Search results for "statistical mechanics"
showing 10 items of 706 documents
Nucleation pathway and kinetics of phase-separating active Brownian particles
2016
Suspensions of purely repulsive but self-propelled Brownian particles might undergo phase separation, a phenomenon that strongly resembles the phase separation of passive particles with attractions. Here we employ computer simulations to study the nucleation kinetics and the microscopic pathway active Brownian disks take in two dimensions when quenched from the homogeneous suspension to propulsion speeds beyond the binodal. We find the same qualitative behavior for the nucleation rate as a function of density as for a passive suspension undergoing liquid-vapor separation, suggesting that the scenario of an effective free energy also extends to the kinetics of phase separation. We study the …
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
Exponential Relaxation out of Nonequilibrium
1989
Simulation results are presented for a quench from a disordered state to a state below the coexistence curve. The model which we consider is the Ising model but with the dynamics governed by the Swendsen-Wang transition probabilities. We show that the resulting domain growth has an exponential instead of a power law behaviour and that the system is non-self-averaging while in nonequilibrium. The simulations were carried out on a parallel computer with up to 128 processors.
Liquid-vapour phase behaviour of a symmetrical binary fluid mixture
1998
Using Monte-Carlo simulation and mean field calculations, we study the liquid-vapour phase diagram of a square well binary fluid mixture as a function of a parameter $\delta$ measuring the relative strength of interactions between particles of dissimilar and similar species. The results reveal a rich variety of liquid-vapour coexistence behaviour as $\delta$ is tuned. Specifically, we uncover critical end point behaviour, a triple point involving a vapour and two liquids of different density, and tricritical behaviour. For a certain range of $\delta$, the mean field calculations also predict a `hidden' (metastable) liquid-vapour binodal.
The droplet evaporation/condensation transition in a finite volume
2003
A fluid in the NVT ensemble at T less than the critical temperature T_c and rho = N/V somewhat in excess of rho_coex (density of the saturated gas in the gas-liquid transition) is considered. For V->infinity, a macroscopic liquid droplet coexists with surrounding saturated gas according to the lever rule. For finite V, droplets can only exist if they exceed a minimum size. A (rounded) first order transition of the system occurs when the droplet evaporates into the supersaturated gas.Simulation evidence for this transition is given for a Lennard-Jones model and interpreted by a phenomenological theory. At the transition, the chemical potential difference mu_t-mu_coex scales like L^(-d/(d+…
Connectivity percolation in suspensions of hard platelets
2012
We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation tran…
Adiabatic-antiadiabatic crossover in a spin-Peierls chain
2004
We consider an XXZ spin-1/2 chain coupled to optical phonons with non-zero frequency $\omega_0$. In the adiabatic limit (small $\omega_0$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large $\omega_0$), phonons are expected to give rise to frustration, so that dimerization and formation of spin-gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the Self Consistent Harmonic Approximation (SCHA)and by Renormalization Group (RG) approach starting from a bosonized description. The SCHA allows to an…
Monogamy Inequality for Distributed Gaussian Entanglement
2007
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
Replica-exchange molecular dynamics simulation for supercooled liquids
2000
We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.