A molecular-dynamics algorithm for mixed hard-core/continuous potentials

We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator splitting techniques similar to those that have been used successfully to generate a variety molecular-dynamics integrators. In numerical experiments, the Impulsive Verlet method is shown to be superior to previous methods with respect to stability and energy conservation in long simulations.Comment: 18 pages, 6 postscript figures, uses rotate.st

Constant-temperature molecular-dynamics algorithms for mixed hard-core/continuous potentials

We present a set of second-order, time-reversible algorithms for the isothermal (NVT) molecular-dynamics (MD) simulation of systems with mixed hard-core/continuous potentials. The methods are generated by combining real-time Nose' thermostats with our previously developed Collision Verlet algorithm [Mol. Phys. 98, 309 (1999)] for constant energy MD simulation of such systems. In all we present 5 methods, one based on the Nose'-Hoover [Phys. Rev. A 31, 1695 (1985)] equations of motion and four based on the Nose'-Poincare' [J.Comp.Phys., 151 114 (1999)] real-time formulation of Nose' dynamics. The methods are tested using a system of hard spheres with attractive tails and all correctly reproduce a canonical distribution of instantaneous temperature. The Nose'-Hoover based method and two of the Nose'-Poincare' methods are shown to have good energy conservation in long simulations.Comment: 9 pages, 5 figure

Kinetic energy choice in Hamiltonian/hybrid Monte Carlo

We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are established on integrator stability and geometric convergence, and we show that choices of kinetic energy that result in heavy-tailed momentum distributions can exhibit an undesirable negligible moves property, which we define. A general efficiency-robustness trade off is outlined, and implementations which rely on approximate gradients are also discussed. Two numerical studies illustrate our theoretical findings, showing that the standard choice which results in a Gaussian momentum distribution is not always optimal in terms of either robustness or efficiency.Comment: 15 pages (+7 page supplement, included here as an appendix), 2 figures (+1 in supplement

Edge insulating topological phases in a two-dimensional long-range superconductor

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups

Molecular Dynamics in a Grand Ensemble: Bergmann-Lebowitz model and Adaptive Resolution Simulation

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz.Despite its conceptual appeal, the model did not gain popularity in the field of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques that mimic open systems. We shall demonstrate that the model can serve as a tool to devise both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. In particular, we discuss the utility of the Bergmann-Lebowitz (BL) model for the calculation of equilibrium time correlation functions within the Grand Canonical Adaptive Resolution method (GC-AdResS) and report numerical results for the case of liquid water.Comment: 31 pages, 6 figure

Fourier Heat Conduction as a phenomenon described within the scope of the Second Law

The historical development of the Carnot cycle necessitated the construction of isothermal and adiabatic pathways within the cycle that were also mechanically "reversible" which lead eventually to the Kelvin-Clausius development of the entropy function where the heat absorption is for the diathermal (isothermal) paths of the cycle only. It is deduced from traditional arguments that Fourier heat conduction involves mechanically "reversible" heat transfer with irreversible entropy increase. Here we model heat conduction as a thermodynamically reversible but mechanically irreversible process. The MD simulations conducted shows excellent agreement with the theory. Such views and results as these, if developed to a successful conclusion could imply that the Carnot cycle be viewed as describing a local process of energy-work conversion and that irreversible local processes might be brought within the scope of this cycle, implying a unified treatment of thermodynamically (i) irreversible, (ii) reversible, (iii) isothermal and (iv) adiabatic processes.Comment: 10 pages, 2 figures. Material for talk at conference and ICNPAA 2014 (Narvik, Norway) Conference Proceeding

On the clustering phase transition in self-gravitating N-body systems

The thermodynamic behaviour of self-gravitating $N$-body systems has been worked out by borrowing a standard method from Molecular Dynamics: the time averages of suitable quantities are numerically computed along the dynamical trajectories to yield thermodynamic observables. The link between dynamics and thermodynamics is made in the microcanonical ensemble of statistical mechanics. The dynamics of self-gravitating $N$-body systems has been computed using two different kinds of regularization of the newtonian interaction: the usual softening and a truncation of the Fourier expansion series of the two-body potential. $N$ particles of equal masses are constrained in a finite three dimensional volume. Through the computation of basic thermodynamic observables and of the equation of state in the $P - V$ plane, new evidence is given of the existence of a second order phase transition from a homogeneous phase to a clustered phase. This corresponds to a crossover from a polytrope of index $n=3$, i.e. $p=K V^{-4/3}$, to a perfect gas law $p=K V^{-1}$, as is shown by the isoenergetic curves on the $P - V$ plane. The dynamical-microcanonical averages are compared to their corresponding canonical ensemble averages, obtained through standard Monte Carlo computations. A major disagreement is found, because the canonical ensemble seems to have completely lost any information about the phase transition. The microcanonical ensemble appears as the only reliable statistical framework to tackle self-gravitating systems. Finally, our results -- obtained in a ``microscopic'' framework -- are compared with some existing theoretical predictions -- obtained in a ``macroscopic'' (thermodynamic) framework: qualitative and quantitative agreement is found, with an interesting exception.Comment: 19 pages, 20 figure