Coherent Destruction of Photon Emission from a Single Molecule Source

The behavior of a single molecule driven simultaneously by a laser and by an electric radio frequency field is investigated using a non-Hermitian Hamiltonian approach. Employing the renormalization group method for differential equations we calculate the average waiting time for the first photon emission event to occur, and determine the conditions for the suppression and enhancement of photon emission. An abrupt transition from localization-like behavior to delocalization behavior is found.Comment: 5 pages, 4 figure

Theory of Single File Diffusion in a Force Field

The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection ${\cal R}$ and transmission ${\cal T}$ coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.Comment: 4 Phys. Rev. page

Distribution of Time-Averaged Observables for Weak Ergodicity Breaking

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $$.Comment: 5 pages, 2 figure

Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights

We study the weight space structure of the parity machine with binary weights by deriving the distribution of volumes associated to the internal representations of the learning examples. The learning behaviour and the symmetry breaking transition are analyzed and the results are found to be in very good agreement with extended numerical simulations.Comment: revtex, 20 pages + 9 figures, to appear in Phys. Rev.

Fluctuations of 1/f1/f noise and the low frequency cutoff paradox

Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is random -- a manifestation of weak ergodicity breaking. Here we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve an outstanding paradox on the non integrability of $1/f$ noise and the violation of Parseval's theorem. We explain why there is no physical low frequency cutoff and therefore cannot be found in experiments.Comment: 5 pages, 2 figures, supplementary material (4 pages

Linear and non linear response in the aging regime of the 1D trap model

We investigate the behaviour of the response function in the one dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time tw+t given that a small bias h is applied at time tw. Several scaling regimes are found, depending on the relative values of t, tw and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation dissipation relation is, in this case, valid even in the aging regime.Comment: 5 pages, 3 figures, 3 references adde

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

Diffusion of Tagged Particle in an Exclusion Process

We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the distribution and the mean square displacement of the tagged center particle valid for rather general external force fields and initial conditions. A wide range of physical behaviors emerge which are very different than the classical single file sub-diffusion $ \sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields. For symmetric initial conditions and potential fields we find $ = {{\cal R} (1 - {\cal R})\over 2 N {\it r} ^2} $ where $2 N$ is the (large) number of particles in the system, ${\cal R}$ is a single particle reflection coefficient obtained from the single particle Green function and initial conditions, and $r$ its derivative. We show that this equation is related to the mathematical theory of order statistics and it can be used to find even when the motion between collision events is not Brownian (e.g. it might be ballistic, or anomalous diffusion). As an example we derive the Percus relation for non Gaussian diffusion

Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.