Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature $T$ is $k_{B}Tln2$ in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time $\tau$ with limited controllability. The energy cost is minimized with the optimal control scheme with and without bound. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time.

We explore the dynamics of a simple liquid whose particles, in addition to standard potential-based interactions, are also subjected to transverse forces preserving the Boltzmann distribution. We derive the effective dynamics of one and two tracer particles in the infinite-dimensional limit. We determine the amount of acceleration of the dynamics caused by the transverse forces, in particular in the vicinity of the glass transition. We analyze the emergence and evolution of odd transport phenomena induced by the transverse forces.

Nanoporous materials provide high surface area per unit mass and are capable of fluids adsorption. While the measurements of the overall amount of fluid adsorbed by a nanoporous sample are straightforward, probing the spatial distribution of fluids is nontrivial. We consider literature data on adsorption and desorption of fluids in nanoporous glasses reported along with the measurements of ultrasonic wave propagation. We analyze these using the so-called dynamic equivalent medium approach, which is based on Biot's theory of dynamic poroelasticity with coefficients that are continuous random functions of position. When further constrained by optical scattering data for similar systems, the calculations show that on adsorption the characteristic patch size is of the order of 100 pore diameters, while on desorption the patch size is comparable to the sample size. Our analysis suggests that one can employ ultrasound to probe the uniformity of the spatial distribution of fluids in nanoporous materials.

Debye relaxation is a simple and unique physical mechanism by which a macroscopic orientational polarization decays monoexponentially with time. However, the very existence of the Debye process in complex systems such as water, aqueous solutions, and monohydroxyl alcohols, among others, is puzzling to date and their microscopic origin is still ambiguously explained. In order to shed light on some of these aspects, orientational dynamics of an orientationally disordered dipolar crystal with an identically structured nonpolar matrix has been studied in the form of solid solutions. A crossover from non-Debye to Debye-type spectral behavior has been observed with increasing concentration of the nonpolar matrix in the solid solutions. Analysis of the dynamic response shows that the evolution of cooperativity and spatial heterogeneity with concentration of nonpolar matrix is responsible for the observed trends. The results not only authenticate a possible mechanism of the Debye process as originating from localized orientational fluctuations due to molecular dipoles but also shed light on the evolution of non-Debye characteristics in these systems.

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impacts their propulsion performance compared with the case of that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this paper, we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.

Here a mechanism for self-compression of laser pulses is presented, based on period density-modulated plasma. In this setup, two pump beams intersect at a small angle within the plasma. This interaction is facilitated by the ponderomotive ion mechanism, which causes a modulation in the density of plasma with long wavelengths and low amplitude. This modulation enhances the backward Raman scattering of the probe pulse. The trailing edge of the probe experiences greater energy loss, resulting in a steeper intensity gradient. This, in turn, induces an asymmetric self-phase modulation, which elevates the instantaneous frequency. It is notable that the laser in plasma exhibits opposite group velocity dispersion compared to traditional solid-state media. This unique property allows laser pulses to undergo dispersion compensation while broadening the spectrum, ultimately leading to self-compression. The 2D-PIC simulations demonstrate these phenomena, highlighting how period density-modulated plasma contributes to an asymmetric spectral distribution. The intricate interplay among self-phase modulation, group velocity, and backward Raman scattering results in the self-compressing of the laser pulse. Specifically, the pulses are compressed from their Fourier transform limit duration of 50 fs to a significantly reduced duration of 8 fs at plasma densities below 1/4 critical density, without the transverse self-focusing effects.

We investigate some topological and spectral properties of Erdős-Rényi (ER) random digraphs of size $n$ and connection probability $p, D(n,p)$. In terms of topological properties, our primary focus lies in analyzing the number of nonisolated vertices $V_x\left(D\right)$ as well as two vertex-degree-based topological indices: the Randić index $R\left(D\right)$ and sum-connectivity index $\chi \left(D\right)$. First, by performing a scaling analysis, we show that the average degree $\langle k\rangle$ serves as a scaling parameter for the average values of $V_x\left(D\right), R\left(D\right)$, and $\chi \left(D\right)$. Then, we also state expressions relating the number of arcs, largest eigenvalue, and closed walks of length 2 to $(n,p)$, the parameters of ER random digraphs. Concerning spectral properties, we observe that the eigenvalue distribution converges to a circle of radius $\sqrt{np(1-p)}$. Subsequently, we compute six different invariants related to the eigenvalues of $D(n,p)$ and observe that these quantities also scale with $\sqrt{np(1-p)}$. Additionally, we reformulate a set of bounds previously reported in the literature for these invariants as a function $(n,p)$. Finally, we phenomenologically state relations between invariants that allow us to extend previously known bounds.

Colloidal particles can create reconfigurable nanomaterials, with applications such as color-changing, self-repairing, and self-regulating materials and reconfigurable drug delivery systems. However, top-down methods for manipulating colloids are limited in the scale they can control. We consider here a new method for using chemical reactions to multiply the effects of existing top-down colloidal manipulation methods to arrange large numbers of colloids with single-particle precision, which we refer to as chemical herding. Using simulation-based methods, we show that if a set of chemically active colloids (herders) can be steered using external forces (i.e., electrophoretic, dielectrophoretic, magnetic, or optical forces), then a larger set of colloids (followers) that move in response to the chemical gradients produced by the herders can be steered using the control algorithms given in this paper. We also derive bounds that predict the maximum number of particles that can be steered in this way, and we illustrate the effectiveness of this approach using Brownian dynamics simulations. Based on the theoretical results and simulations, we conclude that chemical herding is a viable method for multiplying the effects of existing colloidal manipulation methods to create useful structures and materials.

Laser direct drive (LDD) inertial confinement fusion (ICF) involves irradiating a spherical target of thermonuclear fuel coated with an ablator, usually made of polystyrene. Laser energy absorption near the target surface leads to matter ablation, hydrodynamic shocks, and ultimately capsule implosion. The conservation of spherical symmetry is crucial for implosion efficiency, yet spatial modulations in laser intensity can induce nonuniformities, causing the laser imprint phenomenon. Understanding laser imprint, especially considering the initial solid state, is essential for advancing LDD ICF. A first microscopic model of solid-to-plasma transition was built in 2019, accounting for laser absorption in the solid state with a band-structure-based ionization model. This model has been improved to include chemical fragmentation and a more accurate description of electron collision frequency in various matter states. The latest development involves assessing the model's reliability by comparing theoretical predictions with experimental observations. Despite the success of this approach, questions remain, leading to further investigations and observations under different irradiation conditions. This work presents an experiment with a nanosecond pulse, taking into account hydrodynamic effects, and measures transmission dynamics over the entire laser beam area to observe two-dimensional effects. The objective is to adapt the theoretical model, couple it with a hydrodynamic code, and observe additional effects related to the initial solid state.

In this paper we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, three benchmark problems, the Gauss hill problem, the CDE with nonlinear convection and diffusion terms, and the Taylor-Green vortex flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results not only are in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.

We explore the ground-state properties of a lattice of classical dipoles spanned on the surface of a Möbius strip. The dipole equilibrium configurations depend significantly on the geometrical parameters of the Möbius strip, as well as on the lattice dimensions. As a result of the variable dipole spacing on the curved surface of the Möbius strip, the ground state can consist of multiple domains with different dipole orientations which are separated by domain-wall-like boundaries. We analyze in particular the dependence of the ground-state dipole configuration on the width of the Möbius strip and highlight two crossovers in the ground state that can be correspondingly tuned. A first crossover changes the dipole lattice from a phase which resists compression to a phase that favors it. The second crossover leads to an exchange of the topological properties of the two involved domains. We conclude with a brief summary and an outlook on more complex topologically intricate surfaces.

In this paper we study a semiconductor laser system excited by multiplicative Ornstein-Uhlenbeck (OU) noise and additive sine-Wiener (SW) noise with a related real part and imaginary part. The two-dimensional Langevin equation (LE) with cross-correlating complex OU noise and complex SW noise is equivalent to the six-dimensional LE. Based on functional methods and spatial dimension extension methods, the six-dimensional Fokker-Planck equation (FPE) is achieved. Through Taylor expansion approximation and linear transformation, the dimensionality of FPE is reduced, and the exact expression of the probability distribution (SPD) in steady state is obtained. The impacts of noise parameters on laser intensity on SPD are further analyzed. Moreover, based on the reduced FPE, the information entropy of the system is obtained. This calculation is useful for us to understand further the influence of system parameters and noise correlation coefficient on the system. The main work lies in obtaining an alternative method for deriving a FPE corresponding to the two-dimensional stochastic semiconductor laser model, which is more applicable than methods in previous literature. An equivalent expression for cross-correlated OU noise and cross-correlated SW noise as well as a method for approximate solutions of a high-dimensional FPE are also provided.

We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: A broad class of nonlinear classical field theories are believed to have a stationary turbulent state—a far-from-equilibrium state, even at weak coupling. Our method provides an efficient way to derive properties of the weak wave turbulent state. A central object in these studies, which is a reduction of the Liouville equation, is the kinetic equation, which governs the occupation numbers of the modes. All properties of wave turbulence to date are based on the kinetic equation found at leading order in the weak nonlinearity. We explicitly obtain the kinetic equation to next-to-leading order.

We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.

The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy-level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The definition of SFF in most literature only encapsulates the two-level correlation. In this manuscript, we extend the definition of SSF to include the high-order correlation. Specifically, we introduce the standard deviation of energy levels to define correlation functions, from which the generalized spectral form factor (GSFF) can be obtained by Fourier transforms. GSFF provides a more comprehensive knowledge of the dynamics of chaotic systems. Using random matrices as examples, we demonstrate dynamics features that are encoded in GSFF. Remarkably, the GSFF is complex, and the real and imaginary parts exhibit universal dynamics. For instance, in the two-level correlated case, the real part of GSFF shows a dip-ramp-plateau structure akin to the conventional counterpart, and the imaginary part for different system sizes converges in the long-time limit. For the two-level GSFF, the analytical forms of the real part are obtained and consistent with numerical results. The results of the imaginary part are obtained by numerical calculation. Similar analyses are extended to three-level GSFF.

Traditional linear stability analysis based on matrix diagonalization is a computationally intensive process for high-dimensional systems of differential equations, posing substantial limitations for the exploration of Turing systems of pattern formation where an additional wave-number parameter needs to be investigated. In this paper, we introduce an efficient and intuitive technique that leverages Gershgorin's theorem to determine upper limits on regions of parameter space and the wave number beyond which Turing instabilities cannot occur. This method offers a streamlined avenue for exploring the phase diagrams of other complex multi-parametric models, such as those found in gene regulatory networks in systems biology. Due to its suitability for the asymptotic limit of infinitely large systems, it predicts the existence of a sweet spot in network size for maximal Jacobian stability.

Gramicidin A (gA) is a short hydrophobic β-helical peptide that forms cation-selective channels in lipid membranes in the course of transbilayer dimerization. The length of the gA helix is smaller than the thickness of a typical lipid monolayer. Consequently, elastic deformations of the membrane arise in the configurations of gA monomers, conducting dimer, and the intermediate state of coaxial pair, where gA monomers from opposing membrane monolayers are located one on top of the other. The gA channel is characterized by the average lifetime of the conducting state. The elastic properties of the membrane influence the average lifetime, thus making gA a convenient sensor of membrane elasticity. However, the utilization of gA to investigate the elastic properties of mixed membranes comprising two or more components frequently relies on the assumption of ideality, namely that the elastic parameters of mixed-lipid bilayers depend linearly on the concentrations of the components. Here, we developed a general approach that does not rely on the aforementioned assumption. Instead, we explicitly accounted for the possibility of inhomogeneous lateral distribution of all lipid components, as well as for membrane-mediated lateral interactions of gA monomers, dimer, coaxial pair, and minor lipid components. This approach enabled us to derive unknown elastic parameters of lipid monolayer from experimentally determined lifetimes of gA channel in mixed-lipid bilayers. A general algorithm was formulated that allows the unknown elastic parameters of a lipid monolayer to be obtained using gA as a mechanical sensor.

We report on the self-part of the Van Hove correlation function, the correlation function describing the dynamics of a single molecule, of water and deuterated water. The correlation function is determined by transforming inelastic scattering spectra of neutrons or x rays over a wide range of momentum transfer $Q$ and energy transfer $E$ to space $R$ and time $t$. The short-range diffusivity is estimated from the Van Hove correlation function in the framework of the Gaussian approximation. The diffusivity has been found to be different from the long-range macroscopic diffusivity, providing information about local atomic dynamics.