arXiv subjects

Navinder Singh Bathinda

Publications and source records attributed to Navinder Singh Bathinda.

71 records · Page 4Linked to original sources

arXiv2013

A toy model for the pseudogap state of cuprates

A toy model is developed to capture "dance of pre-formed pairs" in the pseudogap state of high temperature cuprate superconductors. The model is a crude description of a hypothetical situation in which spin-driven spatial organization of the pre-formed pairs is analyzed. Within a mean-field theory (a slight generalization of Bragg-Williams theory) we examined the behaviour of heat capacity and an "order parameter" which captures the short range correlations between the pre-formed pairs. Below a transition temperature these short range correlations enhance and leads to a long range order (spin-density wave). This is examined through the breakdown of statistical independence.

cond-mat.supr-con↗

arXiv2012

Charge dynamics in an ideal cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$: optical conductivity from Yang-Rice-Zhang ansatz

We theoretically investigate charge dynamics in weakly coupled $CuO_2$ planes of the cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$ (CNCOC) using Kubo formula for optical conductivity in the underdoped regime. The spectral function needed in Kubo formula is obtained from an analytical form of electron Green's function proposed (ansatz) by Yang-Rice-Zhang (YRZ) for the underdoped cuprates based on their previous renormalized mean field theory and on the investigations of weakly coupled Hubbard ladders. Although to an unaided eye the results of the numerical calculation look very similar to that found experimentally in [K. Waku etal. 2004] but a careful examination with extended Drude formalism shows that YRZ ansatz for the calculation of optical conductivity is not sufficient to understand the charge dynamics in $CuO_2$ planes of the cuprate CNCOC. More physics is needed especially electromagnetic response from bound charges.

cond-mat.supr-con↗

arXiv2012

Quantum effects in biology: master equation studies of exciton motion in photosynthetic systems

The present review is devoted to our recent studies on the excitonic motion in photosynthetic systems. In photosynthesis, the light photon is absorbed to create an exciton in the antenna complex of the photosynthetic pigments. This exciton then migrates along the chain-biomolecules, like FMO complex, to the reaction centre where it initiates the chemical reactions leading to biomass generation. Recently, it has been experimentally observed that the exciton motion is highly quantum mechanical in nature i.e., it involve long time ($\sim 600$ femto sec) quantum coherence effects. Traditional semiclassical theories like Forrester's and second Born master equations cannot be applied. We point out why the 2nd Born non-Markovian master equation and its Markovian limit (also called the Redfield master equation) cannot be used to explain the observed long coherences. Briefly, the reason is that these approaches are perturbative in nature and in real light harvesting systems various couplings (system-system and system-bath) are of the similar order of magnitude. Various new approaches are being developed to go beyond the above two limiting theories. The present review is not a review in the usual sense of the word as we summarize our own approaches and only refer to the literature for the other ones. A brief introduction to the sophisticated 2D photon echo spectroscopy is also given at the end with an emphasis on the underlying physics of the multidimensional echo spectroscopies.

cond-mat.stat-mech↗

arXiv2011

Explaining the observed long coherence effects by 2D photon echo experiments in photosynthetic EET : Two-Component Phonon Spectrum model

We propose a simple stochastic model which successfully explains the long coherence effects observed in photosynthetic Excitation Energy Transport (EET) by 2D photon echo experiments of G. S. Engel et. al. (Nature, {\bf 446} 782, (2007)). Our Two-Component Phonon Spectrum (TCPS) model is based upon the division of phonon degrees of freedom into a systematic component which is treated through polaron transformation and a stochastic component which is treated through dynamical disorder. This model successfully explains the observed long coherence upto $ \sim 600 fsec$ in EET experiments.

physics.chem-ph↗

arXiv2011

Phase controllable dynamical localization: a generalization of the Dunlap-Kenkre result

Dunlap-Kenkre result states that Dynamical Localization (DL) of a field driven quantum particle in a discrete periodic lattice happens when the ratio of the field magnitude to the field frequency (say, $η$) of the diagonal sinusoidal drive is a root of the ordinary Bessel function of order 0. This has been experimentally verified. A generalization of the Dunlap-Kenkre result is presented here. We analytically show that if we have an off-diagonal driving field (with modulation $δ$) and diagonal driving field with different frequencies (say $ω_1$ and $ω_2$ respectively) and a definite phase relationship $ϕ$ between them, one can obtain DL if (1) $η$ is a zero of the Bessel function of order 0 and $ϕ$ is an odd multiple of $π/2$ for equal and $\frac{ω_1}{ω_2}= odd integer$ driving frequencies, (2) $η$ is a zero of the Bessel function of order 0 and $ϕ$ is an integer multiple of $π$ including zero for $\frac{ω_1}{ω_2}= even integer \equiv m$, and (3) $ϕ= -\arcsin(\frac{J_0(η)}{δJ_m(η)})$ and $η$ is not a zero of the Bessel function of the even order $m$.

cond-mat.stat-mech↗

arXiv2011

Non-Markovian Second-Order Quantum Master Equation and Its Markovian Limit: Electronic Energy Transfer in Model Photosynthetic Systems

A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the traditional dimer system that models excitation energy transfer in photosynthesis. 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 computationally assess 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 valid. For example, the use of Redfield theory for $λ> 10 \textrm{cm}^{-1}$ in systems like Fenna-Mathews-Olson (FMO) type systems is shown to be in error. In addition, analytic inequalities are obtained for the regime of validity of the Markov approximation in cases of weak and strong resonance coupling, allowing for a quick determination of the utility of the Markovian dynamics in parameter regions. Finally, results for the evolution of states in a dimer system, with and without initial coherence, are compared in order to assess the role of initial coherences.

physics.chem-ph↗

arXiv2011

How and why does statistical mechanics work

As the title says we want to answer the question; how and why does statistical mechanics work? As we know from the most used prescription of Gibbs we calculate the phase space averages of dynamical quantities and we find that these phase averages agree very well with experiments. Clearly actual experiments are not done on a hypothetical ensemble they are done on the actual system in the laboratory and these experiments take a finite amount of time. Thus it is usually argued that actual measurements are time averages and they are equal to phase averages due to ergodicity. Aim of the present review is to show that ergodicity is not relevant for equilibrium statistical mechanics (with Tolman and Landau). We will see that the solution of the problem is in the very peculiar nature of the macroscopic observables and with the very large number of the degrees of freedom involved in macroscopic systems as first pointed out by Khinchin. Similar arguments are used by Landau based upon the approximate property of "Statistical Independence". We review these ideas in detail and in some cases present a critique. We review the role of chaos (classical and quantum) where it is important and where it is not important. We criticise the ideas of E. T. Jaynes who says that the ergodic problem is conceptual one and is related to the very concept of ensemble itself which is a by-product of frequency theory of probability, and the ergodic problem becomes irrelevant when the probabilities of various micro-states are interpreted with Laplace-Bernoulli theory of Probability (Bayesian viewpoint). In the end we critically review various quantum approaches (quantum-statistical typicality approaches) to the foundations of statistical mechanics.

cond-mat.stat-mech↗

arXiv2010

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 analogue of the Marchenko-Pastur law. A surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out.

math-ph↗

arXiv2010

Dynamical fluctuations for periodically driven diffusions

We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium steady regime. We identify a concept called traffic. This traffic, which was introduced in the context of non-equilibrium steady state statistics, is extended here for time-dependent but periodic forces. We discuss the fluctuation functionals of occupations and currents, and work out some specific examples. The connection between these and non-equilibrium thermodynamic potentials, their corresponding variational principles and their Legendre transforms, are also discussed.

cond-mat.stat-mech↗

arXiv2009

Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analyzed in terms of the average work done on the system per cycle. This is in contrast to the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyze the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.

cond-mat.stat-mech↗

arXiv2009

Two-Temperature Model of non-equilibrium electron relaxation: A Review

The present paper is a review of the phenomena related to non-equilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann-Bloch-Peierls (BBP) 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 non-validity, 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 non-degenerate electrons that goes beyond the TTM.

cond-mat.stat-mech↗

arXiv2009

Transverse diffusion induced phase transition in asymmetric exclusion process on a surface

We extend one dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the forward transition probability $p$ is tuned. The signature of the nonequilibrium transition is in the finite size effects near it. The results are compared with similar couplings operative only at the boundary. It is argued that the nature of the phases can be interpreted in terms of the modifications of boundary layers.

cond-mat.stat-mech↗

arXiv2008

Controllable diffusion of cold atoms in a harmonically driven and tilted optical lattice: Decoherence by spontaneous emission

We have studied some transport properties of cold atoms in an accelerated optical lattice in the presence of decohering effects due to spontaneous emission. One new feature added is the effect of an external AC drive. As a result we obtain a tunable diffusion coefficient and it's nonlinear enhancement with increasing drive amplitude. We report an interesting maximum diffusion condition.

cond-mat.stat-mech↗

arXiv2007

Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle

We extend Tooru-Cohen analysis for nonequilirium 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 an 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.

cond-mat.stat-mech↗

arXiv2006

Relaxation of Femtosecond Non-equilibrium Electrons in a Metallic Sample

A model calculation is given for the energy relaxation of a non-equilibrium distribution of hot electrons prepared in a metallic sample that has been subjected to homogeneous photo-excitation by a femtosecond laser pulse. The model assumes that the delta pulse photoexcitation creates two interpenetrating electronic subsystems, initially comprising a dilute energy-wise higher-lying non-degenerate hot electron subsystem, and a relatively dense, lower-lying electron subsystem which is degenerate. In the femtosecond time regime the relaxation process is taken to be dominated by the electron-(multi) phonon interaction, resulting in a quasi-continuous electron energy loss to the phonon bath. The kinetic model is given for this time regime, beacuse in this time regime the usual Two Temperature model is not applicable. The Two Temperature model assumes that the hot electrons and phonons are in their respective equilibrium states (Fermi and Bose) but at a different temperatures. One uses the Bloch-Boltzmann-Peierls transport formula to calculate the energy transfer rate. In the present Kinetic model a novel physical feature of slowing down (due to Fermionic blocking of interaction phase space) of electron-phonon relaxation mechanism near the Fermi energy of degenerate electronic subsystem is considered. This leads to a peaking of the calculated hot electron distribution at the Fermi energy. This feature, as well as the entire evolution of the hot electron distribution, may be time-resolved by a femto-second pump-probe study.

cond-mat.stat-mech↗

arXiv2006

Relaxation between electrons and surface phonons in nanoscale metal films

The Two Temperature model of M I Kaganov, I M Lifshitz and L V Tanatarov (Sov. Phys. JETP 4, 173 (1957)) about relaxation between electrons and bulk phonons is extended to the case of surface phonons. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. The new feature added is the geometric constraint of surface phonons. We obtain expressions for the energy transfer rate from degenerate hot electrons to surface-phonons, which is order of magnitude less than that for the bulk.

cond-mat.stat-mech↗

arXiv2005

Dissipative electron-phonon system photoexcited far from equilibrium

We derive the steady-state electron distribution function for a semiconductor driven far from equilibrium by the inter-band photoexcitation assumed homogeneous over the nanoscale sample. Our analytical treatment is based on the generalization of a stochastic model known for a driven dissipative granular gas. The generalization is physically realizable in a semiconducting sample where electrons are injected into the conduction band by photoexcitation, and removed through the electron-hole recombination process at the bottom of the conduction band. Here the kinetics of the electron-electron and the electron-phonon (bath) scattering processes, as also the partitioning of the total energy in the inelastic collisions, are duly parametrized by certain rate constants. Our analytical results give the steady-state-energy distribution of the classical (non-degenerate) electron gas as function of the phonon (bath) temperature and the rates of injection (cw pump) and depletion (recombination). Interestingly, we obtain an accumulation of the electrons at the bottom of the conduction band in the form of a delta-function peak $-$ a non-equilibrium classical analogue of condensation. Our model is specially appropriate to a disordered, indirect band-gap, polar semiconducting sample where energy is the only state label, and the electron-phonon coupling is strong while the recombination rate is slow. A possible mechanism for the dissipative inelastic collisions between the electrons is also suggested.

cond-mat.stat-mech↗