Statistical Mechanics. — A Set of Lectures

Plasmons and magnetoplasmons in semiconductor heterostructures

The circuit formed by a nanoscale tunnel junction in series with a capacitance and a voltage source is the building block of most multi-junction circuits of single electronics. The state of this “single electron box” is entirely determined by the numbern of extra electrons on the intermediate “island” electrode between the junction and the capacitance. We have fabricated such a system and measured the charge on the junction capacitance, which is directly related to the average value ofn, as a function of the bias voltage using a Fulton-Dolan electrometer. At low temperature, the junction charge followed thee-periodic sawtooth function expected from the theory of macroscopic charge quantization. Strikingly,e-periodic variations were also observed when the box was superconducting. The thermal rounding of the sawtooth function is well explained by a simple model, except at the lowest temperatures.

Direct Observation of Macroscopic Charge Quantization

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.

https://home.icts.res.in/~abhi/Papers/31-harmlatt-I.pdf

Heat Transport in Harmonic Lattices

In this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices. The result is of relevance to the solution of a variety of problems in mathematics and physics. As an example, the formula is used to derive an exact analytical solution for the one-dimensional discrete Poisson equation with Dirichlet boundary conditions.

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Analytical inversion of symmetric tridiagonal matrices

A heteroquantum‐dots (HQD) model for hydrogenated nanocrystalline silicon films (nc‐Si:H) is proposed. The main features of our model are as follows. (i) the nanocrystalline grains and the amorphous counterparts in which they are embedded have very different band gap and band structures. As a result, they form heterojunctionlike structures in the interface regions, where the band offset effects dramatically reduce the activation energy and the grains act like quantum dots. (ii) In the presence of an external field, the activated electrons in the quantum dots conduct via quantum tunneling through the interface barriers. By means of the HQD model, we have identified the conduction of nc‐Si:H as a thermal‐assisted tunneling process. Our results show that there are two distinct regimes for the conductivity of nc‐Si:H: (i) the low‐temperature regime, where there is a simple activation energy ΔE; (ii) the high‐temperature regime, where ΔE is effectively enhanced by the temperature effect of the electronic tunne...

/pdf/electronic-conductivity-of-hydrogenated-nanocrystalline-5ajzki1uuo.pdf

Electronic conductivity of hydrogenated nanocrystalline silicon films

Calcul analytique des elements de matrice coulombienne d'un systeme quasi-unidimensionnel en utilisant un modele de potentiel de confinement harmonique L'interaction coulombienne intra-sous bande conserve le comportement divergeant de type logarithmique, typique du systeme purement unidimensionnel a la limite des grandes longueurs d'onde, tandis que l'interaction coulombienne inter-sous bande approche des valeurs discretes dependantes des sous-bandes concernees

Electron-electron interactions in quasi-one-dimensional electron systems.

We treat the quantum transport of an interacting system of electrons, impurities, and phonons, in a time-dependent electric field, by using the quantum generalized Langevin equation (GLE), in which the system is shown to be equivalent to a quantum particle in a heat bath. We follow here the philosophy of Ford, Lewis, and O'Connell, who have demonstrated the usefulness of the GLE approach to heat-bath problems. The center of mass of the electrons acts like a quantum particle, while the relative electrons and phonons play the role of heat bath. They are coupled through the electron-impurity and electron-phonon interactions. After eliminating the heat-bath variables, the equation of motion for the quantum particle is written in a form of a quantum generalized Langevin equation, with a memory term which reflects the retarded effects of the heat bath on the quantum particle. The evaluation of the memory term immediately leads to a result for the susceptibility from which we can calculate the conductivity directly, in contrast to Kubo-type calculations which require the evaluation of correlation functions as an intermediate step. As a demonstration of the directness of our approach, we show that the usual random-phase-approximation conductivity results are easily derived. In addition, we derive an expression for the memory function, which incorporates higher-order electron-impurity scattering.

G. Y. Hu

Papers

Analytical inversion of symmetric tridiagonal matrices

Electronic conductivity of hydrogenated nanocrystalline silicon films

Electron-electron interactions in quasi-one-dimensional electron systems.

Quantum transport for a many-body system using a quantum Langevin-equation approach.

Exact solution for the charge soliton in a one-dimensional array of small tunnel junctions.