Comparative Monte Carlo Efficiency by Monte Carlo Analysis

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\lambda_2$ of various Markov chain transition matrices. We first computed ${\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size $\Delta$. Based on the $\lambda_2$ criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule-of-thumb of adjusting $\Delta$ so the Metropolis acceptance rate is around 50% range is often sub-optimal. In general, as a function of temperature or $\Delta$, $\lambda_2$ for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure

Nonlinear microwave response of MgB2

We calculate the intrinsic nonlinear microwave response of the two gap superconductor MgB2 in the clean and dirty limits. Due to the small value of the pi band gap, the nonlinear response at low temperatures is larger than for a single gap Bardeen-Cooper-Schrieffer (BCS) s-wave superconductor with a transition temperature of 40 K. Comparing this result with the intrinsic nonlinear d-wave response of YBa2Cu3O7 (YBCO) we find a comparable response at temperatures around 20 K. Due to its two gap nature, impurity scattering in MgB2 can be used to reduce the nonlinear response if the scattering rate in the pi band is made larger than the one in the sigma band.Comment: 4 pages, 4 figure

Observation of blue-shifted ultralong-range Cs2_{2} Rydberg molecules

We observe ultralong-range blue-shifted Cs$_{2}$ molecular states near $ns_{1/2}$ Rydberg states in an optical dipole trap, where $31\leq n\leq34$. The accidental near degeneracy of $(n-4)l$ and $ns$ Rydberg states for $l>2$ in Cs, due to the small fractional $ns$ quantum defect, leads to non-adiabatic coupling among these states, producing potential wells above the $ns$ thresholds. Two important consequences of admixing high angular momentum states with $ns$ states are the formation of large permanent dipole moments, $\sim 15-100\,$Debye, and accessibility of these states via two-photon association. The observed states are in excellent agreement with theory. Both projections of the total angular momentum on the internuclear axis are visible in the experiment

Photoionization Rates of Cs Rydberg Atoms in a 1064 nm Far Off-Resonance Trap

Experimental measurements of photoionization rates of $nD_{5/2}$ Rydberg states of Cs ($50 \leq n \leq 75$) in a 1064 nm far off-resonance dipole trap are presented. The photoionization rates are obtained by measuring the lifetimes of Rydberg atoms produced inside of a 1064 nm far off-resonance trap and comparing the lifetimes to corresponding control experiments in a magneto-optical trap. Experimental results for the control experiments agree with recent theoretical predictions for Rydberg state lifetimes and measured photoionization rates are in agreement with transition rates calculated from a model potential.Comment: 12 pages, 4 figure

Unforeseen high temperature and humidity stability of FeCl3_3 intercalated few layer graphene

We present the first systematic study of the stability of the structure and electrical properties of FeCl$_3$ intercalated few-layer graphene to high levels of humidity and high temperature. Complementary experimental techniques such as electrical transport, high resolution transmission electron microscopy and Raman spectroscopy conclusively demonstrate the unforeseen stability of this transparent conductor to a relative humidity up to $100 \%$ at room temperature for 25 days, to a temperature up to 150\,^\circC in atmosphere and up to a temperature as high as 620\,^\circC in vacuum, that is more than twice higher than the temperature at which the intercalation is conducted. The stability of FeCl$_3$ intercalated few-layer graphene together with its unique values of low square resistance and high optical transparency, makes this material an attractive transparent conductor in future flexible electronic applications.Comment: Scientific Reports, volume 5, article no. 760

Fundamental properties and applications of quasi-local black hole horizons

The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the quasi-local notions of trapped and marginally trapped surfaces, which lead naturally to the framework of trapping, isolated, and dynamical horizons. This framework allows us to analyze diverse facets of black holes in a unified manner and to significantly generalize several results in black hole physics. It also leads to a number of applications in mathematical general relativity, numerical relativity, astrophysics, and quantum gravity. In this review, I will discuss the basic ideas and recent developments in this framework, and summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th International Conference on General Relativity and Gravitation, 8-13 July 2007, Sydney, Australi

Monte Carlo Determination of Multiple Extremal Eigenpairs

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The new algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow {\it et al.}, and exploited a new sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously-sized two-dimensional, zero field Ising models. While very likely useful for other transfer matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.Comment: 22 pages, no figure

Early, but not late visual distractors affect movement synchronization to a temporal-spatial visual cue

The ease of synchronizing movements to a rhythmic cue is dependent on the modality of the cue presentation: timing accuracy is much higher when synchronizing with discrete auditory rhythms than an equivalent visual stimulus presented through flashes. However, timing accuracy is improved if the visual cue presents spatial as well as temporal information (e.g., a dot following an oscillatory trajectory). Similarly, when synchronizing with an auditory target metronome in the presence of a second visual distracting metronome, the distraction is stronger when the visual cue contains spatial-temporal information rather than temporal only. The present study investigates individuals' ability to synchronize movements to a temporal-spatial visual cue in the presence of same-modality temporal-spatial distractors. Moreover, we investigated how increasing the number of distractor stimuli impacted on maintaining synchrony with the target cue. Participants made oscillatory vertical arm movements in time with a vertically oscillating white target dot centered on a large projection screen. The target dot was surrounded by 2, 8, or 14 distractor dots, which had an identical trajectory to the target but at a phase lead or lag of 0, 100, or 200 ms. We found participants' timing performance was only affected in the phase-lead conditions and when there were large numbers of distractors present (8 and 14). This asymmetry suggests participants still rely on salient events in the stimulus trajectory to synchronize movements. Subsequently, distractions occurring in the window of attention surrounding those events have the maximum impact on timing performance