Continuous Model for Homopolymers

We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a globular to an extended phase. For various values of the temperature, including those at or near the critical value, we consider the limiting behavior of the polymer when its size tends to infinity

Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other

Anomalies of LF signal during seismic activity in November?December 2004

International audienceA signal transmitted by Japan Time Standard LF station (40 kHz, Fukushima prefecture) and recorded in Petropavlovsk-Kamchatski (Russia) is analyzed during a time interval from 1 July 2004 till 24 January 2005. This interval is characterized by quiet seismic conditions up to the beginning of November, but rather strong seismic activity occurs in November and December not far from Hokkaido (Japan) and in the region of northern Kuril Islands. There were three series of earthquakes with M=5.6?7.1 in a zone of sensitivity of our wave path during two months. Nighttime "bay-like" phase and amplitude anomalies of the LF signal are observed several days before and during every series of earthquakes. During the whole period of seismic activity a significant shift in terminator times is also evident. The spectrum of LF seismo-induced anomalies shows a clear increase for the period of about 25 min

ULF magnetic emissions connected with under sea bottom earthquakes

Measurements of ULF electromagnetic disturbances were carried out in Japan before and during a seismic active period (1 February 2000 to 26 July 2000). A network consists of two groups of magnetic stations spaced apart at a distance of &#x2248;140 km. Every group consists of three, 3-component high sensitive magnetic stations arranged in a triangle and spaced apart at a distance of 4–7 km. The results of the ULF magnetic field variation analysis in a frequency range of <i>F</i> = 0.002–0.5 Hz in connection with nearby earth-quakes are presented. Traditional <i>Z</i>/<i>G</i> ratios (<i>Z</i> is the vertical component, <i>G</i> is the total horizontal component), magnetic gradient vectors and phase velocities of ULF waves propagating along the Earth’s surface were constructed in several frequency bands. It was shown that variations of the <i>R</i>(<i>F</i>) = <i>Z</i>/<i>G</i> parameter have a different character in three frequency ranges: <i>F</i>₁ = 0.1 ± 0.005, <i>F</i>₂ = 0.01 ± 0.005 and <i>F</i>₃ = 0.005 ± 0.003 Hz. Ratio <i>R</i>(<i>F</i>₃)/<i>R</i>(<i>F</i>₁)</i> sharply increases 1–3 days before strong seismic shocks. Defined in a frequency range of <i>F</i>₂ = 0.01 ± 0.005 Hz during nighttime intervals (00:00–06:00 LT), the amplitudes of <i>Z</i> and <i>G</i> component variations and the <i>Z</i>/<i>G</i> ratio started to increase &#x2248; 1.5 months before the period of the seismic activity. The ULF emissions of higher frequency ranges sharply increased just after the seismic activity start. The magnetic gradient vectors (<b>&#x2207; <i>B</i></b> &#x2248; 1 – 5 pT/km), determined using horizontal component data (<i>G</i> &#x2248; 0.03 – 0.06 nT) of the magnetic stations of every group in the frequency range <i>F</i> = 0.05 ± 0.005 Hz, started to point to the future center of the seismic activity just before the seismoactive period; furthermore they continued following space displacements of the seismic activity center. The phase velocity vectors (<i>V</i> &#x2248; 20 km/s for <i>F</i> = 0.0067 Hz), determined using horizontal component data, were directed from the seismic activity center. Gradient vectors of the vertical component pointed to the closest seashore (known as the 'sea shore' effect). The location of the seismic activity centers by two gradient vectors, constructed at every group of magnetic stations, gives an &#x2248; 10 km error in this experiment

Spectral flow and level spacing of edge states for quantum Hall hamiltonians

We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference $L$ submitted to a perpendicular magnetic field of strength $B$ and to the potential of impurities of maximal amplitude $w$. This model is of importance in the context of the integer quantum Hall effect. In the regime of strong magnetic field or weak disorder $B>>w$ it is known that there are chiral edge states, which are localised within a few magnetic lengths close to, and extended along the boundary of the cylinder, and whose energy levels lie in the gaps of the bulk system. These energy levels have a spectral flow, uniform in $L$, as a function of a magnetic flux which threads the cylinder along its axis. Through a detailed study of this spectral flow we prove that the spacing between two consecutive levels of edge states is bounded below by $2\pi\alpha L^{-1}$ with $\alpha>0$, independent of $L$, and of the configuration of impurities. This implies that the level repulsion of the chiral edge states is much stronger than that of extended states in the usual Anderson model and their statistics cannot obey one of the Gaussian ensembles. Our analysis uses the notion of relative index between two projections and indicates that the level repulsion is connected to topological aspects of quantum Hall systems.Comment: 22 pages, no figure

Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function $\bar{\mu}(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu}(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if $\bar{\mu}(+\infty)=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.Comment: 19 pages, 4 figures. Accepted for publication in Phys. Rev.

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p