Correlated continuous time random walks

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. This paper develops scaling limits and governing equations in the case of correlated jumps. For long-range dependent jumps, this leads to fractional Brownian motion or linear fractional stable motion, with the time parameter replaced by an inverse stable subordinator in the case of heavy tailed waiting times. These scaling limits provide an interesting class of non-Markovian, non-Gaussian self-similar processes.Comment: 13 page

Large deviations for local time fractional Brownian motion and applications

Let W^H=\{W^H(t), t \in \rr\} be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in \rr, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable L\'evy process $X=\{X_t, t \ge 0\}$ of index $1<\alpha\leq 2$ independent of $W^H$. The \a-stable local time fractional Brownian motion $Z^H=\{Z^H(t), t \ge 0\}$ is defined by $Z^H(t) = W^H(L_t)$. The process $Z^H$ is self-similar with self-similarity index $H(1 - \frac 1 \alpha)$ and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps (\cite{coupleCTRW,limitCTRW}). However, $Z^H$ does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process $Z^H$. As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for $Z^H$.Comment: 20 page

Efficient excitation of a two level atom by a single photon in a propagating mode

State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized \textit{propagating} pulse in free space and study the probability $P_e(t)$ of finding the atom in the excited state at any time $t$. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\Lambda\in[0,8\pi/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then $P_e(t)$ can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single photon Fock state and coherent states and for various temporal shapes of the pulses.Comment: 6 pages, 5 figures, 2 table

Round-Bale Silage Preparation of Rice Straw

Rice straw is an important feed resource for ruminants. In Japan, rice straw cannot be fully dried due to the usually humid autumn season, which leads to about 70% of the production being ploughed back or incinerated. Therefore, the development of techniques to enhance the long-term preservation and quality of rice straw is of great importance. In this work, a new lactic acid bacterium was used as a silage inoculant, and its effect on round-bale silage preparation from fresh rice straw was examined

Full-dimensional (15-dimensional) ab initio analytical potential energy surface for the H 7 + cluster

Full-dimensional ab initio potential energy surface is constructed for the H7+ cluster. The surface is a fit to roughly 160 000 interaction energies obtained with second-order MöllerPlesset perturbation theory and the cc-pVQZ basis set, using the invariant polynomial method [B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009)10.1080/01442350903234923]. We employ permutationally invariant basis functions in Morse-type variables for all the internuclear distances to incorporate permutational symmetry with respect to interchange of H atoms into the representation of the surface. We describe how different configurations are selected in order to create the database of the interaction energies for the linear least squares fitting procedure. The root-mean-square error of the fit is 170 cm -1 for the entire data set. The surface dissociates correctly to the H5+ H 2 fragments. A detailed analysis of its topology, as well as comparison with additional ab initio calculations, including harmonic frequencies, verify the quality and accuracy of the parameterized potential. This is the first attempt to present an analytical representation of the 15-dimensional surface of the H7+ cluster for carrying out dynamics studies. © 2012 American Institute of Physics.. R.P. acknowledges financial support by Ministerio de Ciencia e Innovacion, Spain, Grant No. FIS2010-18132, FIS2011-29596-C02-01 and European Cooperation in Scientific and Technical Research (COST) Action CM1002 (CODECS). P.B. acknowledges a postdoctoral fellowship from the Ramón Areces Foundation, Spain. J.M.B. and Y.W. thank the National Science Foundation (CHE-1145227) for financial support.Peer Reviewe