Linear response theory, as developed within the Zubarev formalism, is a quantum statistical approach for describing systems out of but close to equilibrium, which has been successfully applied to a wide variety of plasmas in an external electric field and/or containing a temperature gradient. We present here an extension of linear response theory to include the effects of an external magnetic field. General expressions for the complete set of relevant transport properties are given. In particular, the Hall effect and the influence of a magnetic field on the dc electrical conductivity are discussed. Low-density limits including electron-electron scattering are presented as well as results for arbitrary degeneracy.

Properties of the dynamical-mode-locking phenomena are studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. Appearance of very large subharmonic steps due to deformation of the substrate potential significantly influences the stability and existence of harmonic steps. Strong correlation among harmonic and subharmonic steps has been observed in which the larger the width of half-integer steps, the smaller that of harmonic steps. Amplitude dependence of harmonic steps significantly changes with the deformation of the potential where deviation from the well-known Bessel-like oscillations appears. Strong influence of the frequency of the ac driving force on the appearance and size of subharmonic steps has been observed.

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu et al. [R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, Phys. Rev. E 76, 026606 (2007)] showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells [C. R. Simovski, Metamaterials 1, 62 (2007)]. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response—such as negative index materials—will generally be complicated by potentially unwanted magnetoelectric coupling.

We consider an elastic neutral dimer formed by two bound equal masses carrying opposite charges and moving along an electrically active filament in one dimension. An ac electrical field drives the two dimer heads, when set free or bound together to form a rigid rod, to opposite directions, thus yielding a zero net dimer current for zero and infinite elastic constants. Under the same driving conditions, an elastically deformable dimer can get rectified and the ensuing net current maximized for an optimal value of dimer elastic constant. The dependence of the dimer current on the periodic charge distribution along the filament is analyzed in terms of global symmetries of the dimer dynamics.

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed “grain boundary scars,” that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars.

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as two characteristics similar to the web: a power-law decay in PageRank that mirrors the decay of PageRank on the world wide web and a sensitivity to the value $\alpha$ in PageRank. The simple dynamical attractors play here the role of popular websites with a strong concentration of PageRank. A variation in the Google parameter $\alpha$ or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.

Steric effects of ions on the charge-related wetting phenomena are studied. Along with a general treatment, three specific problems in two-dimensional system are considered: a droplet on an electrode, a droplet on a charged surface, and an electrowetting phenomenon on a dielectric. For computation of wetting tension, the electromechanical approach is adopted with the principle of mechanical force balance for each phase. The modified Poisson-Boltzmann equation, which was originally proposed by Bikerman [Philos. Mag. 33, 384 (1942)], is adopted for the analysis of the steric effects. It is found that the steric hindrance reduces significantly both the osmotic pressure and the electrical stress near the triple contact line. This reduction results in a considerable decrease in the wetting tension when the ratio of the capacitance per unit area of the electrical double layer to that of the dielectric layer is small.

For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of results, including an explicit formula for the position probability distribution. For a QW of this type, we show that the mixing behavior tends, in the long run, to a uniform distribution regardless of the initial state of the system and irrespective of the parity of the number of nodes $N$. These results confirm the findings of previous authors who arrived at similar conclusions through extensive numerical simulations. In particular, we infer that the mixing time $\overline{M\left(ϵ\right)}$ for the time-averaged probability distribution is of order no greater than $O\left(N^2/ϵ\right)$.

We report combined optical birefringence and neutron scattering measurements on the liquid crystal 12CB nanoconfined in mesoporous silicon layers. This liquid crystal exhibits strong nematic-smectic coupling responsible for a discontinuous isotropic-to-smectic phase transition in the bulk state. Confined in porous silicon, 12CB is subjected to strong anisotropic quenched disorder: a short-ranged smectic state evolves out of a paranematic phase. This transformation appears continuous, losing its bulk first-order character. This contrasts with previously reported observations on liquid crystals under isotropic quenched disorder. In the low temperature phase, both orientational and translational order parameters obey the same power law.

We use a formal correspondence between the isotropic three-wave kinetic equation and the rate equations for a nonlinear fragmentation–aggregation process to study the wave frequency power spectrum of decaying three-wave turbulence in the infinite capacity regime. We show that the transient spectral exponent is $\lambda +1$, where $\lambda$ is the degree of homogeneity of the wave interaction kernel and derive a formula for the decay amplitude. When $\lambda =0$ the transient exponent coincides with the thermodynamic equilibrium exponent leading to logarithmic corrections to scaling which we calculate explicitly for the case of constant interaction kernel.

Brine channels are formed in sea ice under certain constraints and represent a habitat of different microorganisms. The complex system depends on a number of various quantities as salinity, density, pH value, or temperature. Each quantity governs the process of brine channel formation. There exists a strong link between bulk salinity and the presence of brine drainage channels in growing ice with respect to both the horizontal and vertical planes. We develop a suitable phenomenological model for the formation of brine channels both referring to the Ginzburg-Landau theory of phase transitions as well as to the chemical basis of morphogenesis according to Turing. It is possible to conclude from the critical wave number on the size of the structure and the critical parameters. The theoretically deduced transition rates have the same magnitude as the experimental values. The model creates channels of similar size as observed experimentally. An extension of the model toward channels with different sizes is possible. The microstructure of ice determines the albedo feedback and plays therefore an important role for large-scale global circulation models.

The physical mechanisms driving the collimation of dense plasma jets created by low-energy $\left(\sim 0.6\text{J}\right)$ laser pulse irradiation of triangular grooves were studied for different target materials using soft-x-ray interferometry and hydrodynamic code simulations. The degree of collimation of jets created by irradiating C, Al, Cu, and Mo targets at intensities of $I=1\times {10}^{12}\text{W}{\text{cm}}^{-2}$ with 120 ps laser pulses was observed to increase significantly with the atomic number. Radiation cooling is found to be the cause of the increased collimation, while the main effect of the increase in mass is to slow the jet evolution.

We show that $d+1$-dimensional surface growth models can be mapped onto driven lattice gases of $d$-mers. The continuous surface growth corresponds to one dimensional drift of $d$-mers perpendicular to the $\left(d-1\right)$-dimensional “plane” spanned by the $d$-mers. This facilitates efficient bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in $d=2$, 3, 4, 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the $\left(2+1\right)$-dimensional exponents conciliate with the values suggested by Lässig within error margin, for the largest system sizes studied here, but we cannot support his predictions for $\left(3+1\right)d$ numerically.

We report the investigation of glass-forming salol upon different courses of the temperature changes from liquid to glass state and back using FT-IR spectroscopy measurements in the wide spectral and temperature ranges. The formation of the ordered clusters in supercooled liquid salol has been observed at 250 K. When the temperature is decreased further to 11 K these ordered clusters become an element of the glass structure. With increasing temperature to 270 K through the glass transition noticeable evolutions of the IR spectrum occurs up till the ordered clusters are developed into crystal. So produced crystal melts in the temperature range 300–310 K, that corresponds to the melting temperature of the metastable phase $\left(T_{\text{melt}}=302\text{K}\right)$. Thus, the crystalline structure of the ordered clusters corresponds to the structure of metastable phase and is monoclinic.

Finite interacting Fermi systems with a mean-field and a chaos generating two-body interaction are modeled by one plus two-body embedded Gaussian orthogonal ensemble of random matrices with spin degree of freedom [called $\text{EGOE}\left(1+2\right)\text{−}\mathbf{s}$]. Numerical calculations are used to demonstrate that, as $\lambda$, the strength of the interaction (measured in the units of the average spacing of the single-particle levels defining the mean-field), increases, generically there is Poisson to GOE transition in level fluctuations, Breit-Wigner to Gaussian transition in strength functions (also called local density of states) and also a duality region where information entropy will be the same in both the mean-field and interaction defined basis. Spin dependence of the transition points ${\lambda }_c$, ${\lambda }_F$, and ${\lambda }_d$, respectively, is described using the propagator for the spectral variances and the formula for the propagator is derived. We further establish that the duality region corresponds to a region of thermalization. For this purpose we compared the single-particle entropy defined by the occupancies of the single-particle orbitals with thermodynamic entropy and information entropy for various $\lambda$ values and they are very close to each other at $\lambda ={\lambda }_d$.

The influence of quantum effects on the interaction of intense laser fields with plasmas is investigated by using a hydrodynamic model based on the framework of the relativistic quantum theory. Starting from the covariant Wigner function and Dirac equation, the hydrodynamic equations for relativistic quantum plasmas are derived. Based on the relativistic quantum hydrodynamic equations and Poisson equation, the perturbations of electron number densities and the electric field of the laser wakefield containing quantum effects are deduced. It is found that the corrections generated by the quantum effects to the perturbations of electron number densities and the accelerating field of the laser wakefield cannot be neglected. Quantum effects will suppress laser wakefields, which is a classical manifestation of quantum decoherence effects, however, the contribution of quantum effects for the laser wakefield correction will been partially counteracted by the relativistic effects. The analysis also reveals that quantum effects enlarge the effective frequencies of plasmas, and the quantum behavior appears a screening effect for plasma electrons.

The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain.

A derivation is presented of Green’s function in an arbitrary, heterogeneous conductive medium subject to random, ambient, uncorrelated noise sources. The approach for extracting Green’s function is based on the correlation of time series of magnetic field components at two independent locations. As in the related case for the electric field, where the volume distribution of noise sources must be spatially correlated with the heterogeneous conductivity distribution, Green’s function for magnetic field requires noise sources to be spatially correlated with the volume distribution of magnetic permeability. For applications of electromagnetic imaging of Earth’s deep subsurface, the effect of magnetic permeability variations in the subsurface is often assumed to be negligible when compared to the effect of conductivity variations. Hence, the expressions derived here may be useful for passive electromagnetic subsurface imaging, in apparent contrast to their electric field counterparts. Numerical validation exercises are described which validate this theory for Green’s function estimation in the low-frequency limit.

An alternative to periodic boundary conditions is developed and tested in Monte Carlo simulations of the two- and three-dimensional Ising models. The boundary conditions are based on a mean-field approach that incorporates consistency constraints for the magnetization and correlations between nearest neighbors by means of an effective field and an extra coupling between nearest neighbors at the boundary of the simulation box. During the simulation the self-consistent equations are solved, and statistics are accumulated to obtain thermodynamic averages. In comparison with the standard periodic boundary conditions the method gives a more accurate estimation of nonuniversal magnitudes, such as the transition temperature and the behavior of the magnetization, but it cannot compete with the accuracy of other strategies such as finite-size scaling theory or Monte Carlo renormalization group to obtain critical exponents.

Large protein assemblies, such as virus capsids, may be coarse-grained as a set of rigid units linked by generalized (rotational and stretching) harmonic springs. We present an ab initio method to obtain the elastic parameters and overdamped dynamics for these springs from all-atom molecular-dynamics simulations of one pair of units at a time. The computed relaxation times of this pair give a consistency check for the simulation, and we can also find the corrective force needed to null systematic drifts. As a first application we predict the stiffness of an HIV capsid layer and the relaxation time for its breathing mode.