Response function analysis of excited-state kinetic energy functional constructed by splitting k-space

Over the past decade, fundamentals of time independent density functional theory for excited state have been established. However, construction of the corresponding energy functionals for excited states remains a challenging problem. We have developed a method for constructing functionals for excited states by splitting k-space according to the occupation of orbitals. In this paper we first show the accuracy of kinetic energy functional thus obtained. We then perform a response function analysis of the kinetic energy functional proposed by us and show why method of splitting the k-space could be the method of choice for construction of energy functionals for excited states.Comment: 11 page

On the compatibility of causality and symmetry (Comments on "Analysis of causality in time-dependent density functional theory")

It is argued that there exists the only one inverse of the linear response function $\chi$, i.e. $\chi^{-1}$, which depends symmetrically of its spatial-times variables, see M.K. Harbola, and A. Banerjee, Phys. Rev. A {\bf 60}, 5101 (1999). Some brief comments on this consideration are presented. We show instead, that it is possible to construct the causal inverse also. At the same time we confirm the main statement of M.K. Harbola and A. Banerjee that in fact there is no contradiction between the symmetry and causality.Comment: 4 pages, LaTe

Multiple Core-Hole Coherence in X-Ray Four-Wave-Mixing Spectroscopies

Correlation-function expressions are derived for the coherent nonlinear response of molecules to three resonant ultrafast pulses in the x-ray regime. The ability to create two-core-hole states with controlled attosecond timing in four-wave-mixing and pump probe techniques should open up new windows into the response of valence electrons, which are not available from incoherent x-ray Raman and fluorescence techniques. Closed expressions for the necessary four-point correlation functions are derived for the electron-boson model by using the second order cumulant expansion to describe the fluctuating potentials. The information obtained from multidimensional nonlinear techniques could be used to test and refine this model, and establish an anharmonic oscillator picture for electronic excitations

Optimal protocols for Hamiltonian and Schr\"odinger dynamics

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schr\"odinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations of the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.Comment: submitted to J. Stat. Mech.: Theor. Exp

Quantum master equation for electron transport through quantum dots and single molecules

A quantum master equation (QME) is derived for the many-body density matrix of an open current-carrying system weakly coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of number of electrons in the system. We show that coherences between system states with different number of electrons, n, (Fock space coherences) do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order or faster then the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation (when the damping is slow compared to the Bohr frequencies of the system), the dynamics of populations and the coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.Comment: 22 pages, 8 figures, paper accepted in Phys. Rev.

Model for Glass Transition in a Binary fluid from a Mode Coupling approach

We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The resulting model equations are solved in the long time limit to locate the dynamic transition. The transition point from our model is considerably higher than predicted in existing MCT models for binary systems. This is in agreement with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure

Periodic Travelling Waves in Dimer Granular Chains

We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist

Dynamic image potential at an Al(111) surface

We evaluate the electronic self-energy Sigma(E) at an Al(111) surface using the GW space-time method. This self-energy automatically includes the image potential V-im not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure

A self-consistent quantum master equation approach to molecular transport

We propose a self-consistent generalized quantum master equation (GQME) to describe electron transport through molecular junctions. In a previous study [M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a time-nonlocal GQME to cure the lack of broadening effects in Redfield theory. To do so, the free evolution used in the Born-Markov approximation to close the Redfield equation was replaced by a standard Redfield evolution. In the present paper, we propose a backward Redfield evolution leading to a time-local GQME which allows for a self-consistent procedure of the GQME generator. This approach is approximate but properly reproduces the nonequilibrium steady state density matrix and the currents of an exactly solvable model. The approach is less accurate for higher moments such as the noise.Comment: 9 pages, 4 figure