Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The transport efficiency, i.e., the integrated probability of trapping at a certain vertex, is a measure of the success rate of the transfer process. Purely coherent quantum transport is known to be less efficient than the observed excitation transport, e.g., in biological systems, and there is evidence that environmental noise is indeed crucial for excitation transport. At variance with this picture, we here address purely coherent transport on highly symmetric graphs, and show analytically that it is possible to enhance the transport efficiency without environmental noise, i.e., using only a minimal perturbation of the graph. In particular, we show that adding an extra weight to one or two edges, depending on whether the initial state is localized or in a superposition of two vertex states, breaks the inherent symmetries of the graph and may be sufficient to achieve unit transport efficiency. We also briefly discuss the conditions to obtain a null transport efficiency, i.e., to avoid trapping.

Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to (1) noninteracting fermionic systems, (2) noninteracting bosonic systems, (3) thermally driven classical Markovian systems, and (4) unicyclic Markovian networks. Finally, it is demonstrated that violation of the obtained inequalities can provide a broad spectrum of information about the physics of the analyzed system; e.g., it can enable one to infer the presence of interactions or unitary dynamics, unravel the topology of the Markovian network, or characterize the nature of thermodynamic forces driving the system. In particular, relevant information about the microscopic dynamics can be gained even at equilibrium when the current variance—a standard measure of current fluctuations—is determined mostly by the thermal noise.

The expected return time of a fluctuating two-dimensional cluster or vacancy to a given configuration is studied in thermodynamic equilibrium. We define a family of bond-breaking models that preserve the number of particles. This family includes edge diffusion and surface diffusion inside vacancies in the limit of fast particle diffusion and slow attachment-detachment kinetics. Within the frame of these bond-breaking models, the expected return time is found to depend on the energies of the configurations and on the energies of the excited states formed by removing a single particle from the cluster. High- and low-temperature regimes are studied. We clarify the conditions under which the return time is a nonmonotonous function of temperature: a minimum is found when the energy obtained by the average over the excited states of the configuration weighted by their attachment probabilities is lower than the energy averaged over all states. In addition, we show that the optimal temperature at which the return time is minimum is shifted to a higher temperature as compared to the temperature at which the equilibrium probability is maximum. This shift is influenced by the average curvature of the cluster edge, and is therefore larger for vacancies.

In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition $j=0$, where $j$ is a flux. Since an analogous equation for passive Brownian particles is first-order, a second- and third-order term are features of active motion. In all cases, the solution has a form of a convolution of two distributions: the Gaussian distribution representing the Boltzmann distribution of passive particles, and the beta distribution representing active motion at zero temperature.

Using Green's function method, we study thermal transport properties of magnons transmitting through a magnetic nanowire at a certain temperature. In a small part of the nanowire in the middle, we are supposed to have two types of local and nonlocal magnon-phonon interactions. The self-energies for this part due to the other parts of the wire are analytically derived. First, we calculate the phonon mode-dependent magnon transmission coefficient in the classical canonical ensemble. Then, by taking an average of the phonon modes, we obtain the total magnon transmission coefficient and use it for computing magnon thermal conductance. We use the model to investigate four configurations of magnetic nanowires composed of ferromagnetic and/or antiferromagnetic parts. The results show that, when the scattering region has an antiferromagnetic alignment, the magnons transfer in the structure more weakly than for ferromagnetic alignment. There is a phonon-assisted mechanism for tunneling of magnons which are transmitted through the gap or between magnon quasifrequencies of the scattering region. Generally, in the same values for local and nonlocal strengths of magnon-phonon interaction, the nonlocal one has a greater effect on the magnonic thermal transport properties. We found the fitting functions in order to relate the macroscopic quantities of the magnon transmission coefficient and thermal conductivity to microscopic parameters of the strengths of the local and nonlocal magnon-phonon interaction.

Does chaos in the dynamics enable or impede information gain in quantum tomography? We address this question by considering continuous measurement tomography in which the measurement record is obtained as a sequence of expectation values of a Hermitian observable evolving under the repeated application of the Floquet map of the quantum kicked top. For a given dynamics and Hermitian observables, we observe completely opposite behavior in the tomography of well-localized spin coherent states compared to random states. As the chaos in the dynamics increases, the reconstruction fidelity of spin coherent states decreases. This contrasts with the previous results connecting information gain in tomography of random states with the degree of chaos in the dynamics that drives the system. The rate of information gain and hence the fidelity obtained in tomography depends not only on the degree of chaos in the dynamics and to what extent it causes the initial observable to spread in various directions of the operator space, but, more importantly, how well these directions are aligned with the density matrix to be estimated. Our study also gives an operational interpretation for operator spreading in terms of fidelity gain in an actual quantum information tomography protocol.

Steadily moving transition (switching) fronts, associated with local transformation, symmetry breaking, or collapse, are among the most important dynamic coherent structures. The nonlinear mechanical waves of this type play a major role in many modern applications involving the transmission of mechanical information in systems ranging from crystal lattices and metamaterials to macroscopic civil engineering structures. While many different classes of such dynamic fronts are known, the interrelation between them remains obscure. Here we consider a minimal prototypical mechanical system, the Fermi-Pasta-Ulam (FPU) chain with piecewise linear nonlinearity, and show that there are exactly three distinct classes of switching fronts, which differ fundamentally in how (and whether) they produce and transport oscillations. The fact that all three types of fronts could be obtained as explicit Wiener-Hopf solutions of the same discrete FPU problem allows one to identify the exact mathematical origin of the particular features of each class. To make the underlying Hamiltonian dynamics analytically transparent, we construct a minimal quasicontinuum approximation of the FPU model that captures all three classes of the fronts and reveals interrelation between them. This approximation is of higher order than conventional ones (KdV, Boussinesq) and involves mixed space-time derivatives. The proposed framework unifies previous attempts to classify the mechanical transition fronts as radiative, dispersive, topological, or compressive and categorizes them instead as irreducible types of dynamic lattice defects.

We present evidence that the protein structure can be modeled as a stable static equilibrium, determined mainly by compressive supports in the nonpolar interior. That is, protein structures derive their structural strength through the same mechanical principles as do conventional structures like bridges and buildings. This is based on the observation that the experimentally elucidated structural determinants, the interior nonpolar side chains, are engaged in strong compressions in static terms. At the same time, major substructures in proteins, helices and h-bonded strands, because of their geometry, inherently leave gaps in the space they occupy. Under the compressive force, nonpolar side chains from one substructure can protrude into the gaps of another neighboring substructure and block its motion. As a result, interlocking of substructures can form, which builds up the nonpolar core assembly. The native structure then is the one with the structurally most stable core assembly. While intuitively appealing, this is a radical departure from the prevailing thinking that protein native structure is determined by global energy minimum, which is founded on thermodynamic hypothesis. Furthermore, to develop an effective model for analyzing protein structure with conventional tools, a proper mechanical representation must be established. By proving that the stability of the equilibrium in compressive interactions is conditioned on a form of mechanical energy minimum, we show that our notion of native structure can be equally consistent with the thermodynamic hypothesis. By mathematically treating the blocking action, an interaction, as a bar, a physical object, we succeed in representing and analyzing the core assembly as truss, a conventional structure. In this paper we define and expound step-by-step increasingly integrated interlocking patterns. We then analyze the core assemblies of a large set of diverse protein database structures. A native structure can be distinguished from decoys by comparing the composition and strength of their core assemblies. We show the results for two sets of native structures vs decoys.

Collective motion—or flocking—is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal group movements. In this work, we derive scaling relations for the fluctuations of the mean direction of motion and for the static density structure factor (which encodes static density fluctuations) in the presence of a homogeneous, small external field. This allows us to formulate two different and complementary criteria capable of detecting instances of directed motion exclusively from easily measurable dynamical and static signatures of the collective dynamics, without the need to detect correlations with environmental cues. The static one is informative in large enough systems, while the dynamical one requires large observation times to be effective. We believe these criteria may prove useful to detect or confirm the directed nature of collective motion in in vivo experimental observations, which are typically conducted in complex and not fully controlled environments.

Crumpled thin sheets are complex fractal structures whose physical properties are influenced by a hierarchy of ridges. In this paper, we report experiments that measure the stress-strain relation and show the coexistence of phases in the stretching of crumpled surfaces. The pull stress showed a change from a linear Hookean regime to a sublinear scaling with an exponent of $0.65\pm 0.03$, which is identified with the Hurst exponent of the crumpled sheets. The stress fluctuations are studied. The statistical distribution of force peaks is analyzed. It is shown that the unpacking of crumpled sheets is guided by a hierarchical order of ridges.

Inertial range energy transfer in three-dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two-point statistics, exact relations corresponding to the energy cascade are derived in terms of (i) two-point increments and (ii) two-point correlators. Despite having some apparent resemblances, the exact relation in binary fluid turbulence is found to be different from that of the incompressible magnetohydrodynamic turbulence [H. Politano and A. Pouquet, Geophys. Res. Lett. 25, 273 (1998)]. Besides the usual direct cascade of energy, under certain situations, an inverse cascade of energy is also speculated depending upon the strength of the activity parameter and the interplay between the two-point increments of the fluid velocity and the composition gradient fields. An alternative form of the exact relation is also derived in terms of the “upsilon” variables and a subsequent phenomenology is proposed predicting a $k^{-3/2}$ law for the turbulent energy spectrum.

This study concerns the mean-clustering approach to modeling the evolution of lattice dynamics. Instead of tracking the state of individual lattice sites, this approach describes the time evolution of the concentrations of different cluster types. It leads to an infinite hierarchy of ordinary differential equations which must be closed by truncation using a so-called closure condition. This condition approximates the concentrations of higher-order clusters in terms of the concentrations of lower-order ones. The pair approximation is the most common form of closure. Here, we consider its generalization, termed the “optimal approximation,” which we calibrate using a robust data-driven strategy. To fix attention, we focus on a recently proposed structured lattice model for a nickel-based oxide, similar to that used as cathode material in modern commercial Li-ion batteries. The form of the obtained optimal approximation allows us to deduce a simple sparse closure model. In addition to being more accurate than the classical pair approximation, this “sparse approximation” is also physically interpretable which allows us to a posteriori refine the hypotheses underlying construction of this class of closure models. Moreover, the mean-cluster model closed with this sparse approximation is linear and hence analytically solvable such that its parametrization is straightforward, although it offers a good approximation of the actual time evolution of the cluster concentrations on short timescales only. On the other hand, parametrization of the mean-cluster model closed with the pair approximation is shown to lead to an ill-posed inverse problem.

We show that, when cells communicate by contact-mediated interactions, heterogeneity in cell shapes and sizes leads to qualitatively distinct collective behavior in the tissue. For intercellular coupling that implements lateral inhibition, such disorder-driven transitions can substantially alter the asymptotic pattern of differentiated cells by modulating their fate choice through changes in the neighborhood geometry. In addition, when contact-induced signals influence inherent cellular oscillations, disorder leads to the emergence of functionally relevant partially-ordered dynamical states.

There is a significant disagreement between the experimental and theoretical plasma Stark shift of the hydrogenlike helium Paschen-$\alpha$ line ($\lambda =468.568\mathrm{nm}$). Here, it is demonstrated that the controversy can be resolved by accounting for the plasma polarization shift and other related effects arising from the charged plasma particles penetrating the wave-function extent of the bound electron. For experimental verification, a laser-induced helium plasma with $n_e=1.50\times {10}^{24}{\mathrm{m}}^{-3}$ and $T_e=68200\mathrm{K}$, as independently determined by using the Thomson scattering method, was studied. Excellent agreement is observed between the theoretical and experimental line width and line shift, and more generally, for the entire line shape.

We study spectral form factor in periodically kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pairwise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that, for intermediate-range interactions, the random phase approximation can be used to rewrite the spectral form factor in terms of a bistochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pairing terms are absent, the effective Hamiltonian has a non-Abelian $SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless time with the system size, irrespective of the particle number. This is a consequence of degenerate symmetry multiplets of the subleading eigenvalue of the effective Hamiltonian and is broken by the pairing terms. In such a case, we numerically find a nontrivial systematic system-size dependence of the Thouless time, in contrast to a related recent study for kicked fermionic chains.

In a heterogeneous medium, the wave field can be decomposed as an infinite series known as the Born expansion. Each term of the Born expansion corresponds to a scattering order, it is thus theoretically possible to discriminate single and multiple scattering contribution to the field. Experimentally, what is actually measured is the total field in which all scattering orders interfere. Conventional imaging methods usually rely on the assumption that the multiple scattering contribution can be disregarded. In a back-scattering configuration, this assumption is valid for small depths, and begins to fail for depths larger than the scattering mean-free path ${\ell }_s$. It is therefore a key issue to estimate the relative amount of single and multiple scattering in experimental data. To this end, a single-scattering estimator $\widehat{\rho }$ computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wave field. In this paper, the meaning of this estimator is investigated and a particular attention is given to recurrent scattering. In a diffraction-limited experiment, a multiple scattering sequence is said to be recurrent if the first and last scattering events occur in the same resolution cell. Recurrent scattering is shown to be responsible for correlations between single scattering and higher scattering orders of the Born expansion, inducing a bias to the estimator $\widehat{\rho }$ that should rather be termed confocal scattering ratio. Interestingly, a more robust estimator is built by projecting the reflection matrix in a focused basis. The argument is sustained by numerical simulations as well as ultrasonic data obtained around 1.5 MHz in a model medium made of nylon rods immersed in water. From a more general perspective, this work raises fundamental questions about the impact of recurrent scattering on wave imaging.

A precise estimate of allele and haplotype polymorphism is of great interest in theoretical population genetics, but also has practical applications, such as bone marrow registries management. Allele polymorphism is driven mainly by point mutations, while haplotype polymorphism is also affected by recombination. Current estimates treat recombination as mutations in an infinite site model. We here show that even in the simple case of two loci in a haploid individual, for a finite population, most recombination events produce existing haplotypes, and as such are silent. Silent recombination considerably reduces the total number of haplotypes expected from the infinite site model for populations that are not much larger than one over the mutation rate. Moreover, in contrast with mutations, the number of haplotypes does not grow linearly with the population size. We hence propose a more accurate estimate of the total number of haplotypes that takes into account silent recombination. We study large-scale human leukocyte antigen (HLA) haplotype frequencies from human populations to show that the current estimated recombination rate in the HLA region is underestimated.

The paper presents a theoretical description of the light-induced nematic liquid crystal reorientation in a cell with gold nanoparticles deposited on the surface of one of bounding substrates. It is shown that the surface plasmon resonance in the nanoparticles significantly affects the threshold of the director reorientation. The mathematical model of a surface free-energy density of nematic cell is given, which takes into account the influence of the local electric field on the near-surface nematic layer at the substrate with gold nanoparticles. The threshold intensity of a director orientation instability is calculated and its dependence on the wavelength of incident light and the degree of filling of the surface with gold nanoparticles is analyzed. Comparison of the theoretical calculations with experimental data confirms the full adequacy of the proposed theoretical model.

A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is disordered hyperuniformity: the presence of hyperuniform scaling without long-range configurational order. Jammed granular packings have been proposed as an example of disordered hyperuniformity, but recent numerical investigation has revealed that many jammed systems instead exhibit a complex set of distinct behaviors at long, emergent length scales. We use the Voronoi tessellation as a tool to define a set of rescaling transformations that can impose hyperuniformity on an arbitrary weighted point process, and show that these transformations can be used in simulations to iteratively generate hyperuniform, mechanically stable packings of athermal soft spheres. These hyperuniform jammed packings display atypical mechanical properties, particularly in the low-frequency phononic excitations, which exhibit an isolated band of highly collective modes and a band gap around zero frequency.