Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.

We investigate the energetics of a Brownian motor driven by position-dependent temperature, commonly known as the Büttiker-Landauer motor. Overdamped models $\left(M=0\right)$ predict that the motor can attain Carnot efficiency. However, the overdamped limit $\left(M\to 0\right)$ contradicts the previous prediction due to the kinetic energy contribution to the heat transfer. Using molecular dynamics simulation and numerical solution of the inertial Langevin equation, we confirm that the motor can never achieve Carnot efficiency and verify that the heat flow via kinetic energy diverges as $M^{-1/2}$ in the overdamped limit. The reciprocal process of the motor, namely, the Büttiker-Landauer refrigerator, is also examined. In this case, the overdamped approach succeeds in predicting the heat transfer only when there is no temperature gradient. Its found that the Onsager symmetry between the motor and refrigerator does not suffer from the singular behavior of the kinetic energy contribution.

Recent developments in the theory of amorphous plasticity point to the central role played by the concept of an effective disorder temperature $T_{eff}$. An athermal dynamics for $T_{eff}$ is proposed in the framework of a deformation theory and discussed in light of recent steady-state simulations by Haxton and Liu [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)]. The structure of the resulting theory, its parameters and transient dynamics are discussed and compared to available data.

We report the results of an experimental study of a recently observed phase sequence reversal of $\text{smectic-}{C}_{FI2}^{\ast }$ [$\text{Sm}{C}^{\ast }\left(q_T=1/2\right)$; a four layer antiferroelectric] phase appearing in the temperature range above the $\text{smectic-}{C}^{\ast }$ $\left(\text{Sm}{C}^{\ast }\right)$ phase from the results of optical birefringence, spontaneous polarization, selective reflection, conoscopy, and dielectric spectroscopy. The $\text{Sm}{C}_{FI2}^{\ast }$ phase is observed in an antiferroelectric liquid crystalline compound, 10OHF, in a temperature range above that of $\text{Sm}{C}^{\ast }$ phase and is found to be thermodynamically monotropic, i.e., it appears only upon cooling from $\text{Sm}{C}_{\alpha }^{\ast }$ phase. This is also unstable as if it is once transformed to $\text{Sm}{C}^{\ast }$ by the application of the bias, it does not return to its original state unless the sample is heated and cooled again in the absence of the bias. Nevertheless this phase is stabilized by the addition of a chiral smectic compound 9OTBBB1M7 (abbreviated as C9), having a wide temperature range of the $\text{Sm}{C}_{FI2}^{\ast }$ phase. The temperature range of the low temperature $\text{Sm}{C}^{\ast }$ decreases with increase in the concentration of C9 and for a concentration of 55 wt. %, $\text{Sm}{C}^{\ast }$ disappears and the transition takes place directly from $\text{Sm}{C}_{FI2}^{\ast }$ to the crystalline phase on cooling. The existence of such a high-temperature $\text{Sm}{C}_{FI2}^{\ast }$ phase is also supported by a phenomenological model.

In highly frustrated calamitic nematic liquid crystals, a strong elastic distortion can be confined on a few nanometers. The classical elastic theory fails to describe such systems and a more complete description based on the tensor order parameter $\mathbf{Q}$ is required. A finite element method is used to implement the $\mathbf{Q}$ dynamics by a variational principle and it is shown that a uniaxial nematic configuration can evolve passing through transient biaxial states. This solution, which connects two competing uniaxial nematic textures, is known as “nematic order reconstruction.”

A geometric analysis of the global properties of the energy landscape of a minimalistic model of a polypeptide is presented, which is based on the relation between dynamical trajectories and geodesics of a suitable manifold, whose metric is completely determined by the potential energy. We consider different sequences, some with a definite proteinlike behavior, a unique native state and a folding transition, and others undergoing a hydrophobic collapse with no tendency to a unique native state. The global geometry of the energy landscape appears to contain relevant information on the behavior of the various sequences: in particular, the fluctuations of the curvature of the energy landscape, measured by means of numerical simulations, clearly mark the folding transition and allow the proteinlike sequences to be distinguished from the others.

We investigate quantum dynamics in phase-space regions containing “shearless tori.” We show that the properties of these peculiar classical phase-space structures—important to the dynamics of tokamaks—may be exploited for quantum information applications. In particular we show that shearless tori permit the nondispersive transmission of localized wave packets. The quantum many-body Hamiltonian of a Heisenberg ferromagnetic spin chain, subjected to an oscillating magnetic field, can be reduced to a classical one-body “image” dynamical system which is the well-studied Harper map. The Harper map belongs to a class of Hamiltonian systems (nontwist maps) which contain shearless tori. We show that a variant with sinusoidal time driving “driven Harper model” produces shearless tori which are especially suitable for quantum state transfer. The behavior of the concurrence is investigated as an example.

We study the properties of an arbitrary microswimmer towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a microswimmer dragging a distant load is found, and the approximation for finite mutual proximity is derived. We show that, while the swimmer can be arbitrarily efficient, the dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell’s assumption [E. M. Purcell, Proc. Natl. Acad. Sci. U.S.A. 94, 11307 (1997)], the hydrodynamic coupling can “help” the propeller to tow the load. We support our conclusions by rigorous numerical calculations for the rotary swimmer, towing a spherical cargo positioned at a finite distance.

We report numerical evidence of elastic turbulence phenomenology in a two-dimensional periodic Kolmogorov flow. By direct numerical simulations of the Oldroyd-B viscoelastic model at very small Reynolds numbers, we find that above the elastic instability threshold the flow develops an elastic turbulent regime. We observe that both the turbulent drag and the Lyapunov exponent increase with the Weissenberg number, indicating the presence of a disordered, turbulentlike mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.

Finite-amplitude gravity water waves in Bragg resonance with a periodic one-dimensional topography are studied numerically using exact equations of motion for ideal potential free-surface flows. Spontaneous formation of highly nonlinear localized structures is observed in the numerical experiments. These coherent structures consisting of several nearly standing extreme waves are similar in many aspects to the Bragg solitons previously known in nonlinear optics.

We observe numerically, and explain analytically, a previously unknown phenomenon of quantum-Hall-like jumps in saturation spectral rigidity in the semiclassical spectrum of a modified Kepler problem as a function of the interval center. These jumps correspond to integer decreases of the radial winding numbers in classical periodic motion. We also observe and explain single-harmonic-dominated oscillations of the level number variance with the width of the energy interval. The level number variance becomes effectively zero for the interval widths defined by the frequency of the shortest periodic orbit. This signifies that there are virtually no variations from sample to sample in the number of levels on such intervals.

We study the potential and plasma density variations around a solid object in a plasma flow, emphasizing supersonic flows. These objects can be dust grains, for instance. Conducting as well as insulating materials are considered. In a streaming plasma, a dust grain develops an electric dipole moment, which varies systematically with the relative plasma flow. The strength and direction of this dipole moment depends critically on the material. The net charge together with the electric dipole associated with the dust grains gives rise to electric fields, which affects the trajectories of nearby charged particles. The perturbation of ion orbits in streaming plasmas can give rise to a focusing of ions in the wake region facing away from the plasma flow. We study the parameter dependence of this ion focus. Our simulations are carried out in two spatial dimensions by a particle-in-cell code, treating ions and electrons as individual particles.

We numerically investigate the negative index of refraction in a metamaterial composed of metallic split-ring resonators, which exhibits simultaneously negative permittivity and permeability without resorting to additional metallic wires. It is confirmed that, in the left-handed band, negative permittivity is generated in analogy to the cut-wire metamaterial and negative permeability comes from the antisymmetric resonant mode, which occurs at a frequency band about 3 times higher than the fundamental magnetic resonance proposed by Pendry et al. [IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)].

We study the nonequilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of ballistic annihilation therefore constantly loses particles. The dynamics of perturbations around the free decay regime is investigated using the spectral properties of the linearized Boltzmann operator, which characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of molecular dynamics simulations that validate the theoretical predictions.

We develop a theory for fluctuations and correlations in a gas evolving under ballistic annihilation dynamics. Starting from the hierarchy of equations governing the evolution of microscopic densities in phase space, we subsequently restrict our attention to a regime of spatial homogeneity, and obtain explicit predictions for the fluctuations and time correlation of the total number of particles, total linear momentum, and total kinetic energy. Cross correlations between these quantities are worked out as well. These predictions are successfully tested against molecular dynamics and Monte Carlo simulations. This provides strong support for the theoretical approach developed, including the hydrodynamic treatment of the spectrum of the linearized Boltzmann operator. This paper makes use of the spectral analysis reported in the preceding paper [Phys. Rev. E 77, 051127 (2008)].

Recently we considered a stochastic discrete model which describes fronts of cells invading a wound [E. Khain, L. M. Sander, and C. M. Schneider-Mizell, J. Stat. Phys. 128, 209 (2007)]. In the model cells can move, proliferate, and experience cell-cell adhesion. In this work we focus on a continuum description of this phenomenon by means of a generalized Cahn-Hilliard equation (GCH) with a proliferation term. As in the discrete model, there are two interesting regimes. For subcritical adhesion, there are propagating “pulled” fronts, similar to those of the Fisher-Kolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in the good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior, where density profile exhibits a secondary peak. To analyze this regime, we investigated relaxation dynamics for the Cahn-Hilliard equation without proliferation. We found that the relaxation process exhibits self-similar behavior. The results of continuum and discrete models are in good agreement with each other for the different regimes we analyzed.

We present a study, within a mean-field approach, of the kinetics of the mixed spin-1 and spin-3/2 Ising model Hamiltonian with bilinear and biquadratic nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the time dependence of average magnetizations and the quadrupole moments, and the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points and construct the phase diagrams in three different planes. Phase diagrams contain disordered $\left(d\right)$, ferrimagnetic $\left(i\right)$, the antiquadrupolar or staggered $\left(a\right)$ phases, and four coexistence or mixed phase regions, namely, the $i+d$, $i+a$, $i+a+d$, and $a+d$, that strongly depend on interaction parameters. The system also exhibits the dynamic tricritical behavior in most cases, the reentrant behavior in few cases.

A crumpled thin sheet generally exhibits numerous defects each of which store energy. When subjected to a constant compressive force the height of the crumple decreases logarithmically with time in a process of long-term stress relaxation, which scales over several orders of magnitude—i.e., over time periods from seconds to weeks. We have investigated this scaling behavior for thin polymer films and found that a discontinuous stress relaxation is superimposed on the long-term stress relaxation. The former becomes more pronounced as the polymer sheet thickness increases and is systematically characterized in this study. Effects of ridge length and density are discussed.

We show that the continuous cholesteric fingers, which form in homeotropic samples at the unwinding temperature of the cholesteric phase, drift and spiral when they are subjected to a temperature gradient. This phenomenon is attributed to the appearance of a Lehmann thermomechanical torque. Measurements of the finger drift velocity on both sides of the compensation temperature of a cholesteric mixture show that the Lehmann coefficient does not change sign (and so does not vanish) at this temperature contrary to the equilibrium twist. There is thus no direct relationship between the thermomechanical Lehmann coefficient and the equilibrium twist. The nonvanishing of the Lehmann coefficient at the compensation temperature is due to the absence of inversion symmetry in a compensated cholesteric in spite of its nematiclike structure. This comes from the chirality of the molecules. The ratio of the Lehmann coefficient over the rotational viscosity is also measured as a function of temperature.

The dipole flexoelectric (FE) polarization in liquid crystals is derived in the thermodynamic limit at small distortions and small density. General microscopic expressions for the FE coefficients are obtained in the case of the uniaxial and biaxial nematic phases composed of $C_{2v}$ molecules. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. In the case of the biaxial nematic phase, six basic deformations produce FE polarization but there are only five independent FE coefficients.