arXiv subjects

Roberto D'Agosta

Publications and source records attributed to Roberto D'Agosta.

At least 37 records · Page 2Linked to original sources

arXiv2015

Interaction as stochastic noise

Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is often insufficient when not the restraining factor. Many strategies have been devised to control particle-particle interaction and explore the diverse regimes, from weak to strong interaction. Beautiful examples of these achievements are the experiments on Bose condensates, or the recent experiments on the dynamics of spin chains. Here I introduce another possibility, namely replacing the particle-particle interaction with an external stochastic field, and once again reducing the dynamics of a many-body system to the dynamics of single-particle systems. The theory is exact, in the sense that no approximations are introduced in decoupling the many-body system in its non-interacting sub-parts. Moreover, the equations of motion are linear, and no unknown external potential is inserted.

quant-ph↗

arXiv2014

Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation

Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.

cond-mat.stat-mech↗

arXiv2014

Classical to quantum transition of near-field heat transfer between two nanoparticles

Heat transfer between two silica clusters is investigated by using the non-equilibrium Green's function method. In the gap range between 4 Å and three times the cluster size, the thermal conductance decreases as predicted by the surface charge-charge interaction. Above five times the cluster size, the volume dipole-dipole interaction predominates. Finally, when the distance becomes smaller than 4 Å, a quantum interaction where the electrons of both clusters are shared takes place. This quantum interaction leads to the dramatic increase of the thermal coupling between neighbor clusters due to strong interactions. This study finally provides a description of the transition between radiation and heat conduction in gaps smaller than a few nanometers.

cond-mat.mes-hall↗

arXiv2013

Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

cond-mat.mtrl-sci↗

arXiv2012

Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices

Research on thermoelectrical energy conversion, the reuse of waste heat produced by some mechanical or chemical processes to generate electricity, has recently gained some momentum. The calculation of the electronic parameters entering the figure of merit of this energy conversion, and therefore the discovery of efficient materials, is usually performed starting from the Landauer's approach to quantum transport coupled with the Onsager's linear response theory. As it is well known, that approach suffers of certain serious drawbacks. Here, we discuss alternative dynamical methods that can go beyond the validity of the Landauer's/Onsager's approach for electronic transport. They can be used to validate the predictions of the Landauer's/Onsager's approach and to investigate systems for which that approach has shown to be unsatisfactory.

cond-mat.mes-hall↗

arXiv2012

A stochastic approach to open quantum systems

Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somehow bigger system, an environment, that is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In Physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion etc. In this review, we will focus on the so-called stochastic Schrödinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some details the general derivation of a stochastic Schrödinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.

cond-mat.stat-mech↗

arXiv2012

Enhanced thermoelectric properties in hybrid graphene-boron nitride nanoribbons

The thermoelectric properties of hybrid graphene-boron nitride nanoribbons (BCNNRs) are investigated using the non-equilibrium Green's function (NEGF) approach. We find that the thermoelectric figure of merit (ZT) can be remarkably enhanced by periodically embedding hexagonal BN (h-BN) into graphene nanoribbons (GNRs). Compared to pristine GNRs, the ZT for armchair-edged BCNNRs with width index 3p+2 is enhanced up to 10~20 times while the ZT of nanoribbons with other widths is enhanced just by 1.5~3 times. As for zigzag-edge nanoribbons, the ZT is enhanced up to 2~3 times. This improvement comes from the combined increase in the Seebeck coefficient and the reduction in the thermal conductivity outweighing the decrease in the electrical conductance. In addition, the effect of component ratio of h-BN on the thermoelectric transport properties is discussed. These results qualify BCNNRs as a promising candidate for building outstanding thermoelectric devices.

cond-mat.mes-hall↗

arXiv2009

Comment on ``Time-dependent current-density functional theory for generalized open quantum systems" by J. Yuen-Zhou, C. Rodriiguez-Rosario and A. Aspuru-Guzik

We comment on a recent paper by Yuen-Zhou et al. [ Phys. Chem. Chem. Phys. 2009, 11, 4509 ] which extends some of the results of Time-Dependent Current Density Functional Theory applied to open quantum systems. Besides pointing out some incorrect statements in the theorems, we show that in the proof of the main result of the paper an arbitrary condition is introduced. Moreover, we argue that, since this condition has not a physical origin, one can find two systems with different vector potentials that lead to the same dynamics of the physical quantities of interest, the current and particle densities.

cond-mat.mes-hall↗

arXiv2008

Local electron and ionic heating effects on the conductance of nanostructures

Heat production and dissipation induced by current flow in nanostructures is of primary importance to understand the stability of these systems. These effects have contributions from both electron-phonon and electron-electron interactions. Here, we consider the effect of the local electron and ionic heating on the conductance of nanoscale systems. Specifically we show that the non-linear dependence of the conductance on the external bias may be used to infer information about the local heating of both electrons and ions. We compare our results with available experimental data on transport in $\mathrm{D}_2$ and $\mathrm{H}_2$ molecules. The comparison between experiment and theory is reasonably good close to the lowest phonon mode of the molecule, especially for the $\mathrm{D}_2$ molecule. At higher biases we cannot rule out the presence of other effects like, e.g., current-induced forces that make the scenario more complex.

cond-mat.str-el↗

arXiv2007

Stochastic Time-Dependent Current-Density-Functional Theory

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state $|Ψ_0>$ and the particle-bath interaction operator, two external vector potentials ${\bf A}({\bf r},t)$ and ${\bf A}'({\bf r},t)$ that produce the same ensemble-averaged current density, $\bar{{\bf j}({\bf r},t)}$, must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.

cond-mat.mes-hall↗

arXiv2007

Electronic viscosity in a quantum well: A test for the local density approximation

In the local density approximation (LDA) for electronic time-dependent current-density functional theory (TDCDFT) many-body effects are described in terms of the visco-elastic constants of the homogeneous three-dimensional electron gas. In this paper we critically examine the applicability of the three-dimensional LDA to the calculation of the viscous damping of 1-dimensional collective oscillations of angular frequency $ω$ in a quasi 2-dimensional quantum well. We calculate the effective viscosity $ζ(ω)$ from perturbation theory in the screened Coulomb interaction and compare it with the commonly used three-dimensional LDA viscosity $Y(ω)$. Significant differences are found. At low frequency $Y(ω)$ is dominated by a shear term, which is absent in $ζ(ω)$. At high frequency $ζ(ω)$ and $Y(ω)$ exhibit different power law behaviors ($ω^{-3}$ and $ω^{-5/2}$ respectively), reflecting different spectral densities of electron-hole excitations in two and three dimensions. These findings demonstrate the need for better approximations for the exchange-correlation stress tensor in specific systems where the use of the three-dimensional functionals may lead to unphysical results.

cond-mat.mes-hall↗

arXiv2007

Local electron heating in nanoscale conductors

The electron current density in nanoscale junctions is typically several orders of magnitude larger than the corresponding one in bulk electrodes. Consequently, the electron-electron scattering rate increases substantially in the junction. This leads to local electron heating of the underlying Fermi sea in analogy to the local ionic heating that is due to the increased electron-phonon scattering rates. We predict the bias dependence of local electron heating in quasi-ballistic nanoscale conductors, its effect on ionic heating, and discuss possible experimental tests of our results.

cond-mat.mes-hall↗

arXiv2007

Hydrodynamic approach to transport and quantum turbulence in nanoscale conductors

The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in nanoscale systems. In particular, we show that the electron flow in nanoscale conductors can be described by Navier-Stokes type of equations with an effective electron viscosity, i.e., on a par with the dynamics of a viscous and compressible classical fluid. By using this hydrodynamic approach we derive the conditions for the transition from laminar to turbulent flow in nanoscale systems and discuss possible experimental tests of our predictions.

cond-mat.str-el↗

arXiv2005

Relaxation in time-dependent current-density functional theory

We apply the time-dependent current-density functional theory to the study of the relaxation of a closed many-electron system evolving from an non-equilibrium initial state. We show that the self-consistent unitary time evolution generated by the time dependent exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system is related to the entropy production in the real system.

cond-mat.mes-hall↗

arXiv2005

On the non-V-representability of currents in time-dependent many particle systems

We argue that an arbitrarily chosen time-dependent current density is generically non-Vrepresentable in a many-particle system, i.e., it cannot be obtained by applying only a time dependent scalar potential to the system. Furthermore we show by a concrete example that even a current that is V-representable in an interacting many-particle system may (and in general will) turn out to be non-V-representable when the interaction between the particles is turned off.

cond-mat.mes-hall↗

arXiv2004

Temperature Dependence of the Tunneling Amplitude between Quantum Hall Edges

Recent experiments have studied the tunneling current between the edges of a fractional quantum Hall liquid as a function of temperature and voltage. The results of the experiment are puzzling because at "high" temperature (600-900 mK) the behavior of the tunneling conductance is consistent with the theory of tunneling between chiral Luttinger liquids, but at low temperature it strongly deviates from that prediction dropping to zero with decreasing temperature. In this paper we suggest a possible explanation of this behavior in terms of the strong temperature dependence of the tunneling amplitude.

cond-mat.mes-hall↗

arXiv2003

Electrical transport properties of bidimensional electron liquids in the presence of a high magnetic field

In this thesis we derive a hydrodynamical model to describe the dynamics of density excitations localized at the edges of a Quantum Hall bar. In particular we show that the chiral Luttinger liquid model for the edges excitations can be derived from the coarse-graining and a lowest Landau level projection procedure without reference to the Quantum Hall effect. We use this model to calculate the Landauer-Buettiker conductances in generic experimental setups. In the absence of tunneling the ideal Hall conductance is recovered. When the tunneling between the edges is explicitely taken into account we obtain expressions for the corrections to the ideal conductance. We discuss our result vis-a-vis recent experiments in the weak tunneling regime and previous theoretical models.

cond-mat.mes-hall↗

arXiv2003

Transport properties of a two-dimensional electron liquid at high magnetic field

The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors $ν<1$ -- without reference to the quantum Hall effect. Based on this model, we develop a formalism to calculate the Landauer-Büttiker conductances in generic experimental set-ups including multiple leads and voltage probes. In the absence of tunneling between the edges the "ideal" Hall conductances ($G_{ij}= \frac{e^2 ν}{h}$ if lead $j$ is immediately upstream of lead $i$, and $G_{ij}=0$ otherwise) are recovered. Tunneling of quasiparticles of fractional charge $e^*$ between different edges is then included as an additional term in the Hamiltonian. In the limit of weak tunneling we obtain explicit expressions for the corrections to the ideal conductances. As an illustration of the formalism we compute the current- and temperature-dependent resistance $R_{xx}(I,T)$ of a quantum point contact localized at the center of a gate-induced constriction in a quantum Hall bar. The exponent $α$ in the low-current relation $R_{xx}(I,0) \sim I^{α-2}$ shows a nontrivial dependence on the strength of the inter-edge interaction, and its value changes as $e^*V_H$, where $V_H = \frac{h I}{νe^2}$ is the Hall voltage, falls below a characteristic crossover energy $\frac{\hbar c}{d}$, where $c$ is the edge wave velocity and $d$ is the length of the constriction. The consequences of this crossover are discussed vis-a-vis recent experiments in the weak tunneling regime.

cond-mat.mes-hall↗