An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the chain particles have random displacements and random velocities corresponding to a uniform initial temperature. An instant change of parameters of chain initiates a transient process. Analytical expressions for the chain temperature as a function of time are obtained from the statistical analysis of the dynamics equations. It is shown that the transition process is oscillatory and it converges non-monotonically to a new equilibrium state. Such behavior is usually unexpected for thermal processes. The analytical results are supplemented by numerical simulations.
We consider the out-of-equilibrium transport in $T\bar{T}$-deformed (1+1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the the exact non-equilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as the first checks of the $T\bar{T}$-deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusi…
Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation. Further, the challenges encountered resemble those in turbulence, which is exemplified in a comparison with the Rayleigh-Taylor instability.
We address the study of the thermodynamics of a crystalline solid by applying q-deformed algebras. We based part of our study by considering both Einstein and Debye models. We have mainly explored the q-deformed thermal and electric conductivities as a function of the Debye specific heat. The results led to the interpretation of the q-deformation acting as a factor of disorder or impurity modifying the characteristics of a crystalline structure as, for example, in the case of semiconductors.
The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the Wulff construction, is the object of the article.
Equilibrium crystal shape of oxygen-covered tungsten is followed as a function of temperature using field ion microscopy. In the vicinity of the (111) region, at the temperature $970\pm70$ K, the system undergoes a phase transition from a polyhedral form (sharp edges and sharp vertex) to a rounded form (sharp edges, rounded vertex).
A new exponent characterizing the rounding of crystal facets is found by mapping a crystal surface onto the asymmetric six-vertex model (i.e. with external fields h and v) and using the Bethe Ansatz to obtain appropriate expansions of the free energy close to criticality. Leading order exponents in δh, δv are determined along the whole phase boundary and in an arbitrary direction. A possible experimental verification of this result is discussed.
Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.
We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30, 3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state Potts model on the square lattice was calculated, and its equivalence with ECS in the Ising model was established. We confirm these results, giving their alternative derivation applying the transformation properties of the one-particle dispersion relation in the six-vertex model. It is shown, that this dispersion relation is identical with that in the Ising model on the square lattice.
We consider a d-dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with stochastic Langevin heat bath at each site. We develop an integral formalism for the correlation functions that is suitable for the study of their relaxation (time decay) as well as their behavior in space. Furthermore, in a perturbative analysis, for the one-dimensional system with weak coupling between the sites and small quartic anharmonicity, we investigate the steady state and show that the Fourier's law holds. We also obtain an expression for the thermal conductivity (for …
A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order…
In this work, the relaxation process of the spin-3/2 Blume-Capel model with quenched random crystal field on a two dimensional square lattice has been investigated by a method which combines the statistical equilibrium theory and the thermodynamic of linear irreversible processes. Generalized force and flux have been defined in irreversible thermodynamics limit. The kinetic equation for the magnetization has been obtained by using linear response theory. In order to understand effect of the first-order phase transition on the relaxation process, low temperature regions have been analyzed. And …
Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random sequential adsorption with diffusion, creates amorphous structures and terminates at a disordered state with random closest packing density that lies in the equilibrium solid regime. The approach towards random closest packing is characterized by two distinct power-law regimes, reflecting the formation of small densely packed grains in the long time regime o…
We investigate the thermodynamics of a crystalline solid applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We based part of our study on both Einstein and Debye models, exploring primarily (q1,q2)-deformed thermal and electric conductivities as a function of Debye specific heat. The results revealed that q-deformation acts as a factor of disorder or impurity, modifying the characteristics of a crystalline structure. Specially, one may find the possibility of adjusting the Fibonacci oscil…
The equilibrium crystal shape (ECS) of oxygen-covered tungsten micricrystal is studied as a function of temperature. The specially designed ultrafast crystal quenching setup with the cooling rate of 6000 K/s allows to draw conclusions about ECS at high temperatures. The edge-rounding transition is shown to occur between 1300 K and 1430 K. The ratio of surface free energies $γ(111)/γ(211)$ is determined as a function of temperature.
The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a shape parameter c. The total crystallite free energy, including interface energy, is minimized for c=0, yielding in all cases the traditional PT shape (z x3/2). Solutions of the crystal shape for c≠0 are pr…
In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D = 3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase separates and self-organizes into various liquid-crystalline phases that are not…
We demonstrate a novel method of introducing point defects (mono and di-vacancies) in a confined mono-layer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We analyze the topological arrangements of the particles in the defect core and establish their connection with the energetics of the system. It is found that thermal fluctuations excite point defects into \textit{dislocation multipole} configurations. We extract the dislocation pair potential at near field, where cores overlap an…
The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.
The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of…
This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews, particularly in the late 1980's, recapping highlights from them. It contains many ideas and experiments subsequent to those reviews. Alternatives to Wulff constructions are presented. Controversies about the critical behavior near smooth edges on the ECS are recounted, including the eventual resolution. Particular attention is devoted to the origin of sharp edges on the ECS, to the impact of reconst…
We study transient thermal processes in infinite harmonic crystals with complex (polyatomic) lattice. Initially particles have zero displacements and random velocities such that distribution of temperature is spatially uniform. Initial kinetic and potential energies are different and therefore the system is far from thermal equilibrium. Time evolution of kinetic temperatures, corresponding to different degrees of freedom of the unit cell, is investigated. It is shown that the temperatures oscillate in time and tend to generally different equilibrium values. The oscillations are caused by two p…
We present an in-depth study of the non-equilibrium statistics of the irreversible work produced during sudden quenches in proximity to the structural linear-zigzag transition of ion Coulomb crystals in 1+1 dimensions. By employing both an analytical approach based on a harmonic expansion and numerical simulations, we show the divergence of the average irreversible work in proximity to the transition. We show that the non-analytic behaviour of the work fluctuations can be characterized in terms of the critical exponents of the quantum Ising chain. Due to the technological advancements in trapp…
Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallisation of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Though the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determine…
To study the solution growth of crystals composed of chiral organic molecules, a spin-one Ising lattice gas model is proposed. The model turns out to be equivalent to the Blume-Emery-Griffiths model, which shows an equilibrium chiral symmetry breaking at low temperatures. The kinetic Monte Carlo simulation of crystal growth, however, demonstrates that Ostwald ripening is a very slow process with a characteristic time proportional to the system size: The dynamics is nonergodic. It is then argued that by incorporating grinding dynamics, homochirality is achieved in a short time, independent of t…
In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizin…
This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where non-trivial universality classes have been identified theoretically: absorbing-state phase transitions and growing interfaces. First the article summarizes main results obtained for electrically-driven turbulent liquid crystal, which exhibited the scaling laws for the directed percolation class at the transition between two turbulent regimes, and those for the Kardar-Parisi-Zhang class in the supercritical phase where one turbulent regime invades the other. Other…
According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous results concerning this function, in the case of a lattice gas, and apply them to study the shape of the equilibrium crystal and, in particular, the shape of the facets of this crystal.
The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven …
