Primary structural dynamics in graphite

The structural dynamics of graphite and graphene are unique, because of the selective coupling between electron and lattice motions and hence the limit on electric and electro-optic properties. Here, we report on the femtosecond probing of graphite films (1–3 nm) using ultrafast electron crystallography in the transmission mode. Two time scales are observed for the dynamics: a 700 fs initial decrease in diffraction intensity due to lattice phonons in optically dark regions of the Brillouin zone, followed by a 12 ps decrease due to phonon thermalization near the Г and K regions. These results indicate the non-equilibrium distortion of the unit cells at early time and the subsequent role of long-wavelength atomic motions in the thermalization process. Theory and experiment are now in agreement regarding the nature of nuclear motions, but the results suggest that potential change plays a role in the lateral dynamics of the lattice

Structural dynamics of surfaces by ultrafast electron crystallography: Experimental and multiple scattering theory

Recent studies in ultrafast electron crystallography (UEC) using a reflection diffraction geometry have enabled the investigation of a wide range of phenomena on the femtosecond and picosecond time scales. In all these studies, the analysis of the diffraction patterns and their temporal change after excitation was performed within the kinematical scattering theory. In this contribution, we address the question, to what extent dynamical scattering effects have to be included in order to obtain quantitative information about structural dynamics. We discuss different scattering regimes and provide diffraction maps that describe all essential features of scatterings and observables. The effects are quantified by dynamical scattering simulations and examined by direct comparison to the results of ultrafast electron diffraction experiments on an in situ prepared Ni(100) surface, for which structural dynamics can be well described by a two-temperature model. We also report calculations for graphite surfaces. The theoretical framework provided here allows for further UEC studies of surfaces especially at larger penetration depths and for those of heavy-atom materials

Cold dilute neutron matter on the lattice I: Lattice virial coefficients and large scattering lengths

We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this paper we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.Comment: 17 pages, 12 figure

Gluon Condensate and Non-Perturbative Quark-Photon Vertex

We evaluate the quark-photon vertex non-perturbatively taking into account the gluon condensate at finite temperature. This vertex is related to the previously derived effective quark propagator by a QED like Ward-Takahashi identity. The importance of the effective vertex for the dilepton production rate from a quark-gluon plasma is stressed.Comment: 9 pages including two figure

Quickest detection in coupled systems

This work considers the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled a general Ito processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended average Kullback- Leibler divergence criterion is used as a measure of detection delay, with a constraint on the mean time between false alarms. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound.Comment: 6 pages, 48th IEEE Conference on Decision and Control, Shanghai 2009 December 16 - 1

Quickest detection in coupled systems

This work considers the problem of quickest detection of signals in a coupled system of $N$ sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled by general It\^{o} processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. Two main cases are considered; in the first one signal strengths are the same across sensors while in the second one they differ by a constant. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended minimal Kullback-Leibler divergence criterion is used as a measure of detection delay, with a constraint on the mean time to the first false alarm. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of $N$ CUSUMs is asymptotically optimal as the mean time to the first false alarm increases without bound. In particular, in the case of equal signal strengths across sensors, it is seen that the difference in detection delay of the $N$-CUSUM stopping rule and the unknown optimal stopping scheme tends to a constant related to the number of sensors as the mean time to the first false alarm increases without bound. Alternatively, in the case of unequal signal strengths, it is seen that this difference tends to zero.Comment: 29 pages. SIAM Journal on Control and Optimization, forthcomin

Phasing of gravitational waves from inspiralling eccentric binaries

We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling {\it circular} orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of {\it inspiralling eccentric} orbits involves {\it three different time scales}: orbital period, periastron precession and radiation-reaction time scales. By using an improved `method of variation of constants', we show how to combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. We explicitly implement our method at the 2.5PN post-Newtonian accuracy. Our final results can be viewed as computing new `post-adiabatic' short period contributions to the orbital phasing, or equivalently, new short-period contributions to the gravitational wave polarizations, $h_{+,\times}$, that should be explicitly added to the `post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects on the orbital phasing of the latter in the usual adiabatic approximation. Our results should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric gravitational wave detectors (especially if Kozai oscillations turn out to be significant in globular cluster triplets), and for the future space-based interferometer LISA.Comment: 49 pages, 6 figures, high quality figures upon reques

Fidelity amplitude of the scattering matrix in microwave cavities

The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the scattering fidelity is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength could be determined independently from level dynamics of the system, thus providing a parameter free agreement between theory and experiment