Navinder Singh

TWO-TEMPERATURE MODEL OF NONEQUILIBRIUM ELECTRON RELAXATION: A REVIEW

The present paper is a review of the phenomena related to nonequilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann–Bloch–Peierls kinetic equation has been applied to study the ultra-fast (femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro- and nano-scale electronic technology. The aim of this paper is to clarify the TTM, conditions of its validity and nonvalidity, its modifications for nano-systems, to sum-up the progress, and to point out open problems in this field. We also give a phenomenological integro-differential equation for the kinetics of nondegenerate electrons that goes beyond the TTM.

Non-Hermitean Wishart random matrices "I…

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex, and real-quaternion) stochastic time series representing two “remote” complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great emphasis is placed on an asymptotic analysis of the mean eigenvalue density for which we derive, among other results, a complex-plane analog of the Marcenko–Pastur law. A surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out.

Generalized Drude scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result

Abstract An explicit perturbative computation of the Mori’s memory function was performed by Götze and Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case of electron-impurity and electron-phonon scattering in metals by assuming constant electronic density of states at the Fermi energy. In the present investigation, we go beyond this assumption and extend the GW formalism to the case in which there is a gap around the Fermi surface in electron density of states. The resulting GDS is compared with a recent one by Sharapov and Carbotte (SC) obtained through a different route. We find good agreement between the two at finite frequencies. However, we find discrepancies in the dc scattering rate. These are due to a crucial assumption made in SC namely ω ≫ | Σ(ϵ + ω) − Σ∗(ϵ) |. No such high frequency assumption is made in the memory function based technique.

Infrared properties of cuprates in the pseudogap state: a study of Mitrovic-Fiorucci and Sharapov-Carbotte scattering rates

The frequency dependent scattering rate of generalized Drude model contains important information on the electronic structure and on scattering mechanism. In the present investigation, we study the frequency dependent scattering rate of cuprates (Mitrović-Fiorucci/Sharapov-Carbotte scattering rate) in the pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ) density of states. First, with the energy dependent density of states, the scattering rate shows a depression at low energy coming from the opening of the pseudogap. Second, the evolution of 1/τ(ω,T) with temperature shows the observed increase in scattering rate with temperature at lower frequencies and the temperature independence of 1 /τ(ω) at higher frequencies. Third, the signature of the thresholds due to the boson density of states and to the electronic density of states are also observed. These signatures are qualitatively in accord with the experiments.

Efficient computational approach to the non-Markovian second order quantum master equation: electronic energy transfer in model photosynthetic systems

An efficient numerical algorithm for solving the time-non-local non-Markovian master equation in the second Born approximation with exponentially decaying bath correlation function is introduced. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. As an application we consider the traditional dimer system that is used to model excitation energy transfer in photosynthetic systems, examining exact second order results and using them to assess the range of validity of the traditional Markov approximation. The method is also used to examine the dependence of the dynamics on the initial coherences in the case of two coupled oscillators. The computational results are augmented by a set of analytic inequalities obtained for the regime of validity of the Markov approximation in the cases of weak and strong resonance coupling, allowing for a rapid determination of the utility of the Markovian dynamics in various parameter regions.

Electronic energy transfer in model photosynthetic systems: Markovian vs. non-Markovian dynamics

A simple numerical algorithm for solving the non-Markovian master equation in the second Born approximation is developed and used to propagate the traditional dimer system that models electronic energy transfer in photosynthetic systems. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to access the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second-order approximation is useful. For example, the use of Redfield theory for lambda > 10 cm(-1) in Fenna-Mathews-Olson (FMO) type systems is shown to be fundamentally inaccurate.

Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.

Moment expansion to the memory function for generalized Drude scattering rate

Abstract The memory function formalism is an important tool to evaluate the frequency dependent electronic conductivity. It is previously used within some approximations in the case of electrons interacting with various other degrees of freedom in metals with great success. However, one needs to go beyond those approximations as the interaction strengths become stronger. In this work, we propose a systematic expansion of the memory function involving its various moments. We calculate the higher order contribution to the generalized Drude scattering rate in case of electron–impurity interactions. Further we compare our results with the results from previously studied lowest order calculations. We find larger contributions from the higher moments in the low frequency regime and also in the case of larger interaction strength.

Theory of the dynamical thermal conductivity of metals

The Moris projection method, known as the memory function method, is an important theoretical formalism to study various transport coefficients. In the present work, we calculate the dynamical thermal conductivity in the case of metals using the memory function formalism. We introduce thermal memory functions for the first time and discuss the behavior of thermal conductivity in both the zero frequency limit and in the case of nonzero frequencies. We compare our results for the zero frequency case with the results obtained by the Bloch-Boltzmann kinetic approach and find that both approaches agree with each other. Motivated by some recent experimental advancements, we obtain several new results for the ac or the dynamical thermal conductivity.

Hot-electron relaxation in metals within the Götze–Wölfle memory function formalism

We consider nonequilibrium relaxation of electrons due to their coupling with phonons in a simple metal. In our model, electrons are living at a higher temperature than that of the phonon bath, mimicking a nonequilibrium steady-state situation. We study the relaxation of such hot electrons proposing a suitable generalization of the memory function formalism formulated by Gotze and Wolfle (GW) [W. Gotze and P. Wolfle, Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for both the DC or zero frequency scattering rates and the optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies. An interesting feature that the DC scattering rate at high temperatures and optical scattering rate at high frequencies are independent of the temperature difference between the electrons and the phonons is found in this study. The present formalism forms a basis which can also be extended to study hot-electron relaxation in variety of complex mate...