Overdamped Stress Relaxation in Buckled Rods

We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. In the bulk two interesting regimes of generic self--similar intermediate asymptotics are distinguished, which give rise to two classes of approximate and exact power--law solutions, respectively. For the case of open boundary conditions the corresponding non--trivial boundary--layer scenarios are derived by a multiple--scale perturbation (``adiabatic'') method. Our results compare well with -- and provide the theoretical explanation for -- previous results from numerical simulations, and they suggest new directions for further fruitful numerical and experimental investigations.Comment: 20 pages, 12 figure

Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport

We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities

Cognitive performance in multiple system atrophy

The cognitive performance of a group of patients with multiple system atrophy (MSA) of striato-nigral predominance was compared with that of age and IQ matched control subjects, using three tests sensitive to frontal lobe dysfunction and a battery sensitive to memory and learning deficits in Parkinson's disease and dementia of the Alzheimer type. The MSA group showed significant deficits in all three of the tests previously shown to be sensitive to frontal lobe dysfunction. Thus, a significant proportion of patients from the MSA group failed an attentional set-shifting test, specifically at the stage when an extra-dimensional shift was required. They were also impaired in a subject-ordered test of spatial working memory. The MSA group showed deficits mostly confined to measures of speed of thinking, rather than accuracy, on the Tower of London task. These deficits were seen in the absence of consistent impairments in language or visual perception. Moreover, the MSA group showed no significant deficits in tests of spatial and pattern recognition previously shown to be sensitive to patients early in the course of probable Alzheimer's disease and only a few patients exhibited impairment on the Warrington Recognition Memory Test. There were impairments on other tests of visual memory and learning relative to matched controls, but these could not easily be related to fundamental deficits of memory or learning. Thus, on a matching-to-sample task the patients were impaired at simultaneous but not delayed matching to sample, whereas difficulties in a pattern-location learning task were more evident at its initial, easier stages. The MSA group showed no consistent evidence of intellectual deterioration as assessed from their performance on subtests of the Wechsler Adult Intelligence Scale (WAIS) and the National Adult Reading Test (NART). Consideration of individual cases showed that there was some heterogeneity in the pattern of deficits in the MSA group, with one patient showing no impairment, even in the face of considerable physical disability. The results show a distinctive pattern of cognitive deficits, unlike those previously seen using the same tests in patients with Parkinson's and Alzheimer's diseases, and suggesting a prominent frontal-lobe-like component. The implications for concepts of 'subcortical' dementia and 'fronto-striatal' cognitive dysfunction are considered

Tomographic reconstruction of quantum states in N spatial dimensions

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the procedure is that the angular frequencies of the N harmonic potentials are incommensurable. We discuss what kind of information can be found if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite time measurements. As a further example of quantum state reconstruction in N dimensions we consider the two related cases of an N-dimensional free particle with periodic boundary conditions and a particle in an N-dimensional box, where we find a similar condition of incommensurability and finite recurrence time for the one-dimensional system.Comment: 8 pages, 1 figur

Multi-particle entanglement of hot trapped ions

We propose an efficient method to produce multi-particle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.Comment: 4 pages, including 3 figures. To appear in Phys. Rev. Lett. This paper previously appeared under the name "Schrodingers cat in a hot trap". The paper has been revised according to Phys. Rev. policy on Schrodinger cats. No cats were harmed during the production of this manuscrip

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.Comment: 10 pages, 5 figure

Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.Comment: 23 pages, 13 figure

Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_perpendicular" = - beta = 1/2, "nu_parallel" = gamma/2 = 1.Comment: 4 pages of Latex, including 4 Postscript figures. To be published in Phys. Rev. Let