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

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

Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction

We study reaction zones in three different versions of the A+B->0 system. For a steady state formed by opposing currents of A and B particles we derive scaling behavior via renormalization group analysis. By use of a previously developed analogy, these results are extended to the time-dependent case of an initially segregated system. We also consider an initially mixed system, which forms reaction zones for dimension d<4. In this case an extension of the steady-state analogy gives scaling results characterized by new exponents.Comment: 4 pages, REVTeX 3.0 with epsf, 2 uuencoded postscript figures appended, OUTP-94-33

Metastability in Markov processes

We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce restricted Markov chains which are close to the original process but do not leave these regions. Within this context, we identify the conditions under which the decaying system can be considered to be in a metastable state. Furthermore, we show that such metastable states can be described in thermodynamic terms and define their free energy. This is accomplished showing that the probability distribution describing the metastable state is indeed proportional to the equilibrium distribution, as is commonly assumed. We test the formalism numerically in the case of the two-dimensional kinetic Ising model, using the Wang--Landau algorithm to show this proportionality explicitly, and confirm that the proportionality constant is as derived in the theory. Finally, we extend the formalism to situations in which a system can have several metastable states.Comment: 30 pages, 5 figures; version with one higher quality figure available at http://www.fis.unam.mx/~dsanders

Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry

Recently it has been shown that time-reversal invariant systems with discrete symmetries may display in certain irreducible subspaces spectral statistics corresponding to the Gaussian unitary ensemble (GUE) rather than to the expected orthogonal one (GOE). A Kramers type degeneracy is predicted in such situations. We present results for a microwave billiard with a threefold rotational symmetry and with the option to display or break a reflection symmetry. This allows us to observe the change from GOE to GUE statistics for one subset of levels. Since it was not possible to separate the three subspectra reliably, the number variances for the superimposed spectra were studied. The experimental results are compared with a theoretical and numerical study considering the effects of level splitting and level loss

Impact of family structure on long-term survivors of osteosarcoma

Goals of work: Long-term outcomes of osteosarcoma have dramatically improved with the use of modern combination therapies. Such aggressive treatments, however, entail chronic complications. In the present study, we assessed the functional, psychological, and familial status of long-term survivors of osteosarcoma treated at our institution. Materials and methods: Fifteen long-term survivors of osteosarcoma were evaluated for functional and psychological sequelae. Functional assessment was based on a method described by Enneking et al. Psychological assessment was based on General Health Questionnaire 28, Inventory Scale for Traumatic Neurosis, and Family System Test. Main results: Ten patients showed mild functional impairments; only five patients were handicapped more seriously. Depressive symptoms were diagnosed in four patients. A total of six patients revealed unbalanced family structures, including three of the four patients with depressive symptoms, all four patients with symptoms of posttraumatic stress disorder, and five of seven patients who showed poor emotional acceptance. Conclusions: Osteosarcoma survivors will generally recover good functional performance. Only a minority of them remain seriously impaired. One third of the patients present depressive symptoms and posttraumatic stress disorder. Poor coping is closely associated with unbalanced family structures. Therefore, the psychological and familial situation of patients with newly diagnosed osteosarcoma should be carefully assesse

Computer-assisted placement technique in hip resurfacing arthroplasty: improvement in accuracy?

Freehand positioning of the femoral drill guide is difficult during hip resurfacing and the surgeon is often unsure of the implant position achieved peroperatively. The purpose of this study was to find out whether, by using a navigation system, acetabular and femoral component positioning could be made easier and more precise. Eighteen patients operated on by the same surgeon were matched by sex, age, BMI, diagnosis and ASA score (nine patients with computer assistance, nine with the regular ancillary). Pre-operative planning was done on standard AP and axial radiographs with CT scan views for the computer-assisted operations. The final position of implants was evaluated by the same radiographs for all patients. The follow-up was at least 1year. No difference between both groups in terms of femoral component position was observed (p > 0.05). There was also no difference in femoral notching. A trend for a better cup position was observed for the navigated hips, especially for cup anteversion. There was no additional operating time for the navigated hips. Hip navigation for resurfacing surgery may allow improved visualisation and hip implant positioning, but its advantage probably will be more obvious with mini-incisions than with regular incision surger

Correlations between spectra with different symmetry: any chance to be observed?

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular, because in semiclassics spectra of different symmetry are expressed in terms of the same set of periodic orbits. We reexamine this question and find absence of correlation in the universal regime. In the case of continuous symmetry the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time

Kinetic Anomalies in Addition-Aggregation Processes

We investigate irreversible aggregation in which monomer-monomer, monomer-cluster, and cluster-cluster reactions occur with constant but distinct rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For epsilon=0 and gamma<2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For gamma >= 2, there is unusual behavior in which the concentration of clusters of mass k, c_k decays as a stretched exponential in time within a boundary layer k<k* propto t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma >= 2.Comment: 6 pages, 2 column revtex4 format, for submission to J. Phys.