63 research outputs found
Molecular Rydberg states: Classical chaos and its correspondence in quantum mechanics
International audienceThe Rydberg spectrum of Na2 has been shown previously to alternate when increasing energy between "stroboscopic fringes" which correspond to a well known separable Hund's coupling case (a), and a complex, unidentifiable intermediate coupling. We use this system as a prototypic example to test some current ideas on the correspondance between classical chaos and properties of quantum spectra. We first determine the phase space structure and transition to chaos in classical mechanics. We then determine the change in line intensities and level spacing statistics in quantum mechanics. We show that this system has the expected behavior in semi-classical limit in the presence of classical chaos, except for a peculiarity in level spacing statistics, but that this behavior is not a signature of chaos, since the same system show similar behavior for some values of the parameters which correspond to a non chaotic situation in classical mechanics. We discuss also some problems related to the nonvalidity of the semiclassical limit
Topology of event distribution as a generalized definition of phase transitions in finite systems
We propose a definition of phase transitions in finite systems based on
topology anomalies of the event distribution in the space of observations. This
generalizes all the definitions based on the curvature anomalies of
thermodynamical potentials and provides a natural definition of order
parameters. The proposed definition is directly operational from the
experimental point of view. It allows to study phase transitions in Gibbs
equilibria as well as in other ensembles such as the Tsallis ensemble.Comment: 4 pages, 3 figure
First and second order clustering transitions for a system with infinite-range attractive interaction
We consider a Hamiltonian system made of classical particles moving in
two dimensions, coupled via an {\it infinite-range interaction} gauged by a
parameter . This system shows a low energy phase with most of the particles
trapped in a unique cluster. At higher energy it exhibits a transition towards
a homogenous phase. For sufficiently strong coupling an intermediate phase
characterized by two clusters appears. Depending on the value of the
observed transitions can be either second or first order in the canonical
ensemble. In the latter case microcanonical results differ dramatically from
canonical ones. However, a canonical analysis, extended to metastable and
unstable states, is able to describe the microcanonical equilibrium phase. In
particular, a microcanonical negative specific heat regime is observed in the
proximity of the transition whenever it is canonically discontinuous. In this
regime, {\it microcanonically stable} states are shown to correspond to {\it
saddles} of the Helmholtz free energy, located inside the spinodal region.Comment: 4 pages, Latex - 3 EPS Figs - Submitted to Phys. Rev.
Classification of phase transitions in small systems
We present a classification scheme for phase transitions in finite systems
like atomic and molecular clusters based on the Lee-Yang zeros in the complex
temperature plane. In the limit of infinite particle numbers the scheme reduces
to the Ehrenfest definition of phase transitions and gives the right critical
indices. We apply this classification scheme to Bose-Einstein condensates in a
harmonic trap as an example of a higher order phase transitions in a finite
system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let
Curvature fluctuations and Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy molecular
dynamics simulations at the melting transition for finite clusters of 6 to 13
particles (model rare-gas and metallic systems) as well as for bulk rare-gas
solid. For clusters, the Lyapunov exponent generally varies linearly with the
total energy, but the slope changes sharply at the melting transition. In the
bulk system, melting corresponds to a jump in the Lyapunov exponent, and this
corresponds to a singularity in the variance of the curvature of the potential
energy surface. In these systems there are two mechanisms of chaos -- local
instability and parametric instability. We calculate the contribution of the
parametric instability towards the chaoticity of these systems using a recently
proposed formalism. The contribution of parametric instability is a continuous
function of energy in small clusters but not in the bulk where the melting
corresponds to a decrease in this quantity. This implies that the melting in
small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev
The potential energy landscape of a model glass former: thermodynamics, anharmonicities, and finite size effects
It is possible to formulate the thermodynamics of a glass forming system in
terms of the properties of inherent structures, which correspond to the minima
of the potential energy and build up the potential energy landscape in the
high-dimensional configuration space. In this work we quantitatively apply this
general approach to a simulated model glass-forming system. We systematically
vary the system size between N=20 and N=160. This analysis enables us to
determine for which temperature range the properties of the glass former are
governed by the regions of the configuration space, close to the inherent
structures. Furthermore, we obtain detailed information about the nature of
anharmonic contributions. Moreover, we can explain the presence of finite size
effects in terms of specific properties of the energy landscape. Finally,
determination of the total number of inherent structures for very small systems
enables us to estimate the Kauzmann temperature
Thermodynamics of Na_8 and Na_{20} clusters studied with ab-initio electronic structure methods
We study the thermodynamics of Na_8 and Na_{20} clusters using
multiple-histogram methods and an ab initio treatment of the valence electrons
within density functional theory. We consider the influence of various electron
kinetic-energy functionals and pseudopotentials on the canonical ionic specific
heats. The results for all models we consider show qualitative similarities,
but also significant temperature shifts from model to model of peaks and other
features in the specific-heat curves. The use of phenomenological
pseudopotentials shifts the melting peak substantially (~ 50--100 K) when
compared to ab-initio results. It is argued that the choice of a good
pseudopotential and use of better electronic kinetic-energy functionals has the
potential for performing large time scale and large sized thermodynamical
simulations on clusters.Comment: LaTeX file and EPS figures. 24 pages, 13 figures. Submitted to Phys.
Rev.
Thermodynamics of tin clusters
We report the results of detailed thermodynamic investigations of the
Sn cluster using density-functional molecular dynamics. These
simulations have been performed over a temperature range of 150 to 3000 K, with
a total simulation time of order 1 ns. The prolate ground state and low-lying
isomers consist of two tricapped trigonal prism (TTP) units stacked end to end.
The ionic specific heat, calculated via a multihistogram fit, shows a small
peak around 500 K and a shoulder around 850 K. The main peak occurs around 1200
K, about 700 K higher than the bulk melting temperature, but significantly
lower than that for Sn. The main peak is accompanied by a sharp change
in the prolate shape of the cluster due to the fusion of the two TTP units to
form a compact, near spherical structure with a diffusive liquidlike ionic
motion. The small peak at 500 K is associated with rearrangement processes
within the TTP units, while the shoulder at 850 K corresponds to distortion of
at least one TTP unit, preserving the overall prolate shape of the cluster. At
all temperatures observed, the bonding remains covalent.Comment: Latex File and EPS Figures. 18 pages,11 Figures. Submitted to Phys.
Rev.
Equilibrium molecular thermodynamics from Kirkwood sampling.
We present two methods for barrierless equilibrium sampling of molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys. 2009, 130, 134102). Kirkwood sampling employs low-order correlations among internal coordinates of a molecule for random (or non-Markovian) sampling of the high dimensional conformational space. This is a geometrical sampling method independent of the potential energy surface. The first method is a variant of biased Monte Carlo, where Kirkwood sampling is used for generating trial Monte Carlo moves. Using this method, equilibrium distributions corresponding to different temperatures and potential energy functions can be generated from a given set of low-order correlations. Since Kirkwood samples are generated independently, this method is ideally suited for massively parallel distributed computing. The second approach is a variant of reservoir replica exchange, where Kirkwood sampling is used to construct a reservoir of conformations, which exchanges conformations with the replicas performing equilibrium sampling corresponding to different thermodynamic states. Coupling with the Kirkwood reservoir enhances sampling by facilitating global jumps in the conformational space. The efficiency of both methods depends on the overlap of the Kirkwood distribution with the target equilibrium distribution. We present proof-of-concept results for a model nine-atom linear molecule and alanine dipeptide.This research was funded by the European Research Council
and EPSRC grant EP/I001352/1. Y.O. was supported, in part,
by the JSPS Grant-in-Aid for Scientific Research on Innovative
Areas (âDynamical Ordering and Integrated Functionsâ).This is the final published version. It first appeared at http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b01800
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