Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, Phi derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulklike condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is nonexponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments. (C) 2010 American Institute of Physics. doi: 10.1063/1.3474948]

Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use C-13 nuclear spins as qubits and an environment of H-1 nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 mu s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

QCD with dynamical Wilson fermions. II

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Dynamical Resolution of Redundancy for Robot Manipulators

A large class of work in the robot manipulator literature deals with the kinematical resolution of redundancy based on the pseudo-inverse of the manipulator Jacobian. In this paper an alternative dynamical approach to redundancy resolution is developed which utilizes the mapping between the actuator torques and the acceleration of the end-effector, at a given dynamic state of the manipulator. The potential advantages of the approach are discussed and an example of a planar 3R manipulator following a circular end-effector trajectory is used to illustrate the proposed approach as well as to compare it with the more well-known approach based on the pseudo-inverse.

Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are C-13 nuclear spins and the environment consists of a H-1 nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

Synchrotron Study of the Dynamical Effects in the LVV Auger Transitions in the First-Row Transition Elements

The intensity ratio between L2-M45M45 and L3-M45M45 spectral features for both Fe and Co indicates significant tranfer of intensity from L2- to L3-M45M45 region due to Coster-Kronig L2-M45M45 transition. The L2-L3M45 transition can be suppressed by turning the photon energy between the L2 and L3 thresholds; however, the L3-M45M45 spectral shapes for Fe and Co do not change very significantly even at these photom energies unlike the cases of Ni, Cu and Zn, thus establishing that the M45-hole decays predominantly before the L3-hole Auger decay in the early transition elements in contrast to the late ones.

Wavepacket dynamical studies on trans-azobenzene: absorption spectrum and resonance Raman excitation profiles of the n??* transition

Time-dependent wavepacket propagation techniques have been used to calculate the absorption spectrum and the resonance Raman excitation profiles of the n-pi* transition in azobenzene. A comparison of both the calculated absorption spectrum and excitation profiles with experiment has been made. From an analysis of the data, it is concluded that the Raman intensities are mainly due to resonance from the n-pi* transition and not from the pre-resonance of the pi-pi* transition, as reported earlier. We find that the isomerization pathway is through the inversion mechanism rather than by rotation. This is the first direct spectroscopic evidence for the isomerization pathway in trans-azobenzene.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.