Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.Comment: 4 pages, 2 figure

Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]

The quantization of phase is still an open problem. In the approach of Susskind and Glogower so called cosine and sine operators play a fundamental role. Their eigenstates in the Fock representation are related with the Chebyshev polynomials of the second kind. Here we introduce more general cosine and sine operators whose eigenfunctions in the Fock basis are related in a similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1]. To each polynomial set defined in terms of a weight function there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function we distinguish generalized or extended operators. Their eigenstates are used to define cosine and sine representations and probability distributions. We consider also the inverse arccosine and arcsine operators and use their eigenstates to define cosine-phase and sine-phase distributions, respectively. Specific, numerical and graphical results are given for the classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure

Toward a microscopic description of flow near the jamming threshold

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that (i) the viscosity {\eta} diverges with the coordination z as {\eta} ~ (z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure

Bose-Einstein condensation of quasiparticles in graphene

The collective properties of different quasiparticles in various graphene based structures in high magnetic field have been studied. We predict Bose-Einstein condensation (BEC) and superfluidity of 2D spatially indirect magnetoexcitons in two-layer graphene. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition are shown to be increasing functions of the excitonic density but decreasing functions of magnetic field and the interlayer separation. The instability of the ground state of the interacting 2D indirect magnetoexcitons in a slab of superlattice with alternating electron and hole graphene layers (GLs) is established. The stable system of indirect 2D magnetobiexcitons, consisting of pair of indirect excitons with opposite dipole moments, is considered in graphene superlattice. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition for magnetobiexcitons in graphene superlattice are obtained. Besides, the BEC of excitonic polaritons in GL embedded in a semiconductor microcavity in high magnetic field is predicted. While superfluid phase in this magnetoexciton polariton system is absent due to vanishing of magnetoexciton-magnetoexciton interaction in a single layer in the limit of high magnetic field, the critical temperature of BEC formation is calculated. The essential property of magnetoexcitonic systems based on graphene (in contrast, e.g., to a quantum well) is stronger influence of magnetic field and weaker influence of disorder. Observation of the BEC and superfluidity of 2D quasiparticles in graphene in high magnetic field would be interesting confirmation of the phenomena we have described.Comment: 13 pages, 5 figure

Temporal Correlations of Local Network Losses

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. {\em By construction}, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics