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

Intruder States and their Local Effect on Spectral Statistics

The effect on spectral statistics and on the revival probability of intruder states in a random background is analysed numerically and with perturbative methods. For random coupling the intruder does not affect the GOE spectral statistics of the background significantly, while a constant coupling causes very strong correlations at short range with a fourth power dependence of the spectral two-point function at the origin.The revival probability is significantly depressed for constant coupling as compared to random coupling.Comment: 18 pages, 10 Postscript figure

Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry

The spectral properties of a two-dimensional microwave billiard showing threefold symmetry have been studied with a new experimental technique. This method is based on the behavior of the eigenmodes under variation of a phase shift between two input channels, which strongly depends on the symmetries of the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been identified by a simple and purely experimental method. This set clearly shows Gaussian unitary ensemble statistics, although the system is time-reversal invariant.Comment: RevTex 4, 5 figure

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

Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions

Recently, there has been some vigorous interest in the out-of-equilibrium quasistationary states (QSSs), with lifetimes diverging with the number N of degrees of freedom, emerging from numerical simulations of the ferromagnetic XY Hamiltonian Mean Field (HMF) starting from some special initial conditions. Phase transitions have been reported between low-energy magnetized QSSs and large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization. This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is argued that the time-asymptotic states emerging in the Vlasov limit can be related to simple generic time-asymptotic forms for the force field. The proposed picture unveils the nature of the out-of-equilibrium phase transitions reported for the ferromagnetic HMF: this is a bifurcation point connecting an effective integrable Vlasov one-particle time-asymptotic dynamics to a partly ergodic one which means a brutal open-up of the Vlasov one-particle phase space. Illustration is given by investigating the time-asymptotic value of the magnetization at the phase transition, under the assumption of a sufficiently rapid time-asymptotic decay of the transient force field

Transition from Poisson to gaussian unitary statistics: The two-point correlation function

We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the Poisson and gaussian limit.Comment: 19 pages, no figure

Long-Term Remission of an Aggressive Sebaceous Carcinoma following Chemotherapy

Sebaceous carcinoma (SC) is an uncommon neoplasm manifesting itself either in the eyelid or extraocularly in the head and neck area. Surgery is the standard of care. Irradiation is rarely proposed as monotherapy but is frequently administered as an adjuvant regimen following surgical resection. There is no known strategy concerning chemotherapeutic treatment in highly aggressive recurrent - or metastatic - forms of the disease. Our patient presented with an aggressive SC of the scalp recurring after multiple excisions and local radiotherapy. Chemotherapy with 5-fluorouracil, cisplatin and docetaxel was then initiated; 4 cycles were administered, followed by capecitabine maintenance. Shortly after starting chemotherapy, dermal lesions had completely disappeared and radiological response could be seen. The patient experienced an extended period (>20 months) of complete remission. In this report, we show an excellent response of a highly aggressive SC after a combination of chemotherapy as for head and neck cancers

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.

Inhomogeneous Quasi-stationary States in a Mean-field Model with Repulsive Cosine Interactions

The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial conditions. The object of this paper is to show in a detailed manner how these structures arise and to explain their stability. By a convenient canonical transformation we rewrite the Hamiltonian in such a way that fast and slow variables are singled out and the canonical coordinates of a collective mode are naturally introduced. If, initially, enough energy is put in this mode, its decay can be extremely slow. However, both analytical arguments and numerical simulations suggest that these structures eventually decay to the spatially uniform equilibrium state, although this can happen on impressively long time scales. Finally, we heuristically introduce a one-particle time dependent Hamiltonian that well reproduces most of the observed phenomenology.Comment: to be published in J. Phys.

Post-traumatic overload or acute syndrome of the os trigonum: a possible cause of posterior ankle impingement

The purpose of this paper is to discuss the post-traumatic overload syndrome of the os trigonum as a possible cause of posterior ankle impingement and hindfoot pain. We have reviewed 19 athletes who were referred to our foot unit between 1995 and 2001 because of posterior ankle pain, and in whom a post-traumatic overload syndrome of os trigonum was diagnosed. All these patients were followed up over a period of 2 years. In 11 cases a chronic repetitive movements in forced plantar flexion was found. In the other eight cases the pain appeared to persist after a standard treatment of an ankle sprain in inversion plantar flexion. The diagnosis was based on clinical history, physical examination and X-rays that revealed a non-fused os trigonum. The confirmation of diagnosis was carried-out injecting local anaesthetic under fluoroscopic control. In all cases a corticosteroid injection as first line treatment was performed. In 6 cases a second injection was necessary to alleviate pain because incomplete recovery with the first injection. Three cases (16%) were recalcitrant to this treatment and in these three cases a surgical excision of the os trigonum was carried out. Our conclusion is that after some chronic athletic activity or an acute ankle sprain the os trigonum, if present, may undergo mechanical overload, remain undisrupted and become painful. Treatment by corticosteroid injection often resolves the proble