We provide the necessary framework for carrying out stochastic positive-$P$ and gauge-$P$ simulations of bosonic systems with long-range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. We show that the long-range character of these interactions does not further increase the limitations of these methods, in contrast to the situation for alternatives such as the density matrix renormalization group. Furthermore, stochastic gauge techniques can also successfully extend simulation times in the long-range-interaction case, by making using of parameters that affect the noise properties of trajectories, without affecting physical observables. We derive essential results that significantly aid the use of these methods: estimates of the available simulation time, optimized stochastic gauges, a general form of the characteristic stochastic variance, and adaptations for very large systems. Testing the performance of particular drift and diffusion gauges for nonlocal interactions, we find that, for small to medium systems, drift gauges are beneficial, whereas for sufficiently large systems, it is optimal to use only a diffusion gauge. The methods are illustrated with direct numerical simulations of interaction quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg states in a Bose-Einstein condensate, also without the need for the typical frozen gas approximation. We demonstrate that gauges can indeed lengthen the useful simulation time.

Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present an alternative method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use the eigenvector centrality probability distribution to compute the entropy as an indicator of the “mixing capacity” of the system.

Spontaneous formation of spinning pairs of particles, or torsions, is studied in a single-layer complex plasma crystal by reducing the discharge power at constant neutral gas pressure. At higher gas pressures, torsions spontaneously form below a certain power threshold. Further reduction of the discharge power leads to the formation of multiple torsions. However, at lower gas pressures the torsion formation is preceded by mode-coupling instability (MCI). The crystal dynamics are studied with the help of the fluctuation spectra of crystal particles' in-plane velocities. Surprisingly, the spectra of the crystal with torsions and MCI are rather similar and contain hot spots at similar locations on the $(k,\omega )$ plane, despite very different appearances of the respective particle trajectories. The torsion rotation speed is close (slightly below) to the maximum frequency of the in-plane compressional mode. When multiple torsions form, their rotation speeds are distributed in a narrow range slightly below the maximum frequency.

The stationary states of the prisoner's dilemma model are studied on a square lattice taking into account the role of a noise parameter in the decision-making process. Only first neighboring players—defectors and cooperators—are considered in each step of the game. Through Monte Carlo simulations we determined the phase diagrams of the model in the plane noise versus the temptation to defect for a large range of values of the noise parameter. We observed three phases: cooperators and defectors absorbing phases, and a coexistence phase between them. The phase transitions as well as the critical exponents associated with them were determined using both static and dynamical scaling laws.

We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum $j$, with both microcanonical and canonical ensembles. We focus on both the excited-state quantum phase transition, appearing in the microcanonical description of the maximum angular momentum sector, $j=N/2$, and the thermal phase transition, which occurs when all the sectors are taken into account. We show that two different features characterize the full version of the Dicke model. If the system is in contact with a thermal bath and is described by means of the canonical ensemble, the parity symmetry becomes spontaneously broken at the critical temperature. In the microcanonical ensemble, and despite that all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the $j$ sectors are considered, there still exists a critical energy (or temperature) dividing the spectrum into two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.

The functions of the smallest self-contained thermal machine consisting of a single qutrit are studied when the weak internal coupling assumption is relaxed. It is shown that in the presence of one target to be cooled the strong coupling is not beneficial to the refrigeration. The reason is explained by examining the effect of the strong coupling on the contributions of all eigenstates transitions to the heat current of the related thermal reservoir. When acting simultaneously on two targets, the machine can be manipulated to implement distributed tasks on them, such as cooling one target and meanwhile heating another one, by adjusting the coupling strengths between the machine with the two targets. In particular, we show that the machine can realize temperature reversal for the two qubits, namely, the qubit that is coupled to the high temperature reservoir is refrigerated to a temperature below that of the qubit contacting with the low temperature reservoir.

We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a Maxwell-Boltzmann distribution with a spatially uniform temperature and a spatially varying local center-of-mass velocity. We construct the local equilibrium Carnot cycle of an ideal gas, based on this distribution, and show that the efficiency of the present cycle is given by the endoreversible Carnot efficiency using the molecular kinetic temperatures of the gas. We also obtain an analytic expression of the efficiency at maximum power of our cycle under a small temperature difference. Our theory is also confirmed by a molecular dynamics simulation.

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing ${\eta }_f$ at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions $\eta >{\eta }_f$ of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field $\rho \left(\mathbf{x}\right)$ characterizing the metastable state is primarily described by a pair function $g_s(\eta /{\eta }_0)$. ${\eta }_0$ is a structural parameter such that for $\eta ={\eta }_0$ the pair function is identical to that for the Bernal random structure. The configurational entropy ${\mathcal{S}}_c$ of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated ${\mathcal{S}}_c$ vanishes as $\eta \to {\eta }_{\mathrm{K}}$ and ${\eta }_{\mathrm{K}}$ is in agreement with other works. The dependence of ${\eta }_{\mathrm{K}}$ on the structural parameter ${\eta }_0$ is obtained.

We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. This is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.

Continuous-time random walks of a particle that is randomly reset to an initial position are considered. The distribution of the waiting time between the reset events is represented as a sum of an arbitrary number of exponentials. The governing equation of this stochastic process is established. The mean first-passage time to a particular position is calculated. It is shown that anomalous subdiffusion has a significant impact on the shape of the stationary state.

An alternative approach of detecting unstable periodic orbits in chaotic time series is proposed using synchronization techniques. A master-slave synchronization scheme is developed, in which the chaotic system drives a system of harmonic oscillators through a proper coupling condition. The proposed scheme is designed so that the power of the coupling signal exhibits notches that drop to zero once the system approaches an unstable orbit yielding an explicit indication of the presence of a periodic motion. The results shows that the proposed approach is particularly suitable in practical situations, where the time series is short and noisy, or it is obtained from high-dimensional chaotic systems.

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the $\alpha$-Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.

Microtubules provide the mechanical force required for chromosome separation during mitosis. However, little is known about the dynamic (high-frequency) mechanical properties of microtubules. Here, we theoretically propose to control the vibrations of a doubly clamped microtubule by tip electrodes and to detect its motion via the optomechanical coupling between the vibrational modes of the microtubule and an optical cavity. In the presence of a red-detuned strong pump laser, this coupling leads to optomechanical-induced transparency of an optical probe field, which can be detected with state-of-the art technology. The center frequency and line width of the transparency peak give the resonance frequency and damping rate of the microtubule, respectively, while the height of the peak reveals information about the microtubule-cavity field coupling. Our method opens the new possibilities to gain information about the physical properties of microtubules, which will enhance our capability to design physical cancer treatment protocols as alternatives to chemotherapeutic drugs.

We study anisotropic collective motions of two-dimensional granular particles under simple shear deformations. Employing molecular-dynamics simulations of large system sizes, we find that anisotropic fluidized bands develop in the system yielding under quasistatic deformations, where the spectrum of nonaffine velocities, which is associated with the energy spectrum for turbulent flows, exhibits a quadrupole structure. To explain theoretically the anisotropic spectrum, we derive hydrodynamic modes from a continuum model of dense granular materials, where we find that fluidized bands are caused by long-lived hydrodynamic fluctuations characterized by compressibility.

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperatures and smallest strain rates.

The Thomas-Fermi model for warm and hot dense matter is widely used to predict material properties such as the equation of state. However, for practical reasons current implementations use pseudopotentials for the electron-nucleus interaction instead of the bare Coulomb potential. This complicates the calculation and quantities such as free energy cannot be converged with respect to the pseudopotential parameters. We present a method that retains the bare Coulomb potential for the electron-nucleus interaction and does not use pseudopotentials. We demonstrate that accurate free energies are obtained by checking variational consistency. Examples for aluminum and iron plasmas are presented.

This study shows that a relativistic Hall effect significantly changes the properties of wave propagation by deriving a linear dispersion relation for relativistic Hall magnetohydrodynamics (HMHD). Whereas, in nonrelativistic HMHD, the phase and group velocities of fast magnetosonic wave become anisotropic with an increasing Hall effect, the relativistic Hall effect brings upper bounds to the anisotropies. The Alfvén wave group velocity with strong Hall effect also becomes less anisotropic than the nonrelativistic case. Moreover, the group velocity surfaces of Alfvén and fast waves coalesce into a single surface in the direction other than near perpendicular to the ambient magnetic field. It is also remarkable that a characteristic scale length of the relativistic HMHD depends on ion temperature, magnetic field strength, and density while the nonrelativistic HMHD scale length, i.e., ion skin depth, depends only on density. The modified characteristic scale length increases as the ion temperature increases and decreases as the magnetic field strength increases.

The critical behavior of the two-state rotational sandpile model proposed by Santra et al. [Phys. Rev. E 75, 041122 (2007)] and the locally deterministic and globally stochastic three-state sandpile model are investigated via Monte Carlo simulations. Through these simulations, we are able to estimate critical exponents that characterize the avalanche properties, i.e., the probability distributions of the avalanche size, area, lifetime, and gyration radius, and the expectation values of the avalanche size and area against time and of the size against area. The results are compared with those of the known universality classes. The two models are found to yield consistent results within the range of statistical error, and appear to be consistent with the stochastic two-state Manna sandpile model; therefore, both models appear to belong to the Manna universality class. Our results contradict the earlier conclusion of Santra et al., which we attribute to the slow convergence of the probability distribution to the asymptotic power-law behavior, particularly for the size and lifetime of avalanches.

We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.