36 research outputs found
A Definition of Metastability for Markov Processes with Detailed Balance
A definition of metastable states applicable to arbitrary finite state Markov
processes satisfying detailed balance is discussed. In particular, we identify
a crucial condition that distinguishes genuine metastable states from other
types of slowly decaying modes and which leads to properties similar to those
postulated in the restricted ensemble approach \cite{pen71}. The intuitive
physical meaning of this condition is simply that the total equilibrium
probability of finding the system in the metastable state is negligible. As a
concrete application of our formalism we present preliminary results on a 2D
kinetic Ising model.Comment: 5 pp. 1 Figure, presented in News, Expectations and Trends in
Statistical Physics-3rd International Conference, 13-18 August 2005,
Kolymbari Cret
Ensemble inequivalence in systems with long-range interactions
Ensemble inequivalence has been observed in several systems. In particular it
has been recently shown that negative specific heat can arise in the
microcanonical ensemble in the thermodynamic limit for systems with long-range
interactions. We display a connection between such behaviour and a mean-field
like structure of the partition function. Since short-range models cannot
display this kind of behaviour, this strongly suggests that such systems are
necessarily non-mean field in the sense indicated here. We illustrate our
results showing an application to the Blume-Emery-Griffiths model. We further
show that a broad class of systems with non-integrable interactions are indeed
of mean-field type in the sense specified, so that they are expected to display
ensemble inequivalence as well as the peculiar behaviour described above in the
microcanonical ensemble.Comment: 12 pages, no figure
Time-independent Hamiltonians describing systems with friction: the "cyclotron with friction"
As is well-known, any ordinary differential equation in one dimension can be cast as the Euler–Lagrange equation of an appropriate Lagrangian. Additionally, if the initial equation is autonomous, the Lagrangian can always be chosen to be time-independent. In two dimensions, however, the situation is more complex, and there exist systems of ODEs which cannot be described by any Lagrangian. In this paper we display Hamiltonians which describe the behaviour of a charged particle moving in a plane under the combined influence of a constant electric field (in the plane) and a constant magnetic field (orthogonal to the plane) as well as a friction force proportional to the velocity ("cyclotron with friction")