open ring to one-dimensional leads for uniform dephasing in the ring threaded by magnetic flux. We show with this extension conductance remains symmetric under flux reversal, and Aharonov-Bohm oscillations with changing magnetic flux reduce to zero as a function of the decoherence parameter, thus indicating dephasing in the ring. This extension enables us to find local chemical potential profiles of the ring sites with changing magnetic flux and the decoherence parameter analogously to the four probe measurement. The local electrochemical potential oscillates in the ring sites because of quantum-interference effects. It predicts that measured four-point resistance also fluctuates and even can be negative. Then we point out the role of the closed ring's electronic eigenstates in the persistent current around Fano antiresonances of an asymmetric open ring for both ideal leads and tunnel barriers. Determining the real eigenvalues of the non-Hermitian effective Hamiltonian of the ring, we show that there exist discrete bound states in the continuum of scattering states for the asymmetric ring even in the absence of magnetic flux. Our approach involves quantum Langevin equations and non-equilibrium Green's functions.

cond-mat.mes-hall↗

arXiv2007

Random-phase reservoir and a quantum resistor: The Lloyd model

We introduce phase disorder in a 1D quantum resistor through the formal device of `fake channels' distributed uniformly over its length such that the out-coupled wave amplitude is re-injected back into the system, but with a phase which is random. The associated scattering problem is treated via invariant imbedding in the continuum limit, and the resulting transport equation is found to correspond exactly to the Lloyd model. The latter has been a subject of much interest in recent years. This conversion of the random phase into the random Cauchy potential is a notable feature of our work. It is further argued that our phase-randomizing reservoir, as distinct from the well known phase-breaking reservoirs, induces no decoherence, but essentially destroys all interference effects other than the coherent back scattering.

cond-mat.mes-hall↗

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↗