Localization of Light: Dual Symmetry between Absorption and Amplification

We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $\epsilon$, and show that dual systems, which differ only in the sign of the imaginary part of $\epsilon$, have the same localization length. Paradoxically, absorption and stimulated emission of radiation suppress the transmittance of the waveguide in the same way.Comment: Added a reference to the paper by Z.Q. Zhang, Phys.Rev.B. 52, 7960 (1995

Is Strong Gravitational Radiation predicted by TeV-Gravity?

In TeV-gravity models the gravitational coupling to particles with energies E\sim m_{Pl} \sim 10 TeV is not suppressed by powers of ultra-small ratio E/M_{Pl} with M_{Pl} \sim 10^{19} GeV. Therefore one could imagine strong synchrotron radiation of gravitons by the accelerating particles to become the most pronounced manifestation of TeV-gravity at LHC. However, this turns out to be not true: considerable damping continues to exist, only the place of E/M_{Pl} it taken by a power of a ratio \theta\omega/E, where the typical frequency \omega of emitted radiation, while increased by a number of \gamma-factors, can not reach E/\vartheta unless particles are accelerated by nearly critical fields. Moreover, for currently available magnetic fields B \sim 10 Tesla, multi-dimensionality does not enhance gravitational radiation at all even if TeV-gravity is correct.Comment: 7 pages, LaTe

Transmission through a many-channel random waveguide with absorption

We compute the statistical distribution of the transmittance of a random waveguide with absorption in the limit of many propagating channels. We consider the average and fluctuations of the conductance T = tr t^{\dagger} t, where t is the transmission matrix, the density of transmission eigenvalues \tau (the eigenvalues of t^{\dagger} t), and the distribution of the plane-wave transmittances T_a and T_{ab}. For weak absorption (length L smaller than the exponential absorption length \xi_a), we compute moments of the distributions, while for strong absorption (L >> \xi_a), we can find the complete distributions. Our findings explain recent experiments on the transmittance of random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].Comment: 13 pages, RevTeX; 9 figures include

Non-perturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide

A non-perturbative random-matrix theory is applied to the transmission of a monochromatic scalar wave through a disordered waveguide. The probability distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident mode n are calculated in the thick-waveguide limit, for broken time-reversal symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the diffusive regime to lognormal statistics in the localized regime. A qualitatively different crossover occurs if the disordered region is replaced by a chaotic cavity. ***Submitted to Physical Review E.***Comment: 7 pages, REVTeX-3.0, 5 postscript figures appended as self-extracting archive. A complete postscript file with figures and text (4 pages) is available from http://rulgm4.LeidenUniv.nl/preprints.htm

Plasmon-graviton conversion in a magnetic field in TeV-scale gravity

Kaluza-Klein (KK) gravitons emission rates due to plasmon-graviton conversion in magnetic field are computed within the ADD model of TeV-scale gravity. Plasma is described in the kinetic approach as the system of charged particles and Maxwell field both confined on the brane. Interaction with multidimensional gravity living in the bulk with $n$ compact extra dimensions is introduced within the linearized theory. Plasma collective effects enter through the two-point correlation function of the fluctuations of the energy-momentum tensor. The estimate for magnetic stars is presented leading to the lower limit of the D-dimensional Plank mass.Comment: Submitted to Proceedings of "RusGrav-14" International Conference, 27.06-02.07 2011, Ulyanovks, Russi

Photon-graviton mixing in an electromagnetic field

Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic field. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases.Comment: 13 pages, 1 figure, talk given by C. Schubert at QFEXT07, Leipzig, 17-21 Sep 2007, final published version (slightly extended

Point-Contact Conductances at the Quantum Hall Transition

On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2|2) symmetry, and postulating a two-point correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be X_t = 0.640 +/- 0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by X_t. Our results demonstrate that multifractality can show up in appropriate transport experiments.Comment: 18 pages, 15 figures included, revised versio

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is examined. Each particle can split into two particles only once at Poisson paced times and deviates orthogonally when splitted. At time $t$, after $N(t)$ Poisson events, there are $N(t)+1$ particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as $t$ increases and for different values of the parameters $c$ (hyperbolic velocity of motion) and $\lambda$ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented

Local correlations of different eigenfunctions in a disordered wire

We calculate the correlator of the local density of states in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r_1-r_2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric sigma-model, which is done exactly by the mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r_1-r_2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.Comment: 5 pages, 2 figures. v2: an error in treating the spatial dependence of correlations is correcte

DIFFUSION IN ONE DIMENSIONAL RANDOM MEDIUM AND HYPERBOLIC BROWNIAN MOTION

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this relationship and study various distributions using stochastic calculus and functional integration.Comment: 18 page