Using a collective coordinate numerical optimization procedure, we construct ground-state configurations of interacting particle systems in various space dimensions so that the scattering of radiation exactly matches a prescribed pattern for a set of wave vectors. We show that the constructed ground states are, counterintuitively, disordered (i.e., possess no long-range order) in the infinite-volume limit. We focus on three classes of configurations with unique radiation scattering characteristics: (i)``stealth'' materials, which are transparent to incident radiation at certain wavelengths; (ii)``super-ideal'' gases, which scatter radiation identically to that of an ensemble of ideal gas configurations for a selected set of wave vectors; and (iii)``equi-luminous'' materials, which scatter radiation equally intensely for a selected set of wave vectors. We find that ground-state configurations have an increased tendency to contain clusters of particles as one increases the prescribed luminosity. Limitations and consequences of this procedure are detailed.
The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-size limit (e.g., equilibrium liquid states) is non-zero. Such "hole" statistics are intimately linked to the physical properties of the system. Disordered "stealthy' many-particle configurations in $d$-dimensional Euclidean space $\mathbb{R}^d$ are exotic amorphous states of matter that lie between a liquid and crystal that prohibit single-scattering events for a range of wave vectors and possess no Bragg peaks [Torquato et al., Phys. Rev. X, 2015, 5, 0…
Disordered hyperuniform many-particle systems have attracted considerable recent attention. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a tuning parameter. Previous studies have shown that these ground-state point configurations can be counterintuitively disordered, infinitely degenerate, and endowed with novel physical properties (e.g., negative thermal expansion behavior). In this paper, we focus on the disordered regime in which there is no long-range order, and control the degree of short-…
It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform and highly degenerate. Disordered hyperuniform systems have been receiving recent attention because they are distinguishable exotic states of matter poised between a crystal and liquid with novel properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degener…
Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical e…
We show that the recently discovered thermodynamic equivalence between noninteracting Bose and Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble, are special cases of a larger class of equivalences of noninteracting systems having an energy-independent single-particle density of states. We also conjecture that the same equivalence will hold in the grand-canonical ensemble for any noninteracting quantum gas with a discrete ladder-type spectrum whenever $σΔ/ N k_{\rm B} T$ is small, where $N$ is the aver…
We use the non-equilibrium statistical field theory for classical particles recently developed by Mazenko and Das and Mazenko, together with the free generating functional for particles initially correlated in phase space derived in Bartelmann et al. to study the impact of initial correlations on the equation of state of real gases. We first show that we can reproduce the well known van der Waals equation of state for uncorrelated initial conditions using this approach. We then impose correlated initial conditions and study their qualitative and quantitative effect on the equation of state of …
An operator that governs the discrete time evolution of the velocity distribution of an out-of-equilibrium ideal gas will be presented. This nonlinear map, which conserves the momentum and the energy of the ideal gas, has the Maxwellian Velocity Distribution (MVD) as an asymptotic equilibrium. Moreover, the system displays the increasing of the entropy during the decay to the MVD.
We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general $p$-ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the mixtures exhibit non-additive interactions. In this situation the out-of-equilibrium evolution is chara…
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We establish that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature $T$, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of th…
We investigate the entanglement properties of the equilibrium and nonequilibrium quantum dynamics of 2D and 3D Fermi gases, by computing entanglement entropies of extended space regions, which generally show multiplicative logarithmic corrections to the leading power-law behaviors, corresponding to the logarithmic corrections to the area law. We consider 2D and 3D Fermi gases of N particles constrained within a limited space region, for example by a hard-wall trap, at equilibrium at T=0, i.e. in their ground state, and compute the first few terms of the asymptotic large-N behaviors of entangle…
The non-equilibrium dynamics of a gas of cold atoms in which Rydberg states are off-resonantly excited is studied in the presence of noise. The interplay between interaction and off-resonant excitation leads to an initial dynamics where aggregates of excited Rydberg atoms slowly nucleate and grow, eventually reaching long-lived meta-stable arrangements which then relax further on much longer timescales. This growth dynamics is governed by an effective Master equation which permits a transparent and largely analytical understanding of the underlying physics. By means of extensive numerical simu…
Advances in controlling and measuring systems of ultra-cold atoms provided strong motivation to theoretical investigations of quantum dynamics in closed many-body systems. Fundamental questions on quantum dynamics and statistical mechanics are now within experimental reach: How is thermalization achieved in a closed quantum system? How does quantum dynamics cross over to effective classical physics? Can such a thermal or classical fate be evaded? In these lectures, given at the Les Houches Summer School of Physics "Strongly Interacting Quantum Systems Out of Equilibrium", I introduce the stude…
Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators and correlation functions. We…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decade…
We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston remains at the so called mechanical equilibrium. However, the temperatures and densities of the gases may differ across the piston. In that case some earlier studies by Gruber, Piasecki and others reveal a very slow motion (drift) of the piston in the direction of the hotter gas. At the same time the hotter gas slowly transfers its energy (heat) across the …
In this work, a new model in kinetic gas theory for deriving the Maxwellian Velocity Distribution (MVD) is proposed. We construct an operator that governs the discrete time evolution of the velocity distribution. This operator, which conserves the momentum and the energy of the ideal gas, has the MVD as a fixed point. Moreover, for any initial out-of-equilibrium velocity distribution, it is shown that the gas decays to the equilibrium distribution, that is, to the MVD.
In this work we revisit the concept of chemical potential $μ$ in both classical and quantum gases from a perspective of Equilibrium Statistical Mechanics (ESM). Two new results regarding the equation of state $μ=μ(n,T)$, where $n$ is the particle density and $T$ the absolute temperature, are given for the classical interacting gas and for the weakly-interacting quantum Bose gas. In order to make this review self-contained and adequate for a general reader we provide all the basic elements in an advanced-undergraduate or graduate statistical mechanics course required to follow all the calculati…
We propose a comprehensive theoretical description of hysteresis in capillary condensation of gases in mesoporous disordered materials. Applying mean-field density functional theory to a coarse-grained lattice-gas model, we show that the morphology of the hysteresis loops is influenced by out-of-equilibrium transitions that are different on filling and on draining. In particular, desorption may be associated to a depinning process and be percolation-like without explicit pore-blocking effects.
Equilibrium measures for higher dimensional rotationally symmetric Riesz gases
Seoul National University（首尔大学）；The University of Melbourne（墨尔本大学）；CNRS, Univ. Paris-Sud, Université Paris-Saclay（法国国家科学研究中心，巴黎南大学，巴黎萨克雷大学）；Sorbonne Université（索邦大学）
A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behaviour in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is prov…
Universal Family-Vicsek scaling in quantum gases far from equilibrium
Massachusetts Institute of Technology（麻省理工学院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute of Science Tokyo（东京科学大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先导研究本部）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心）；Nagoya University（名古屋大学）
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between universal properties, (quasi-)topological field configurations and turbulent dynamics. We demonstrate that the isolated Bose gas, on its way back to thermal equilibrium, can approach metastable non-equilibrium configurations and spend a long time in their vicinity. In such configurations, which have been termed non-thermal fixed points, the system shows univers…
Kinetically constrained lattice gases (KCLG) are interacting particle systems on the integer lattice $\mathbb Z^d$ with hard core exclusion and Kawasaki type dynamics. Their peculiarity is that jumps are allowed only if the configuration satisfies a constraint which asks for enough empty sites in a certain local neighborhood. KCLG have been introduced and extensively studied in physics literature as models of glassy dynamics. We focus on the most studied class of KCLG, the Kob Andersen (KA) models. We analyze the behavior of a tracer (i.e. a tagged particle) at equilibrium. We prove that for a…
