For a prepared state exact expressions for the time-dependent mean fidelity as well as for the mean inverse participation ratio are obtained analytically. The prepared state is taken as an eigenstate of the unperturbed system, and the studied fidelity is identical to the survival probability. The full distribution functions of fidelity in the long-time limit and of inverse participation ratio are studied numerically and analytically. Surprising features such as fidelity revival and nonergodicity are observed. The roles of the coupling coefficients and of complexity of background are studied as well.

An integrable asymmetric exclusion process with impurities is formulated. The model displays the full spectrum of the stochastic asymmetric XXZ chain plus new levels. We derive the Bethe equations and calculate the spectral gap for the totally asymmetric diffusion at half filling. While the standard asymmetric exclusion process without impurities belongs to the KPZ universality class with an exponent $\frac{3}{2}$, our model has a scaling exponent $\frac{5}{3}$.

We derive an integrodifferential diffusion equation for decoupled continuous time random walk that is valid for a generic waiting time probability density function and external force. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, a combination of power law and generalized Mittag-Leffler function and a sum of exponentials under the influence of a harmonic trap. We show that first two waiting time probability density functions can reproduce the results of the ordinary and fractional diffusion equations for all the time regions from small to large times. But the third one shows a much more complicated pattern. Furthermore, from the integrodifferential diffusion equation we show that the second Einstein relation can hold for any waiting time probability density function.

We investigate decoherence and equilibration in the experimentally relevant situation of weak coupling to an environment. We consider small subsystems of large closed quantum systems that evolve according to the von Neumann equation. Without approximations and without making any special assumptions on the form of the interaction we prove that, for almost all initial states and almost all times, the off-diagonal elements of the density matrix of the subsystem in the eigenbasis of its local Hamiltonian must be small whenever the energy difference of the corresponding eigenstates is larger than the interaction energy. This proves that decoherence with respect to the local energy eigenbasis is a natural property of weakly interacting quantum systems.

We study $D$-dimensional elastic manifolds driven by ac forces in a disordered environment using a perturbation expansion in the disorder strength and the mean-field approximation. We find that for $D\le 4$, perturbation theory produces nonregular terms that grow unboundedly in time. The origin of these nonregular terms is explained. By using a graphical representation we argue that the perturbation expansion is regular to all orders for $D>4$. Moreover, for the corresponding mean-field problem we prove that ill-behaved diagrams can be resummed in a way that their unbounded parts mutually cancel. Our analytical results are supported by numerical investigations. Furthermore, we conjecture the scaling of the Fourier coefficients of the mean velocity with the amplitude of the driving force $h$.

We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively $\left(\theta \equiv T_c/T_h<1\right)$. The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and vice versa. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two systems. The efficiency is then found to be bounded from below by ${\zeta }_{\text{CA}}=\frac{1}{\sqrt{1-\theta }}-1$ (an analog of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency ${\zeta }_{\text{C}}=\frac{1}{1-\theta }-1$. The lower bound is reached in the equilibrium limit $\theta \to 1$. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for $\text{ln}n⪢1$. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ${\zeta }_{\text{CA}}$ and converges to it for $n⪢1$.

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general nonequilibrium thermodynamic description of the system when it is out of thermal and mechanical equilibrium with the medium. Our approach allows us to identify the correct form of the Gibbs free energy and enthalpy. We also obtain an extension of the classical nonequilibrium thermodynamics due to de Donder in which one normally assumes thermal and mechanical equilibrium with the medium; see text. We find that the temperature and pressure differences between the system and the medium act as thermodynamic forces, which are normally neglected in the classical nonequilibrium thermodynamics. The Prigogine-Defay ratio is found to be greater than 1 merely due to the lack of equilibrium with the medium, even though we do not consider any internal order parameters. This shows that these forces should play an important role in relaxation processes. We then apply our approach to study the general trend during structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.

We investigate the thermodynamics of complexation of functionalized charged nanospheres with viral proteins. The physics of this problem is governed not only by electrostatic interaction between the proteins and the nanosphere cores (screened by salt ions), but also by configurational degrees of freedom of the charged protein $N$ tails. We approach the problem by constructing an appropriate complexation free-energy functional. On the basis of both numerical and analytical studies of this functional we construct the phase diagram for the assembly which contains the information on the assembled structures that appear in the thermodynamical equilibrium, depending on the size and surface charge density of the nanosphere cores. We show that both the nanosphere core charge and its radius determine the size of the capsid that forms around the core.

We propose an inanimate system composed of camphor boats in an annular water channel in order to understand the collective motions. The boats move on the water surface spontaneously and interact with one another through the concentration of the camphor molecules on the water. We observed several modes of collective motion, e.g., behaviors analogous to traffic flow or an ant trail. Our system provides a convenient experimental setup for the investigation of a variety of collective motions.

The scaling relations for bubbles induced by different external sources are investigated based on a modified Rayleigh model and experimental observations. The equations derived from the modified Rayleigh model are presented to describe the collapse of bubbles induced by the different external sources such as electrical spark, laser, and underwater explosion. A scaling law is then formulated to establish the scaling relations between the different types of bubbles. The scaling law reveals the fact that the characteristic length scale factor differs from the characteristic time scale factor for the different types of bubbles. It is then validated by our experimental observations of the spark- and laser-generated bubbles as well as the bubbles induced by underwater explosions from previous published reports. With the present scaling law, studies on spark- or laser-generated bubbles as well as their applications (for example, in industrial or biomedical related applications) can benefit from the experiences and information built up over the years in underwater explosion bubbles. Conversely, it is possible to substitute a spark- or laser-generated bubble for an underwater explosion bubble in the study of a large-scale and complex physical problem.

The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise $\left\{Z_t\right\}$ and a stochastic process with strictly positive values $\left\{V_t\right\}$ referred to as volatility. The probability density function (pdf) of the process $X_t=V_t{Z}_t$ is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of $\left\{X_t\right\}$ can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.

We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination numbers between the species and (ii) the dependence of the coordination numbers with the concentration of species; quantities that are calculated analytically. The model predicts the density of random close packing and random loose packing of polydisperse systems for a given distribution of ball size and describes packings for any interparticle friction coefficient. The formalism allows to determine the optimal packing over different distributions and may help to treat packing problems of nonspherical particles which are notoriously difficult to solve.

The outcome of water addition in ferroelectric liquid crystal (FLC) has been investigated in uniform and defect-free homogeneous and homeotropically aligned monodomain sample cells from electro-optical and dielectric spectroscopic measurements. The lagging in optical response between nonconducting (spatially variable switching) and conducting (conventional switching) portions of water added FLC sample cell has been observed by frequency-dependent electro-optical studies. The bias-dependent water related new relaxation peak near the conventional Goldstone mode relaxation process has been observed only in the homogeneous alignment and not in the homeotropic one. Further, the significant increment in dielectric anisotropy as well as faster diffusion of water along long molecular axis than short molecular axis has also been monitored. These studies strongly suggest that the distribution of water is anisotropic in FLC medium and could be the reason for new relaxation peak in the water added FLC sample.

A herringbone “easy axis” pattern is scribed into a polyimide alignment layer for liquid-crystal orientation using the stylus of an atomic force microscope. Owing to the liquid crystal’s bend elasticity $K_{33}$, the nematic director is unable to follow the sharp turn in the scribed easy axis, but instead relaxes over an extrapolation length $L=K_{33}/W_2^{\phi }$, where $W_2^{\phi }$ is the quadratic azimuthal anchoring strength coefficient. By immersing a tapered optical fiber into the liquid crystal, illuminating the fiber with polarized light, and scanning the fiber close to the substrate, a visualization and direct measurement of $L$ are obtained on approaching the nematic–smectic-$A$ phase transition temperature $T_{NA}$ from above. $L$ is found to exhibit a sharp pretransitional increase near $T_{NA}$, consistent with a diverging bend elastic constant.

Time delay is an important dynamical issue in a multistep chemical reaction. We present a theoretical scheme for delayed reaction-diffusion systems where the time delay in kinetics is stochastic in nature. It has been shown that a small but finite strength of delay may result in generic change in the nature of spatiotemporal instability in the dynamics. Our theoretical analysis has been corroborated by numerical simulations on two reaction-diffusion systems.

When a dynamical system exhibits transient chaos and a nonchaotic attractor, as in a periodic window, noise can induce a chaotic attractor. In particular, when the noise amplitude exceeds a critical value, the largest Lyapunov exponent of the attractor of the system starts to increase from zero. While a scaling law for the variation of the Lyapunov exponent with noise was uncovered previously, it is mostly based on numerical evidence and a heuristic analysis. This paper presents a more general approach to the scaling law, one based on the concept of quasipotentials. Besides providing deeper insights into the problem of noise-induced chaos, the quasipotential approach enables previously unresolved issues to be addressed. The fractal properties of noise-induced chaotic attractors and applications to biological systems are also discussed.

Numerical and experimental results are presented for an edge-emitting diode laser with delayed optical feedback, where the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. We examine the bifurcation structure and dynamics that give rise to a class of periodic, polarization-modulated solutions, the simplest of which is a square wave solution with a period related to but longer than twice the external cavity roundtrip time. Such solutions typically emerge when the feedback is strong and the differential losses in the normally unsupported polarization mode are small. We also observe more complex waveforms that maintain the same periodicity.

We compute the spectra and fluxes of the velocity and temperature fields in Rayleigh-Bénard convection in turbulent regime for a wide range of Prandtl numbers using pseudospectral simulations on ${512}^3$ grids. Our spectral and flux results support the Kolmogorov-Obukhov (KO) scaling for zero Prandtl number and low Prandtl number $\left(P=0.02\right)$ convection. The KO scaling for the velocity field in zero-Prandtl number and low-Prandtl number convection is because of the weak buoyancy in the inertial range (buoyancy is active only at the very low wave numbers). We also observe that for intermediate Prandtl numbers $\left(P=0.2\right)$ the KO scaling fits better with the numerical results than the Bolgiano-Obukhov (BO) scaling. For large Prandtl number $\left(P=6.8\right)$, the spectra and flux results are somewhat inconclusive on the validity of the KO or BO scaling, yet the BO scaling is preferred over the KO scaling for these cases. The numerical results for $P=1$ is rather inconclusive.

To efficiently solve the three-dimensional (3D) time-dependent linear and nonlinear Schrödinger equation, we have developed a large-scale parallel code RSP-FEDVR [B. I. Schneider, L. A. Collins, and S. X. Hu, Phys. Rev. E 73, 036708 (2006)], which combines the finite-element discrete variable representation (FEDVR) with the real-space product algorithm. Using the similar algorithm, we have derived an accurate approach to solve the time-dependent close-coupling (TDCC) equation for exploring two-electron dynamics in linearly polarized intense laser pulses. However, when the number $\left(N\right)$ of partial waves used for the TDCC expansion increases, the FEDVR-TDCC code unfortunately slows down, because the potential-matrix operation scales as $\sim O\left(N^2\right)$. In this paper, we show that the full potential-matrix operation can be decomposed into a series of small-matrix operations utilizing the sparse property of the $\left[N\times N\right]$ potential matrix. Such optimization speeds up the FEDVR-TDCC code by an order of magnitude for $N=256$. This may facilitate the ultimate solution to the 3D two-electron quantum dynamics in ultrashort intense optical laser pulses, where a large number of partial waves are required.

We study the optimality conditions of information transfer in systems with memory in the low signal-to-noise ratio regime of vanishing input amplitude. We find that the optimal mutual information is represented by a maximum variance of the signal time course, with correlation structure determined by the Fisher information matrix. We provide illustration of the method on a simple biologically inspired model of electrosensory neuron. Our general results apply also to the study of information transfer in single neurons subject to weak stimulation, with implications to the problem of coding efficiency in biological systems.