We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.

We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)]. Our investigation further justifies the definition of quantum work via two-point energy measurements.

Actin polymerization is ubiquitously utilized to power the locomotion of eukaryotic cells and pathogenic bacteria in living systems. Inevitably, actin polymerization and depolymerization proceed in a fluctuating environment that renders the locomotion stochastic. Previously, we have introduced a deterministic model that manages to reproduce actin-propelled trajectories in experiments, but not to address fluctuations around them. To remedy this, here we supplement the deterministic model with noise terms. It enables us to compute the effects of fluctuating actin density and forces on the trajectories. Specifically, the mean-squared displacement (MSD) of the trajectories is computed and found to show a super-ballistic scaling with an exponent 3 in the early stage, followed by a crossover to a normal, diffusive scaling of exponent 1 in the late stage. For open-end trajectories such as straights and S-shaped curves, the time of crossover matches the decay time of orientational order of the velocities along trajectories, suggesting that it is the spreading of velocities that leads to the crossover. We show that the super-ballistic scaling of MSD arises from the initial, linearly increasing correlation of velocities, before time translational symmetry is established. When the spreading of velocities reaches a steady state in the long-time limit, short-range correlation then yields a diffusive scaling in MSD. In contrast, close-loop trajectories like circles exhibit localized periodic motion, which inhibits spreading. The initial super-ballistic scaling of MSD arises from velocity correlation that both linearly increases and oscillates in time. Finally, we find that the above statistical features of the trajectories transcend the nature of noises, be it additive or multiplicative, and generalize to other self-propelled systems that are not necessarily actin based.

Nebulin is an about $1\mu \mathrm{m}$ long intrinsically disordered scaffold for the thin filaments of skeletal muscle sarcomere. It is a multifunctional elastic protein that wraps around actin filament, stabilizes thin filaments, and regulates Ca-dependent actomyosin interactions. This study investigates whether the disorder profile of nebulin might encode guidelines for thin and thick filament interactions in the sarcomere of the skeletal muscle. The question was addressed computationally by analyzing the predicted disorder profile of human nebulin (6669 residues, $\sim 200$ actin-binding repeats) by pondr and the periodicity of the A-band stripes (reflecting the locations of myosin-associated proteins) in the electron micrographs of the sarcomere. Using the detrended fluctuation analysis, a scale factor for the A-band stripe image data with respect to the nebulin disorder profile was determined to make the thin and thick filaments aligned to have maximum correlation. The empirical mode decomposition method was then applied to identify hidden periodicities in both the nebulin disorder profile and the rescaled A-band data. The decomposition reveals three characteristic length scales (45 nm, 100 nm, and 200 nm) that are relevant for correlational analysis. The dynamical cross-correlation analyses with moving windows at various sarcomere lengths depict a vernierlike design for both periodicities, thus enabling nebulin to sense position and fine tune sarcomere overlap. This shows that the disorder profile of scaffolding proteins may encode a guideline for cellular architecture.

Excluded-volume arguments are applied toward modeling the pore-size distribution in systems of randomly arranged cylindrical rods with finite and nonuniform aspect ratios. An explicit expression for the pore-size distribution is obtained by way of an analogy to a hypothetical system of fully penetrable objects, through a mapping that is designed to preserve the volume fraction occupied by the particle cores and the specific surface area. Results are presented for the mean value and standard deviation of the pore radius as functions of the rod aspect ratio, volume fraction, and polydispersity (degree of nonuniformity in the aspect ratios of the particles).

The influence of a low ac electric field on phase transitions is discussed in the case of a nematic liquid crystal $4-n-\text{octyl}-4{}^{\prime }$-cyanobiphenyl (8CB) doped with ${\text{Sn}}_2{\text{P}}_2{\text{S}}_6$ ferroelectric nanoparticles. The phase-transition temperatures obtained from temperature-dependent dielectric measurements were higher than those determined by the calorimetric method. This difference is explained by the presence of the measuring electric field which induces two effects. The first one is the amplification of the interactions between the nanoparticle polarization and the liquid-crystal order parameter. The second one is the field-induced disaggregation or aggregation process at high nanoparticle concentrations.

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

We report on a study of the superconducting order parameter thermodynamic fluctuations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta },{\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$, and ${\mathrm{KOs}}_2{\mathrm{O}}_6$ compounds. A nonperturbative technique within the framework of the renormalized Gaussian approach is proposed. The essential features are reported (analytically and numerically) through Ginzburg-Landau (GL) model-based calculations which take into account both the dimension and the microscopic parameters of the system. By presenting a self-consistent approach improvement on the GL theory, a technique for obtaining corrections to the asymptotic critical behavior in terms of nonuniversal parameters is developed. Therefore, corrections to the specific heat and the critical transition temperature for one-, two-, and three-dimensional samples are found taking into account the fact that fluctuations occur at all length scales as the critical point of a system is approached. The GL model in the free-field approximation and the 3D-$XY$ model are suitable for describing the weak and strong fluctuation regimes respectively. However, with a modified quadratic coefficient, the renormalized GL model is able to explain certain experimental observations including the specific heat of complicated systems, such as the cup-rate superconductors and the $\beta$-pyrochlore oxides. It is clearly shown that the enhancement, suppression, or rounding of the specific heat jump of high-$T_c$ cup-rate superconductors at the transition are indicative of the order parameter thermodynamic fluctuations according to the dimension and the nature of interactions.

Linear response theory, the backbone of nonequilibrium statistical physics, has recently been extended to explain how and why nonergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation results between an external stimulus and the response of a complex system generating nonergodic renewal processes, when the stimulus is a similar nonergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the nonergodic case using time averages and a single time series, hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied.

Imperfection sensitivity is essential for mechanical behavior of biopolymer shells [such as ultrasound contrast agents (UCAs) and spherical viruses] characterized by high geometric heterogeneity. In this work, an imperfection sensitivity analysis is conducted based on a refined shell model recently developed for spherical biopolymer shells of high structural heterogeneity and thickness nonuniformity. The influence of related parameters (including the ratio of radius to average shell thickness, the ratio of transverse shear modulus to in-plane shear modulus, and the ratio of effective bending thickness to average shell thickness) on imperfection sensitivity is examined for pressured buckling. Our results show that the ratio of effective bending thickness to average shell thickness has a major effect on the imperfection sensitivity, while the effect of the ratio of transverse shear modulus to in-plane shear modulus is usually negligible. For example, with physically realistic parameters for typical imperfect spherical biopolymer shells, the present model predicts that actual maximum external pressure could be reduced to as low as 60% of that of a perfect UCA spherical shell or 55%–65% of that of a perfect spherical virus shell, respectively. The moderate imperfection sensitivity of spherical biopolymer shells with physically realistic imperfection is largely attributed to the fact that biopolymer shells are relatively thicker (defined by smaller radius-to-thickness ratio) and therefore practically realistic imperfection amplitude normalized by thickness is very small as compared to that of classical elastic thin shells which have much larger radius-to-thickness ratio.

In a jammed solid of granular particles, the applied stress is in-homogeneously distributed within the packing. A full experimental characterization requires measurement of all the interparticle forces, but so far such measurements are limited to a few systems in two and even fewer in three dimensions. Particles with the topology of (elastic) shells are good local force sensors as relatively large deformations of the shells result from relatively small forces. We recently introduced such fluorescent shells as a model granular system in which force distributions can be determined in three dimensions using confocal microscopy and quantitative image analysis. An interesting aspect about these shells that differentiates them from other soft deformable particles is their buckling behavior at higher compression. This leads to deformations that do not conserve the inner volume of the particle. Here we use this system to accurately measure the contact forces in a three-dimensional packing of shells subjected to a static anisotropic compression and to shear. At small deformations forces are linear, however, for a buckled contact, the restoring force is related to the amount of deformation by a square root law, as follows from the theory of elasticity of shells. Near the unjamming-jamming transition (point $J$), we found the probability distribution of the interparticle forces $P\left(f\right)$ to decay nearly exponentially at large forces, with little evidence of long-range force chains in the packings. As the packing density is increased, the tail of the distribution was found to crossover to a Gaussian, in line with other experimental and simulation studies. Under a small shear strain, up to 0.216, applied at an extremely low shear rate, we observed a shear-induced anisotropy in both the pair correlation function and contact force network; however, no appreciable change was seen in the number of contacts per particle.

We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in $d=2$ and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in $d=3$ or Kraichnan-Batchelor in $d=2$) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.

We compute the time evolution of correlation functions after quantum quenches in the sine-Gordon model within the semiclassical approximation, which is expected to yield accurate results for small and slow quenches producing slow quasiparticles with low density. We demonstrate this by reproducing results of a recent form-factor calculation of the relaxation of expectation values [B. Bertini, D. Schuricht, and F. H. L. Essler, J. Stat. Mech. (2014) P10035]. Extending these results, we find that—in the universal limit of vanishingly small quasiparticle velocities—the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions and show that they have diffusive behavior for large timelike separation.

The Newtonian dynamics of strongly confined fluids exhibits a rich behavior. Its confined and unconfined degrees of freedom decouple for confinement length $L\to 0$. In that case and for a slit geometry the intermediate scattering functions $S_{\mu \nu }(q,t)$ simplify, resulting for $(\mu ,\nu )\ne (0,0)$ in a Knudsen-gas-like behavior of the confined degrees of freedom, and otherwise in $S_{\parallel }(q,t)$, describing the structural relaxation of the unconfined ones. Taking the coupling into account we prove that the energy fluctuations relax exponentially. For smooth potentials the relaxation times diverge as $L^{-3}$ and $L^{-4}$, respectively, for the confined and unconfined degrees of freedom. The strength of the $L^{-3}$ divergence can be calculated analytically. It depends on the pair potential and the two-dimensional pair distribution function. Experimental setups are suggested to test these predictions.

We introduce a general class of $\mathrm{su}\left(1\right|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the $\mathrm{su}\left(1\right|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the $\mathrm{su}\left(1\right|1)$ permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal{E}\left(\pi \right))$, $\mathcal{E}\left(p\right)$ being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the $\mathrm{su}\left(1\right|1)$ elliptic chain.

We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed.

The electrical properties of a set of seven-helix transmembrane proteins, whose space arrangement [three-dimensional (3D) structure] is known, are investigated by using regular arrays of the amino acids. These structures, specifically cubes, have topological features similar to those shown by the chosen proteins. The theoretical results show a good agreement between the predicted current-voltage characteristics obtained from a cubic array and those obtained from a detailed 3D structure. The agreement is confirmed by available experiments on bacteriorhodopsin. Furthermore, all the analyzed proteins are found to share the same critical behavior of the voltage-dependent conductance and of its variance. In particular, the cubic arrangement evidences a short plateau of the excess conductance and its variance at high voltages. The results of the present investigation show the possibility to predict the $I\text{−}V$ characteristics of a multiple-protein sample even in the absence of detailed knowledge of the proteins' 3D structure.

The songs and calls of many bird species, like human speech, form distinct regional dialects. We suggest that the process of dialect formation is analogous to the physical process of magnetic domain formation. We take the coastal breeding grounds of the Puget Sound white crowned sparrow as an example. Previous field studies suggest that birds of this species learn multiple songs early in life, and when establishing a territory for the first time, retain one of these dialects in order to match the majority of their neighbors. We introduce a simple lattice model of the process, showing that this matching behavior can produce single dialect domains provided the death rate of adult birds is sufficiently low. We relate death rate to thermodynamic temperature in magnetic materials, and calculate the critical death rate by analogy with the Ising model. Using parameters consistent with the known behavior of these birds we show that coastal dialect domain shapes may be explained by viewing them as low-temperature “stripe states.”

The possibility of biaxial orientational order in nematic liquid crystals is a subject of intense current interest. We explore the tendencies toward local and global biaxial ordering in the recently synthesized trimethylated oxadiazole-based bent-core mesogens with a pronounced asymmetric (bow-type) shape of molecules. The combination of x-ray diffraction and optical studies suggests that the biaxial order is expressed differently at the short- and long-range scales. Locally, at the scale of a few molecules, x-ray-diffraction data demonstrate biaxial packing. However, above the mesoscopic scale, the global orientational order in all three compounds is uniaxial, as evidenced by uniform homeotropic alignment of the nematic phase which is optically tested over the entire temperature range and by the observations of topological defects induced by individual and aggregated colloidal spheres in the nematic bulk.

In ground-based experiments with complex (dusty) plasmas, charged microparticles are levitated against gravity by an electric field, which also drives ion flow in the parent gas. Existing analytical approaches to describe the electrostatic interaction between microparticles in such conditions generally ignore the field and ion-neutral collisions, assuming free ion flow with a certain approximation for the ion velocity distribution function (usually a shifted Maxwellian). We provide a comprehensive analysis of our previously proposed self-consistent kinetic theory including the field, ion-neutral collisions, and the corresponding ion velocity distribution. We focus on various limiting cases and demonstrate how the interplay of these factors results in different forms of the shielding potential.