The impact of a molecule of $N$ atoms with a speed of $v_0$ on the free end of the Frenkel-Kontorova chain is numerically simulated. Depending on the values of $N$ and $v_0$, different scenarios of the molecule-chain interaction are observed. Molecules with low speed stick to the chain. At somewhat higher speeds, the molecules bounce off the chain. Further increase in $v_0$ results in bouncing off a molecule larger than the incident one. At even higher speed, bouncing of the molecule off the chain takes place simultaneously with the formation of a supersonic crowdion (antikink) propagating along the chain. A very high collision velocity leads to the sputtering of atoms from the chain and the formation of single and multiple supersonic crowdions. Interestingly, the sputtering yield $Y$ as the function of $v_0$ demonstrates a nonmonotonous dependence. This is explained by the fact that supersonic crowdions can have a discrete set of propagation velocities. When $v_0$ is such that supersonic crowdions are effectively excited, the latter transfer energy deep into the chain, and the sputtering is minimal. For some $v_0$ ranges, the formation of supersonic crowdions is suppressed. In these cases, the energy transferred from the impact of the molecule to the chain is spent mainly on the sputtering of atoms. The results obtained qualitatively explain the physics of bombardment of a crystal surface by atomic clusters with applications in physical vapor deposition, ion implantation, ion-beam sputtering, and similar experimental techniques.

We study, analytically and numerically, stationary fluctuations in two models involving $N$ Brownian particles undergoing stochastic resetting in one dimension. We start with the well-known reset model where the particles reset to the origin independently (model A). Then we introduce nonlocal interparticle correlations by postulating that only the particle farthest from the origin can be reset to the origin (model B). At long times, models A and B approach nonequilibrium steady states. In the limit of $N\to \infty$, the steady-state particle density in model A has an infinite support, whereas in model B, it has a compact support, like the recently studied Brownian bees model. A finite system radius, which scales at large $N$ as $lnN$, appears in model A when $N$ is finite. In both models, we study stationary fluctuations of the center of mass of the system and of the radius of the system due to the random character of the Brownian motion and of the resetting events. In model A, we determine exact distributions of these two quantities. The variance of the center of mass for both models scales as $1/N$. The variance of the radius is independent of $N$ in model A and exhibits an unusual scaling $(lnN)/N$ in model B. The latter scaling is intimately related to the $1/f$ noise in the radius autocorrelation. Finally, we evaluate the mean first-passage time (MFPT) to a distant target in model A, model B, and the Brownian bees model. For model A, we obtain an exact asymptotic expression for the MFPT which scales as $1/N$. For model B and the Brownian bees model, we propose a sharp upper bound for the MFPT. The bound assumes an evaporation scenario, where the first passage requires multiple attempts of a single particle, which breaks away from the rest of the particles, to reach the target. The resulting MFPT for model B and the Brownian bees model scales exponentially with $\sqrt{N}$. We verify this bound by performing highly efficient weighted-ensemble simulations of the first passage in model B.

Gain switching is a simple technique for generating short pulses through direct modulation of optical gain in lasers. Its mathematical description requires the connection between a slowly varying, low intensity solution and a short, high intensity solution. Previous studies constructed a complete pulse by patching these two partial solutions at an arbitrary point in the phase plane. Here, we develop an asymptotic theory in which slow and fast solutions are matched together through a third intermediate solution. The mathematical analysis of the laser problem benefits from a preliminary study of the Lotka-Volterra equations when the two competing populations exhibit different timescales. Since this particular limit has never been explored, we first analyze the Lotka-Volterra equations before applying the theory to the more complex laser equations. We show a significant effect of the transition layer on the pulse intensity. Last, we discuss the case of sustained laser pulses generated through the $Q$-switching technique and show how their description may benefit from our theory.

We obtain the spectrum of bound states for modified Pöschl-Teller and square-potential wells in the nonlinear Schrödinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite number of multinode localized states. Soliton scattering by these two potentials confirmed the existence of the localized states which form as trapped modes. Critical speed for quantum reflection was calculated using the energies of the trapped modes.

Nucleosomes are the fundamental building blocks of chromatin that not only help in the folding of chromatin, but also in carrying epigenetic information. It is known that nucleosome sliding is responsible for dynamically organizing chromatin structure and the resulting gene regulation. Since sliding can move two neighboring nucleosomes physically close or away, can it play a role in the spreading of histone modifications? We investigate this by simulating a stochastic model that couples nucleosome dynamics with the kinetics of histone modifications. We show that the sliding of nucleosomes can affect the modification pattern as well as the time it takes to modify a given region of chromatin. Exploring different nucleosome densities and modification kinetic parameters, we show that nucleosome sliding can be important for creating histone modification domains. Our model predicts that nucleosome density coupled with sliding dynamics can create an asymmetric histone modification profile around regulatory regions. We also compute the probability distribution of modified nucleosomes and relaxation kinetics of modifications. Our predictions are comparable with known experimental results.

The structure of the nematic (cholesteric) drops that form at the clearing temperature of a mixture of the bent-core molecule CB7CB and the rodlike molecule 8CB doped with a surfactant is optically determined. Using experimental observations and numerical simulations, it is demonstrated that the director field inside these drops is not escaped concentric, as previously proposed, but twisted bipolar. The Lehmann rotation of these drops in the presence of a temperature gradient is described. Their rotation velocity is shown to be proportional to the temperature gradient and to the surface twist angle of the director field and inversely proportional to the drop radius, thus revealing a fundamental scaling law for the Lehmann effect of nematic and cholesteric twisted-bipolar droplets.

We report on differential evolution for analytic continuation: a parameter-free evolutionary algorithm to generate the dynamic structure factor from imaginary time correlation functions. Our approach to this long-standing problem in quantum many-body physics achieves enhanced spectral fidelity while using fewer compute (CPU) hours. The need for fine-tuning of algorithmic control parameters is eliminated by embedding them within the genome to be optimized for this evolutionary computation-based algorithm. Benchmarks are presented for models where the dynamic structure factor is known exactly and experimentally relevant results are included for quantum Monte Carlo simulations of bulk ${}^4\mathrm{He}$ below the superfluid transition temperature.

We study the time correlation in the von Neumann entropy fluctuation of the tunable discrete-time quantum walk in one dimension, induced by the coin disorder arising from the temporal fractional Gaussian noise (fGn). The fGn is characterized by the Hurst exponent $H$, which provides three different correlation scenarios, namely antipersistent ($0<H<0.5$), memoryless ($H=0.5$), and persistent ($0.5<H<1$). We show the correlation of fGn is transferred to the coin's degree of entanglement and eventually transpires in the time correlation of the von Neumann entropy fluctuation. This study hints at the potential of using noise correlation as a resource to sustain information backflow via the interaction of quantum system with the noisy environment.

In this paper we write exactly solvable generalizations of one-dimensional quantum $XY$ and Ising-like models by using $2^d$-dimensional gamma matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner-like transformations. We illustrate the techniques using a specific case of four-dimensional gamma matrices and explore the quantum phase transitions present in the model.

We consider the steepest entropy ascent (SEA) ansatz to describe the nonlinear thermodynamic evolution of a quantum system. Recently this principle has been dubbed the fourth law of thermodynamics [Beretta, Phil. Trans. R. Soc. A 378, 20190168 (2020)]. A unique global equilibrium state exists in this context, and any other state is driven by the maximum entropy generation principle towards this equilibrium. We study the SEA evolution of a continuous-time quantum walker (CTQW) on a cycle graph with $N$ nodes. SEA solutions are difficult to find analytically. We provide an approximate scheme to find a general single-particle evolution equation governed by the SEA principle, whose solution produces dissipation dynamics. We call this scheme the fixed Lagrange's multiplier (FLM) method. In the Bloch sphere representation, we find trajectories traced out by the Bloch vector within the sphere itself. We have discussed these trajectories under various initial conditions for the case of a qubit. A similar dissipative motion is also observed in the case of CTQW, where probability amplitudes have been used to characterize decoherence. Our FLM scheme shows good agreement with numerical results. As we report, in CTQW, a strong delocalization exists for low system relaxation time.

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have uncovered a rich structure regarding its scaling exponents and fluctuation statistics. However, the zero surface tension or zero viscosity case eludes such analytical solutions and has remained ill-understood. Using numerical simulations, we elucidate a well-defined universality class for this case that differs from that of the viscous case, featuring intrinsically anomalous kinetic roughening (despite previous expectations for systems with local interactions and time-dependent noise) and ballistic dynamics. The latter may be relevant to recent quantum spin chain experiments which measure KPZ and ballistic relaxation under different conditions. We identify the ensuing set of scaling exponents in previous discrete interface growth models related with isotropic percolation, and show it to describe the fluctuations of additional continuum systems related with the noisy Korteweg–de Vries equation. Along this process, we additionally elucidate the universality class of the related inviscid stochastic Burgers equation.

A unique electron nanobunching mechanism using a two-color laser pulse interacting with a microstructured foil is proposed for directly generating ultraintense isolated attosecond pulses in the transmission direction without requiring extra filters and gating techniques. The unique nanobunching mechanism ensures that only one electron sheet contributes to the transmitted radiation. Accordingly, the generated attosecond pulses are unipolar and have durations at the full width at half-maximum about 5 attoseconds. The emitted ultrahigh-amplitude isolated attosecond pulses have intensities of up to $\sim {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$, which are beyond the limitations of weak attosecond pulses generated by gas harmonics sources and may open a new regime of nonlinear attosecond studies. Unipolar pulses can be useful for probing ultrafast electron dynamics in matter via asymmetric manipulation.

An accessibility enhanced efficient fundamental X-mode electron cyclotron heating (ECH) current start-up regime was identified for a reactorlike toroidal magnetic field range which has more than 100 times higher current drive efficiency compared to more conventional ECH methods for the relevant start-up temperature range. Very high current drive efficiency is possible due to the strong cyclotron interaction only with unidirectional passing electrons constrained by the wave accessibility conditions. This efficient electron cyclotron current drive regime may help facilitate the design of innovative economical solenoid-free tokamak fusion reactor systems.

Brownian yet non-Gaussian processes have recently been observed in numerous biological systems, and corresponding theories have been constructed based on random diffusivity models. Considering the particularity of random diffusivity, this paper studies the effect of an external force acting on two kinds of random diffusivity models whose difference is embodied in whether the fluctuation-dissipation theorem is valid. Based on the two random diffusivity models, we derive the Fokker-Planck equations with an arbitrary external force, and we analyze various observables in the case with a constant force, including the Einstein relation, the moments, the kurtosis, and the asymptotic behaviors of the probability density function of particle displacement at different timescales. Both the theoretical results and numerical simulations of these observables show a significant difference between the two kinds of random diffusivity models, which implies the important role of the fluctuation-dissipation theorem in random diffusivity systems.

A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic interaction. The 2SCP is known to exhibit a complex behavior with a rich phase diagram, including continuous and discontinuous transitions between the active phase and extinction. In this work, we advance the understanding of the phase transition of the 2SCP on uncorrelated networks by developing a heterogeneous mean-field (HMF) theory, in which the heterogeneity of contacts is explicitly reckoned. The HMF theory for networks with power-law degree distribution shows that the region of bistability (active and inactive phases) in the phase diagram shrinks as the heterogeneity level is increased by reducing the degree exponent. Finite-size analysis reveals a complex behavior where a pseudodiscontinuous transition at a finite size can be converted into a continuous one in the thermodynamic limit, depending on degree exponent and symbiotic coupling. The theoretical results are supported by extensive numerical simulations.

We investigate the ground-state configurations of two-dimensional liquid crystals with $p$-fold rotational symmetry ($p$-atics) on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle $\beta$, the apex develops an effective topological charge of $-\chi$, where $2\pi \chi =2\pi (1-sin\beta )$ is the deficit angle of the cone, and a topological defect of charge $\sigma$ behaves as if it had an effective topological charge $Q_{\mathrm{eff}}=(\sigma -{\sigma }^2/2)$ when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. For total topological defect charge 1, e.g., imposed by tangential boundary conditions at the edge, we find that for a disk the ground-state configuration consists of $p$ defects each of charge $+1/p$ lying equally spaced on a concentric ring of radius $d={\left(\frac{p-1}{3p-1}\right)}^{\frac{1}{2p}}R$, where $R$ is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground-state configurations as a function of cone angle: (i) for sharp cones, all of the $+1/p$ defects are absorbed by the apex; (ii) at intermediate cone angles, some of the $+1/p$ defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the $+1/p$ defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on $p$ and the deficit angle, which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

The flow of Newtonian fluid at low Reynolds number is, in general, regular and time-reversible due to absence of nonlinear effects. For example, if the fluid is sheared by its boundary motion that is subsequently reversed, then all the fluid elements return to their initial positions. Consequently, mixing in microchannels happens solely due to molecular diffusion and is very slow. Here, we show, numerically, that the introduction of a single, freely floating, flexible filament in a time-periodic linear shear flow can break reversibility and give rise to chaos due to elastic nonlinearities, if the bending rigidity of the filament is within a carefully chosen range. Within this range, not only the shape of the filament is spatiotemporally chaotic, but also the flow is an efficient mixer. Overall, we find five dynamical phases: the shape of a stiff filament is time-invariant—either straight or buckled; it undergoes a period-two bifurcation as the filament is made softer; becomes spatiotemporally chaotic for even softer filaments but, surprisingly, the chaos is suppressed if bending rigidity is decreased further.

The search for controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory. In particular, the most employed approximation scheme in this context, the derivative expansion, was recently shown to converge and yield accurate and very precise results. However, this convergence strongly depends on the shape of the employed regulator. In this paper we clarify the reason for this dependence and justify, simultaneously, the most commonly employed procedure to fix this dependence, the principle of minimal sensitivity.