An introduction to the statistical physics of active matter: motility-induced phase separation and the “generic instability” of active gels

In this work we review some statistical physics techniques to coarse grain active matter systems, writing down a set of continuum fields which track the evolution of macroscopic fields such as density, momentum, etc. While the method can be applied in general, we will focus here on two simple and by now well-studied, active matter examples. First, we will consider motility-induced phase separation, the phenomenon by which a concentrated suspension of self-propelled particles spontaneously separates into a dense and a dilute phase. Second, we will review the so-called “generic instability” of active gels, which refers to the nonequilibrium phase transition between a quiescent and a spontaneously flowing phase in a concentrated suspension of rodlike active particles. For both these cases, we also outline recent developments in the literature.     

Density fluctuations of two-dimensional active-passive mixtures

Dimension-dependent giant density fluctuations are a typical feature of active matter systems. In this work, we study the density fluctuation in two-dimensional mixtures of active and passive particles by Brownian dynamics simulations. The boundary of motility-induced phase separation is determined by the transition from unimodal to bimodal density distribution. A rapid increase of the fluctuation exponent near the boundary of phase separation in the plane of density and Péclet number was observed. When phase separation occurs, the fluctuation exponent is an approximate constant of $0.85.$     

Transport phenomena and dynamics of externally and self-propelled colloids in confined geometry

Over the last decades, colloidal suspensions have been proven as powerful model systems to reveal fundamental questions in soft matter or general physics. In this work, we will focus on the influence of interaction and confinement to the mobility of colloidal particles as well as to the transport behavior of particles over obstacles placed in a micro-channel. Both experiments are supported with Brownian dynamics simulations to complete the experimental work. The paper concludes with the investigation of the behavior of single active swimmers close to a wall.     

Active suspensions and their nonlinear models

Active suspensions, such as suspensions of self-propelled microorganisms and related synthetic microswimmers, are known to undergo complex dynamics and pattern formation as a result of hydrodynamic interactions. In this review, we summarize recent efforts to model these systems using continuum kinetic theories. We first derive a basic kinetic model for a suspension of self-propelled rodlike particles and discuss its stability and nonlinear dynamics. We then present extensions of this model to analyze the effective rheology of active suspensions in external flows, the effect of steric interactions in concentrated systems, and the dynamics of chemotactically responsive suspensions in chemical fields.     

活力物质的非平衡结构和动力学

活力物质是一类典型的非平衡态体系,已成为软凝聚态物理新近发展的一个重要研究方向.活力物质由微驱动粒子组成,驱动力独立地施加在体系中的每个粒子上.文章概述了作者平时研究中所关注的一些活力物质系统中出现的十分有意义的现象,着重介绍了活力物质系统的构成,以及活力物质的气液态、铁磁态、向列相态和凝胶状态中涌现出的非平衡结构及其特殊的动力学行为.     

Implications of the Higgs boson discovery

With the discovery of the Higgs boson by the LHC in 2012, a new era started in which we have direct experimental information on the physics behind the breaking of the electroweak (EW) symmetry. This breaking plays a fundamental role in our understanding of particle physics and sits at the high-energy frontier beyond which we expect new physics that supersedes the Standard Model (SM). In this review we summarize what we have learned so far from LHC data in this respect. In the absence of new particles having been discovered, we discuss how the scrutiny of the properties of the Higgs boson (in search for deviations from SM expectations) is crucial as it can point the way for physics beyond the SM. We also emphasize how the value of the Higgs mass could have far-reaching implications for the stability of the EW vacuum if there is no new physics up to extremely large energies.     

Mixtures of anisotropic and spherical colloids: Phase behavior, confinement, percolation phenomena and kinetics

Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. An insulating polymer resin that is mixed with conductive filler particles becomes conductive when the filler percolates. In this context the mathematical topic of connectivity percolation finds an application in modern nano-technology. In this article, we briefly review recent work on the phase behavior, confinement effects, percolation transition and phase transition kinetics in hard particle models. In the first part, we discuss the effects that particle anisotropy and depletion have on the percolation transition. In the second part, we present results on the kinetics of the liquid-to-crystal transition in suspensions of spheres and of ellipsoids.     

Particles inside electrolytes with ion-specific interactions,their effective charge distributions,and effective interactions

In this work, we explore the statistical physics of colloidal particles that interact with electrolytes via ion-specific interactions. Firstly we study particles interacting weakly with electrolyte using linear response theory. We find that the mean potential around a particle is linearly determined by the effective charge distribution of the particle, which depends both on the bare charge distribution and on ion-specific interactions. We also discuss the effective interaction between two such particles and show that, in the far field regime, it is bilinear in the effective charge distributions of two particles. We subsequently generalize the above results to the more complicated case where particles interact strongly with the electrolyte.Our results indicate that in order to understand the statistical physics of non-dilute electrolytes, both ion-specific interactions and ionic correlations have to be addressed in a single unified and consistent framework.     

Quantum Emulation of Extreme Non‐Equilibrium Phenomena with Trapped Atoms

Ultracold atomic physics experiments offer a nearly ideal context for the investigation of quantum systems far from equilibrium. We describe three related emerging directions of research into extreme non‐equilibrium phenomena in atom traps: quantum emulation of ultrafast atom‐light interactions, coherent phasonic spectroscopy in tunable quasicrystals, and realization of Floquet matter in strongly‐driven lattice systems. We show that all three should enable quantum emulation in parameter regimes inaccessible in solid‐state experiments, facilitating a complementary approach to open problems in non‐equilibrium condensed matter.     

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.     

Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.     

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.     

Equilibrium cluster phases and low-density arrested disordered states: the role of short-range attraction and long-range repulsion

We study a model in which particles interact with short-ranged attractive and long-ranged repulsive interactions, in an attempt to model the equilibrium cluster phase recently discovered in sterically stabilized colloidal systems in the presence of depletion interactions. At low packing fractions, particles form stable equilibrium clusters which act as building blocks of a cluster fluid. We study the possibility that cluster fluids generate a low-density disordered arrested phase, a gel, via a glass transition driven by the repulsive interaction. In this model the gel formation is formally described with the same physics of the glass formation.     

Colloidal particles at fluid interfaces: Effective interactions, dynamics and a gravitation–like instability

Colloidal particles of micrometer size usually become irreversibly trapped at fluid interfaces if they are partially wetted by one phase. This opens the chance to create two–dimensional model systems where the effective interactions between the particles are possibly influenced by the presence of the interface to a great extent. We will review recent developments in the quantitive understanding of these effective interactions with a special emphasis on electrostatics and capillarity. Charged colloids of micrometer size at an interface form effective dipoles whose strength sensitively depends on the double layer structure. We discuss the success of modified Poisson–Boltzmann equations with regard to measured colloidal dipole moments. On the other hand, for somewhat larger particles capillary interactions arise which are long–ranged and analogous to two–dimensional screened Newtonian gravity with the capillary length λ as the screening length. For colloidal diameters of around 10 micrometer, the collective effect of these long–ranged capillary interactions will dominate thermal motion and residual, short–ranged repulsions, and results in an instability towards a collapsed state for a finite patch of particles. Such long–ranged interactions with the associated instability are also of interest in other branches of physics, such as self-gravitating fluids in cosmology, two–dimensional vortex flow in hydrodynamics, and bacterial chemotaxis in biology. Starting from the colloidal case we develop and discuss a dynamical “phase diagram” in the temperature and interaction range variables which appears to be of more general scope and applicable also to other systems.     

Anomalous transport in heterogeneous media

The diffusion dynamics of particles in heterogeneous media is studied using particle-based simulation techniques. A special focus is placed on systems where the transport of particles at long times exhibits anomalies such as subdiffusive or superdiffusive behavior. First, a two-dimensional model system is considered containing gas particles (tracers) that diffuse through a random arrangement of pinned, disk-shaped particles. This system is similar to a classical Lorentz gas. However, different from the original Lorentz model, soft instead of hard interactions are considered and we also discuss the case where the tracer particles interact with each other. We show that the modification from hard to soft interactions strongly affects anomalous-diffusive transport at high obstacle densities. Second, non-linear active micro-rheology in a glass-forming binary Yukawa mixture is investigated, pulling single particles through a deeply supercooled state by applying a constant force. Here, we observe superdiffusion in force direction and analyze its origin. Finally, we consider the Brownian dynamics of a particle which is pulled through a two-dimensional random force field. We discuss the similarities of this model with the Lorentz gas as well as active micro-rheology in glass-forming systems.     

From space-time chaos to stochastic thermodynamics

We summarize the results of several experiments that show the evolution of some scientific interests and goals of the statistical and nonlinear physics community in the last 40 years. Specifically, we present how the ideas of extending concepts of equilibrium statistical physics to out-of-equilibrium physics have been developed to characterize various phenomena such as, for example, transition to space-time chaos and glass aging. We then discuss the applications of this out-of-equilibrium thermodynamics to microsystems driven out of equilibrium either by external forces or by temperature gradients. We show that in these systems thermal fluctuations play a role and that all thermodynamics quantities, such as work, heat, and entropy fluctuate. We recall general concepts such as fluctuation theorems and fluctuation dissipation relations used to characterize the statistical properties of these small systems. We describe experiments where all these concepts have been applied and tested with high accuracy. Finally, we show how these theoretical concepts and the experiments allowed us to improve our knowledge on the connection between information and thermodynamics.     

胶体晶体和基于胶体晶体的纳米结构

胶体晶体及基于胶体晶体的各种纳米结构的制备和物理性质是近来物理学和材料科学共同关注的一个热点，文章简要阐述了胶体颗粒间的基本相互作用，着重介绍了各种胶体晶体的制备方法；结合我们近期的工作，综合评述了胶体晶体在二维纳米颗粒阵列、二维有序孔单层膜及三维光子晶体等纳米结构材料研究中的应用，并对未来的发展进行了展望。     

Granular matter: A wonderful world of clusters in far-from-equilibrium systems

We review several theoretical and experimental methods of modeling and investigating granular matter far from equilibrium. The theoretical methods include an extension of the classical Boltzmann equation to inelastic gases, scalar internal degrees of freedom, and Hamiltonian-like grain–grain interactions; the experimental technique is concerned with thermal properties of electrically conducting clusters. We discuss the results, focusing on phenomena nonexistent in physics of gases, fluids or solids, e.g. anomalous temperature gradients or electric resistance. One of the models is used to study the interplay between classical and self-organized criticality.