We investigate the excitation dynamics at a first-order quantum phase transition (QPT). More specifically, we consider the quench-induced QPT in the quantum search algorithm, which aims at finding out a marked element in an unstructured list. We begin by deriving the exact dynamics of the model, which is shown to obey a Riccati differential equation. Then, we discuss the probabilities of success by adopting either global or local adiabaticity strategies. Moreover, we determine the disturbance of the quantum criticality as a function of the system size. In particular, we show that the critical point exponentially converges to its thermodynamic limit even in a fast evolution regime, which is characterized by both entanglement QPT estimators and the Schmidt gap. The excitation pattern is manifested in terms of quantum domain walls separated by kinks. The kink density is then shown to follow an exponential scaling as a function of the evolution speed, which can be interpreted as a Kibble-Zurek mechanism for first-order QPTs.

We demonstrate that two interacting spinlike systems characterized by different excitation frequencies and coupled to a thermal bath each, can be used as a quantum thermal diode capable of efficiently rectifying the heat current. This is done by deriving analytical expressions for both the heat current and rectification factor of the diode, based on the solution of a master equation for the density matrix. Higher rectification factors are obtained for lower heat currents, whose magnitude takes their maximum values for a given interaction coupling proportional to the temperature of the hotter thermal bath. It is shown that the rectification ability of the diode increases with the excitation frequencies difference, which drives the asymmetry of the heat current, when the temperatures of the thermal baths are inverted. Furthermore, explicit conditions for the optimization of the rectification factor and heat current are explicitly found.

Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a system of $N$ spherical particles, and directly account for the singularities that arise in the sticky limit where the pairwise interaction is strong and short ranged. Although the contribution to the partition function from singular clusters diverges in the limit, its asymptotic value can be calculated and depends on only two parameters, characterizing the depth and range of the potential. The result holds for systems that are second-order rigid, a geometric characterization that describes all known ground-state (rigid) sticky clusters. To illustrate the applications of our theory we address the question of emergence: how does crystalline order arise in large systems when it is strongly disfavored in small ones? We calculate the partition functions of all known rigid clusters up to $N\le 21$ and show the cluster landscape is dominated by hyperstatic clusters (those with more than $3N-6$ contacts); singular and isostatic clusters are far less frequent, despite their extra vibrational and configurational entropies. Since the most hyperstatic clusters are close to fragments of a close-packed lattice, this underlies the emergence of order in sticky-sphere systems, even those as small as $N=10$.

It is widely accepted that neuronal firing rates contain a significant amount of information about the stimulus intensity. Nevertheless, theoretical studies on the coding accuracy inferred from the exact spike counting distributions are rare. We present an analysis based on the number of observed spikes assuming the stochastic perfect integrate-and-fire model with a change point, representing the stimulus onset, for which we calculate the corresponding Fisher information to investigate the accuracy of rate coding. We analyze the effect of changing the duration of the time window and the influence of several parameters of the model, in particular the level of the presynaptic spontaneous activity and the level of random fluctuation of the membrane potential, which can be interpreted as noise of the system. The results show that the Fisher information is nonmonotonic with respect to the length of the observation period. This counterintuitive result is caused by the discrete nature of the count of spikes. We observe also that the signal can be enhanced by noise, since the Fisher information is nonmonotonic with respect to the level of spontaneous activity and, in some cases, also with respect to the level of fluctuation of the membrane potential.

Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.

Thin fluid membranes embedded in a bulk fluid of different viscosity are of fundamental interest as experimental realizations of quasi-two-dimensional fluids and as models of biological membranes. We have probed the hydrodynamics of thin fluid membranes by active microrheology using small tracer particles to observe the highly anisotropic flow fields generated around a rigid oscillating post inserted into a freely suspended smectic liquid crystal film that is surrounded by air. In general, at distances more than a few Saffman lengths from the meniscus around the post, the measured velocities are larger than the flow computed by modeling a moving disklike inclusion of finite extent by superposing Levine-MacKintosh response functions for pointlike inclusions in a viscous membrane. The observed discrepancy is attributed to additional coupling of the film with the air below the film that is displaced directly by the shaft of the moving post.

Hydrodynamic fields, macroscopic boundary conditions, and non-Newtonian rheology of the acceleration-driven Poiseuille flow of a dilute granular gas are probed using “direct simulation Monte Carlo” method for a range of Knudsen numbers ($\text{Kn}$, the ratio between the mean free path and the macroscopic length), spanning the rarefied regime of slip and transitional flows. It is shown that the “dissipation-induced clustering” (for $1-e_n>0$, where $e_n$ is the restitution coefficient), leading to inhomogeneous density profiles along the transverse direction, competes with “rarefaction-induced declustering” (for $\text{Kn}>0$) phenomenon, leaving seemingly “anomalous” footprints on several hydrodynamic and rheological quantities; one example is the well-known rarefaction-induced temperature bimodality, which could also result from inelastic dissipation that dominates in the continuum limit ($\text{Kn}\to 0$) as found recently [Alam et al., J. Fluid Mech. 782, 99 (2015)]. The simulation data on the slip velocity and the temperature slip are contrasted with well-established boundary conditions for molecular gases. A modified Maxwell-Navier-type boundary condition is found to hold in granular Poiseuille flow, with the velocity slip length following a power-law relation with Knudsen number ${\text{Kn}}^{\delta }$, with $\delta \approx 0.95$, for $\text{Kn}\le 0.1$. Transverse profiles of both first $\left[{\mathcal{N}}_1\left(y\right)\right]$ and second $\left[{\mathcal{N}}_2\left(y\right)\right]$ normal stress differences seem to correlate well with respective density profiles at small $\text{Kn}$; their centerline values $[{\mathcal{N}}_1\left(0\right)$ and ${\mathcal{N}}_2\left(0\right)]$ can be of “odd” sign with respect to their counterparts in molecular gases. The phase diagrams are constructed in the ($\text{Kn},1-e_n$) plane that demarcates the regions of influence of inelasticity and rarefaction, which compete with each other resulting in the sign change of both ${\mathcal{N}}_1\left(0\right)$ and ${\mathcal{N}}_2\left(0\right)$. The results on normal stress differences are rationalized via a comparison with a Burnett-order theory [Sela and Goldhirsch,  J. Fluid Mech. 361, 41 (1998)], which is able to predict their correct behavior at small values of the Knudsen number. Lastly, the Knudsen paradox and its dependence on inelasticity are analyzed and contrasted with related recent works.

We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.

Electrokinetic (EK) turbulence or electrohydrodynamic (EHD) turbulence has been recently achieved in different fluids under both ac [G. Wang et al., Lab Chip 14, 1452 (2014); Phys. Rev. E 93, 013106 (2016)] and dc electric fields [A. Varshney et al., Soft Matter 12, 1759 (2016)]. Here, through dimensional analysis, scaling laws of both velocity and electric conductivity structure functions in the forced cascade region of ac EK turbulence can be predicated (similar to Bolgiano-Obukhov scaling law in turbulent Rayleigh-Bénard convection), in either macroscale or microscale flows. In the forced cascade region, EK force, which relies on the direct cascade of conductivity structures, injects energy directly into a wide spectral region to sustain the flow disturbance. The scaling exponents of the second-order velocity and conductivity structures are 2/5 and 4/5, respectively. In addition to the scaling regions, two characteristic small length scales are derived for both weak and strong electric body forces, respectively. This theoretical investigation can significantly enhance our understanding of EK or EHD turbulence while forced by an ac electric field. It can further broaden our understanding of the forced cascade region of forced turbulence and make the manipulation of the turbulent cascade process more flexible and controllable.

Magnetic Archimedes Coriolis (MAC) waves are omnipresent in several geophysical and astrophysical flows such as the solar tachocline. In the present study, we use linear spectral theory (LST) and investigate the energy partition, scale by scale, in MAC weak wave turbulence for a Boussinesq fluid. At the scale $k^{-1},$ the maximal frequencies of magnetic (Alfvén) waves, gravity (Archimedes) waves, and inertial (Coriolis) waves are, respectively, $V_{A}k,N$, and $f.$ By using the induction potential scalar, which is a Lagrangian invariant for a diffusionless Boussinesq fluid [Salhi et al., Phys. Rev. E 85, 026301 (2012)], we derive a dispersion relation for the three-dimensional MAC waves, generalizing previous ones including that of $f$-plane MHD “shallow water” waves [Schecter et al., Astrophys. J. 551, L185 (2001)]. A solution for the Fourier amplitude of perturbation fields (velocity, magnetic field, and density) is derived analytically considering a diffusive fluid for which both the magnetic and thermal Prandtl numbers are one. The radial spectrum of kinetic, $S_{\kappa }(k,t),$ magnetic, $S_m(k,t),$ and potential, $S_p(k,t),$ energies is determined considering initial isotropic conditions. For magnetic Coriolis (MC) weak wave turbulence, it is shown that, at large scales such that $V_{A}k/f\ll 1,$ the Alfvén ratio $S_{\kappa }(k,t)/S_m(k,t)$ behaves like $k^{-2}$ if the rotation axis is aligned with the magnetic field, in agreement with previous direct numerical simulations [Favier et al., Geophys. Astrophys. Fluid Dyn. (2012)] and like $k^{-1}$ if the rotation axis is perpendicular to the magnetic field. At small scales, such that $V_{A}k/f\gg 1,$ there is an equipartition of energy between magnetic and kinetic components. For magnetic Archimedes weak wave turbulence, it is demonstrated that, at large scales, such that ($V_{A}k/N\ll 1),$ there is an equipartition of energy between magnetic and potential components, while at small scales ($V_{A}k/N\gg 1),$ the ratio $S_p(k,t)/S_{\kappa }(k,t)$ behaves like $k^{-1}$ and $S_{\kappa }(k,t)/S_m(k,t)=1.$ Also, for MAC weak wave turbulence, it is shown that, at small scales ($V_{A}k/\sqrt{N^2+f^2}\gg 1),$ the ratio $S_p(k,t)/S_{\kappa }\left(t\right)$ behaves like $k^{-1}$ and $S_{\kappa }(k,t)/S_m(k,t)=1.$

We study quantum enhancement of transport in open systems in the presence of disorder and dephasing. Quantum coherence effects may significantly enhance transport in open systems even in the semiclassical regime (where the decoherence rate is greater than the intersite hopping amplitude), as long as the disorder is sufficiently strong. When the strengths of disorder and dephasing are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected in the Fenna-Matthews-Olson (FMO) photosynthetic complex, which may be viewed as intermediate between these paradigmatic models.

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.

Thermodynamic fluxes (diffusion fluxes, heat flux, etc.) are often proportional to thermodynamic forces (gradients of chemical potentials, temperature, etc.) via the matrix of phenomenological coefficients. Onsager's relations imply that the matrix is symmetric, which reduces the number of unknown coefficients is reduced. In this article we demonstrate that for a class of nonequilibrium thermodynamic models in addition to Onsager's relations the phenomenological coefficients must share the same functional dependence on the local thermodynamic state variables. Thermodynamic models and experimental data should be validated through consistency with the functional constraint. We present examples of coupled heat and mass transport (thermodiffusion) and coupled charge and mass transport (electro-osmotic drag). Additionally, these newly identified constraints further reduce the number of experiments needed to describe the phenomenological coefficient.

The trajectory equations for classical periodic orbits in the equilateral-triangular and circular billiards are systematically extracted from quantum stationary coherent states. The relationship between the phase factors of quantum stationary coherent states and the initial positions of classical periodic orbits is analytically derived. In addition, the stationary coherent states with noncoprime parametric numbers are shown to correspond to the multiple periodic orbits, which cannot be explicable in the one-particle picture. The stationary coherent states are further verified to be linked to the resonant modes that are generally observed in the experimental wave system excited by a localized and unidirectional source. The excellent agreement between the resonant modes and the stationary coherent states not only manifests the importance of classical features in experimental systems but also paves the way to manipulate the mesoscopic wave functions localized on the periodic orbits for applications.

Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume “fully mixed” approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory “length” decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a “constraint” is analyzed and discussed.

Our study considers the mechanism of the spontaneous oscillations of molecular motors that are driven by the power stroke principle by applying linear stability analysis around the stationary solution. By representing the coupling equation of microscopic molecular motor dynamics and mesoscopic sarcomeric dynamics by a rank-1 updated matrix system, we derived the analytical representations of the eigenmodes of the Jacobian matrix that cause the oscillation. Based on these analytical representations, we successfully derived the essential conditions for the oscillation in terms of the rate constants of the power stroke and the reversal stroke transitions of the molecular motor. Unlike the two-state model, in which the dependence of the detachment rates on the motor coordinates or the applied forces on the motors plays a key role for the oscillation, our three-state power stroke model demonstrates that the dependence of the rate constants of the power and reversal strokes on the strains in the elastic elements in the motor molecules plays a key role, where these rate constants are rationally determined from the free energy available for the power stroke, the stiffness of the elastic element in the molecular motor, and the working stroke size. By applying the experimentally confirmed values to the free energy, the stiffness, and the working stroke size, our numerical model reproduces well the experimentally observed oscillatory behavior. Furthermore, our analysis shows that two eigenmodes with real positive eigenvalues characterize the oscillatory behavior, where the eigenmode with the larger eigenvalue indicates the transient of the system of the quick sarcomeric lengthening induced by the collective reversal strokes, and the smaller eigenvalue correlates with the speed of sarcomeric shortening, which is much slower than lengthening. Applying the perturbation analyses with primal physical parameters, we find that these two real eigenvalues occur on two branches derived from a merge point of a pair of complex-conjugate eigenvalues generated by Hopf bifurcation.