Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from the beginning, whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. The essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\le \Lambda <\infty$ (interaction strength) and $0\le \alpha \le \pi /2$ (integrability switch). In the classical limit, this system has two distinct integrable regimes, $\alpha =0$ and $\alpha =\pi /2$. For each integrable regime we can express the quantum Hamiltonian as a function of two action operators. Their eigenvalues (multiples of $\hslash$) are the natural quantum numbers for the complete level spectrum. This functional dependence cannot be extended into the nonintegrable regime $\left(0<\alpha <\pi /2\right)$. Here level crossings are prohibited and the level spectrum is naturally described by a single (energy sorting) quantum number. In consequence, the tracking of individual eigenstates along closed paths through both regimes leads to conflicting assignments of quantum numbers. This effect is a useful and reliable indicator of quantum chaos—a diagnostic tool that is independent of any level-statistical analysis.

The dynamics of thermal capillary waves (CWs) on an ionic liquid’s surface are studied at the transition from propagating to overdamped CWs by x-ray photon correlation spectroscopy. The analysis considers both homodyne and heterodyne contributions, and yields excellent full line-shape experiment-theory agreement for the structure factor. The CWs' Brillouin scattering becomes extinct at a critical temperature $T_c^{JK}\sim 10\mathrm{K}$ above $T_c^{LL}$, the propagating modes' hydrodynamic limit, in agreement with linear response theory. Surprisingly, the same power law applies at both $T_c$. The results rule out the presence of a suggested surface dipole layer.

Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.

We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species, where most dissipative particles submerge in the less dissipative ones. The segregation occurs even if one type of the particles is elastic. In order to have a complete description of the system, we study the structure of the fluid at microscopic scale (few particle diameters). The density and temperature pair distribution functions show strong enhancements with respect to the equilibrium ones at the same density. In particular, there is an increase in the probability that the more inelastic particles group together in pairs (microsegregation). Microscopically the segregation is buoyancy driven, by the appearance of a dense and cold region around the more inelastic particles.

A possible clarification of memory effect observed in crack patterns of drying pastes [A. Nakahara and Y. Matsuo, J. Phys. Soc. Jpn. 74, 1362 (2005)] is presented in terms of a macroscopic elastoplastic model of isotropic pastes. We study flows driven by steady gravitational force instead of external oscillation. The model predicts creation of residual tension in favor of cracks perpendicular to the flow direction, thus causing the same type of memory effect as that reported by Nakahara and Matsuo for oscillated ${\mathrm{CaCO}}_3$ pastes.

We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings.

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome et al., Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.

The development of a large noncoding fraction in eukaryotic DNA and the phenomenon of the code bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code cannot be attained without maintaining a large inactive fraction. To test this hypothesis we performed computer simulations of an evolutionary toy model for Turing machines, studying the relations among fitness and coding versus noncoding ratio while varying mutation and code growth rates. The results suggest that, in our model, having a large reservoir of noncoding states constitutes a great (long term) evolutionary advantage.

The Berezinskii-Kosterlitz-Thouless-type continuous phase transition observed in the three-spin interaction model is discussed. The relevant field theory describes the topological defects involved and enables us to perform the renormalization-group analysis. Based on it, we shall propose the finite-size-scaling ansatz for the helicity modulus, which exhibits the exponent $\overline{\nu }=3/5$ for the correlation length in the disordered phase. We perform the Monte Carlo simulations to confirm the ansatz. Also, we argue its relevance to the ground-state phase transition in the quantum spin chain.

We analyze the properties of discrete breathers excited near the edge of a one-dimensional metamaterial created by a truncated array of nonlinear split-ring resonators. We study a crossover between nonlinear surface states and discrete breathers by analyzing the modes centered at finite distances from the array edge and demonstrate the existence of a class of nonlinear localized surface states, the so-called nonlinear Tamm states or surface breathers, which exhibit features that have no counterparts either in the continuous systems or in linear arrays.

A model for epidemics on an adaptive network is considered. Nodes follow a susceptible-infective-recovered-susceptible pattern. Connections are rewired to break links from noninfected nodes to infected nodes and are reformed to connect to other noninfected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.

On the basis of numerical simulation of fiber laser passive mode locking with anomalous dispersion we have found the dissipative solitons with powerful pedestals having oscillating structure. The pedestal structure causes a complex structural spectrum. These solitons can be multistable: with the same laser parameters the pedestals can have different structures. For some nonlinear-dispersion parameters there exist solitons with asymmetric structural pedestals moving relatively solitons with symmetric ones.

The exponential splitting of the classical evolution operator yields symplectic integrators if the canonical Hamiltonian is separable. Similar splitting of the noncanonical evolution operator for a charged particle in a magnetic field produces exact energy-conserving algorithms. The latter algorithms evaluate the magnetic field directly with no need of a vector potential and are more stable with far less phase errors than symplectic integrators. For a combined electric and magnetic field, these algorithms from splitting the noncanonical evolution operator are neither fully symplectic nor exactly energy conserving, yet they behave exactly like symplectic algorithms in having qualitatively correct trajectories and bounded periodic energy errors. This work shows that exponential-splitting algorithms of any order for solving particle trajectories in a general electric and magnetic field can be systematically derived by use of the angular momentum operator of quantum mechanics. The use of operator analysis in this work fully comprehends the intertwining interaction between electric and magnetic forces and makes possible the derivation of highly nontrivial integrators.

In earlier work a systematic extension of the van der Waals square gradient model to nonequilibrium one-component systems was given. In this work the focus was on heat and mass transfer through the liquid-vapor interface as caused by a temperature difference or an over- or underpressure. We will give an extension of this approach to multicomponent nonequilibrium systems in the systematic context of nonequilibrium thermodynamics. An explicit expression for the pressure tensor is derived valid also for curved surfaces. It is shown how the Gibbs relation should be modified in the interfacial region, in both equilibrium and nonequilibrium. The two-dimensional isotropy of a curved interface is discussed. Furthermore, we give numerically obtained profiles of the concentration, the mole fraction, and the temperature, which illustrate the solution for some special cases.

An experimental study of the heat capacity, mass density, magnetic-field-induced optical birefringence, linewidth and intensity of scattered light, and the viscosities associated with nematic order parameter fluctuations and fluid flow has been performed on an achiral bent-core liquid crystal above its clearing point temperature. The measurements reveal a transition between two optically isotropic phases that is consistent with recent theoretical predictions of a “tetrahedratic” form of orientational order.

The stylus of an atomic force microscope is used to scribe herringbone patterns of various wavelengths into a polyimide-coated substrate. The patterns serve as a template for alignment of the liquid crystal octyloxycyanobiphenyl and impose a bend distortion in the liquid crystal in the vicinity of the herringbone apexes. The pretransitional behavior of the liquid crystal is observed by polarized microscopy as it is cooled through the nematic–smectic-$A$ phase transition, facilitating direct visualization of the extrapolation length, which is related to the trade-off between elastic and anchoring forces. Just above the phase transition temperature the expulsion of bend deformation is observed and is shown to be in good quantitative agreement with continuum theory. Very close to the transition temperature a weak threshold behavior is observed, wherein the smectic-$A$ phase forms a monodomain for short period herringbones, but breaks into multiple domains when the patterned period is large.

We report dynamic Monte Carlo simulations of immiscible binary polymer blends, which exhibit weakly enhanced crystal nucleation near interfaces between two phase-separated polymers. We found that this enhancement is not accompanied by any preferred crystal orientation, implying its origin is mainly of enthalpic rather than entropic nature. Mean-field theory of polymer blends predicts that for immiscible polymers the melting point of the crystallizable component increases upon dilution in the other component, while it normally decreases for miscible blends. A local dilution is forced to occur at the diffuse interface of immiscible polymers; therefore the melting point of crystallizable polymers rises, which, in turn, enhances the thermodynamic driving force for crystal nucleation near the interface.