No Arabic abstract
We present a fundamental classification of forces relevant in nonequilibrium structure formation under collective flow in Brownian many-body systems. The internal one-body force field is systematically split into contributions relevant for the spatial structure and for the coupled motion. We demonstrate that both contributions can be obtained straightforwardly in computer simulations, and present a power functional theory that describes all types of forces quantitatively. Our conclusions and methods are relevant for flow in inertial systems, such as molecular liquids and granular media.
When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex and obtaining a detailed physical understanding often requires case-by-case considerations. In order to facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.
We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some landmarks within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).
Driving an inertial many-body system out of equilibrium generates complex dynamics due to memory effects and the intricate relationships between the external driving force, internal forces, and transport effects. Understanding the underlying physics is challenging and often requires carrying out case-by-case analysis. To systematically study the interplay between all types of forces that contribute to the dynamics, a method to generate prescribed flow patterns could be of great help. We develop a custom flow method to numerically construct the external force field required to obtain the desired time evolution of an inertial many-body system, as prescribed by its one-body current and density profiles. We validate the custom flow method in a Newtonian system of purely repulsive particles by creating a slow motion dynamics of an out-of-equilibrium process and by prescribing the full time evolution between two distinct equilibrium states. The method can also be used with thermostat algorithms to control the temperature.
The active Brownian particle (ABP) model describes a swimmer, synthetic or living, whose direction of swimming is a Brownian motion. The swimming is due to a propulsion force, and the fluctuations are typically thermal in origin. We present a 2D model where the fluctuations arise from nonthermal noise in a propelling force acting at a single point, such as that due to a flagellum. We take the overdamped limit and find several modifications to the traditional ABP model. Since the fluctuating force causes a fluctuating torque, the diffusion tensor describing the process has a coupling between translational and rotational degrees of freedom. An anisotropic particle also exhibits a noise-induced induced drift. We show that these effects have measurable consequences for the long-time diffusivity of active particles, in particular adding a contribution that is independent of where the force acts.
We develop a general approach for calculating the characteristic function of the work distribution of quantum many-body systems in a time-varying potential, whose many-body wave function can be cast in the Slater determinant form. Our results are applicable to a wide range of systems including an ideal gas of spinless fermions in one dimension (1D), the Tonks-Girardeau (TG) gas of hard-core bosons, as well as a 1D gas of hard-core anyons. In order to illustrate the utility of our approach, we focus on the TG gas confined to an arbitrary time-dependent trapping potential. In particular, we use the determinant representation of the many-body wave function to characterize the nonequilibrium thermodynamics of the TG gas and obtain exact and computationally tractable expressions---in terms of Fredholm determinants---for the mean work, the work probability distribution function, the nonadiabaticity parameter, and the Loschmidt amplitude. When applied to a harmonically trapped TG gas, our results for the mean work and the nonadiabaticity parameter reduce to those derived previously using an alternative approach. We next propose to use periodic modulation of the trap frequency in order to drive the system to highly non-equilibrium states by taking advantage of the phenomenon of parametric resonance. Under such driving protocol, the nonadiabaticity parameter may reach large values, which indicates a large amount of irreversible work being done on the system as compared to sudden quench protocols considered previously. This scenario is realizable in ultracold atom experiments, aiding fundamental understanding of all thermodynamic properties of the system.