Molecular Dynamics at Low Time Resolution

The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale, in order not to cut-off important physical effects. We show that, in systems obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs at time scales smaller than dt can be analytically integrated out and gives raise to a time-dependent correction to the diffusion coefficient, which we rigorously compute. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps dt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy-model and the denaturation of a protein.Comment: 12 pages, 5 figure

A time lens for high resolution neutron time of flight spectrometers

We examine in analytic and numeric ways the imaging effects of temporal neutron lenses created by traveling magnetic fields. For fields of parabolic shape we derive the imaging equations, investigate the time-magnification, the evolution of the phase space element, the gain factor and the effect of finite beam size. The main aberration effects are calculated numerically. The system is technologically feasible and should convert neutron time of flight instruments from pinhole- to imaging configuration in time, thus enhancing intensity and/or time resolution. New fields of application for high resolution spectrometry may be opened.Comment: 8 pages, 11 figure

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Super-Resolution from Short-Time Fourier Transform Measurements

While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum spacing, $\Delta$, between spikes is not too small. Specifically, for a cutoff frequency of $f_c$, Donoho [2] shows that exact recovery is possible if $\Delta > 1/f_c$, but does not specify a corresponding recovery method. On the other hand, Cand\`es and Fernandez-Granda [3] provide a recovery method based on convex optimization, which provably succeeds as long as $\Delta > 2/f_c$. In practical applications one often has access to windowed Fourier transform measurements, i.e., short-time Fourier transform (STFT) measurements, only. In this paper, we develop a theory of super-resolution from STFT measurements, and we propose a method that provably succeeds in recovering spike trains from STFT measurements provided that $\Delta > 1/f_c$.Comment: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), May 2014, to appea

Versatile scanning tunneling microscopy with 120ps time resolution

We describe a fully ultra-high vacuum compatible scanning tunneling microscope (STM) optimized for radio-frequency signals. It includes in-situ exchangeable tips adapted to high frequency cabling and a standard sample holder, which offer access to the whole range of samples typically investigated by STM. We demonstrate a time resolution of 120 ps using the nonlinear I(V)-characteristic of the surface of highly oriented pyrolithic graphite. We provide atomically resolved images in pulse mode related to a spatially varying nonlinearity of the local density of states of the sample, thus, demonstrating the possible spatial resolution of the instrument in pulse mode. Analysis of the noise reveals that changes in the tunneling junction of 50 pA are dynamically detectable at 120 ps time resolution.Comment: 4 pages, 4 figure

High time-resolution observations of the Vela pulsar

We present high time resolution observations of single pulses from the Vela pulsar (PSR B0833-45) made with a baseband recording system at observing frequencies of 660 and 1413 MHz. We have discovered two startling features in the 1413 MHz single pulse data. The first is the presence of giant micro-pulses which are confined to the leading edge of the pulse profile. One of these pulses has a peak flux density in excess of 2500 Jy, more than 40 times the integrated pulse peak. The second new result is the presence of a large amplitude gaussian component on the trailing edge of the pulse profile. This component can exceed the main pulse in intensity but is switched on only relatively rarely. Fluctutation spectra reveal a possible periodicity in this feature of 140 pulse periods. Unlike the rest of the profile, this component has low net polarization and emits predominantly in the orthogonal mode. This feature appears to be unique to the Vela pulsar. We have also detected microstructure in the Vela pulsar for the first time. These same features are present in the 660 MHz data. We suggest that the full width of the Vela pulse profile might be as large as 10 ms but that the conal edges emit only rarely.Comment: 6 pages, 5 figures, In Press with ApJ Letter