Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.Comment: 29 pages, 5 figure

Do Binary Hard Disks Exhibit an Ideal Glass Transition?

We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted ``amorphous'' glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al, Phys. Rev. Lett., 84, 2064 (2000)].Comment: Submitted for publicatio

Paleolinguistics brings more light on the earliest history of the traditional Eurasian pulse crops

Traditional pulse crops such as pea, lentil, field bean, bitter vetch, chickpea and common vetch originate from Middle East, Mediterranean and Central Asia^1^. They were a part of human diets in hunter-gatherers communities^2^ and are one of the most ancient cultivated crops^3,4^. Europe has always been rich in languages^5^, with individual families still preserving common vocabularies related to agriculture^6,7^. The evidence on the early pulse history witnessed by the attested roots in diverse Eurasian proto-languages remains insufficiently clarified and its potential for supporting archaeobotanical findings is still non-assessed. Here we show that the paleolinguistic research may contribute to archaeobotany in understanding the role traditional Eurasian pulse crops had in the everyday life of ancient Europeans. It was found that the Proto-Indo-European language^8,9^ had the largest number of roots directly related to pulses, such as *arnk(')- (a leguminous plant), *bhabh- (field bean), *erəgw[h]- (a kernel of leguminous plant; pea), *ghArs- (a leguminous plant), *kek-, *k'ik'- (pea) and *lent- (lentil)^10,11,12^, numerous words subsequently related to pulses^13,14^ and borrowings from one branch to another^15^, confirming their essential place in the nutrition of Proto-Indo-Europeans^16,17,18^. It was also determined that pea was the most important among Proto-Uralic people^19,20,21^, while pea and lentil were the most significant in the agriculture of Proto-Altaic people^22,23,24^. Pea and bean were most common among Caucasians^25,26^, Basques^27,28^ and their hypothetical common forefathers^29^ and bean and lentil among the Afro-Asiatic ancestors of modern Maltese^30^. Our results demonstrate that pulses were common among the ancestors of present European nations and that paleolinguistics and its lexicological and etymological analysis may be useful in better understanding the earliest days of traditional Eurasian crops. We believe our results could be a basis for advanced multidisciplinary approach to the pulse crop domestication, involving plant scientists, archaeobotanists and linguists, and for reconstructing even earlier periods of pulse history

Fermat's principle of least time in the presence of uniformly moving boundaries and media

The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: a) the material half-space is moving parallel to the interface; b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtained refraction formula is provided, and in the latter case, an intriguing backward refraction of light is noticed and thoroughly discussed. The results confirm the validity of Fermat's principle when the optical media and the boundaries between them are moving at relativistic speeds.Comment: 11 pages, 6 figures, RevTeX 4, comments welcome; V2: revised, Fig. 7 added; V3: several typos corrected, accepted for publication in European Journal of Physics (online at: http://stacks.iop.org/EJP/28/933

A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking

Existing walking models used for vibration serviceability assessment of structures carrying pedestrians are typically based on measurements of single footfalls replicated at precise intervals. This assumed perfect periodicity allows walking forces to be modelled as a Fourier series based on the walking pace and its integer multiples. This paper examines real continuous walking forces obtained from an instrumented treadmill and the effect of their random imperfections through time simulations of structural response and shows that there are significant differences between responses due to the imperfect real walking forces and the equivalent perfectly periodic simulation. These differences are most significant for higher harmonics where the simulated vibration response is overestimated. As a realistic representation of imperfect walking is an auto-spectral density function, the random character naturally leads to a stochastic approach to treatment of pedestrian loading applied in the frequency domain. The approach can be used for single pedestrians as well as crowd loading where correlation between pedestrians as well as statistics of their pacing rates is used

Disclosure of the quackery: Testing of the bactericidal action of products based on the 'Hydronic' technology ("informed glass") on ATCC strains of Enterococcus faecalis, Salmonella enteridis and Candida

To disclose a quackery called “revitalisation of tired water by hydronic technology”, scientific experiments have been conducted with drinking water kept in ‘‘ordinary, everyday-use’’ drinking glasses and so-called ‘informed’ glasses, a patent-protected product supposed to have an effect on the ‘‘structure, vitality and memory of water‘‘. Drinking “informed” water is claimed to have a wide range of positive revitalising health effects (blue informed glass), to facilitate weight loss (red informed glass) and to have a stress-relieving action (green informed glass). Allegedly, by the use of the “orgon methodology”, information is coded into the glass, which action is additionally enforced by the addition of the ‘‘magic life’’ symbol – a specially designed energy condenser which, together with the selected information, is permanently introduced into the liquid contained in the glass. Since the manufacturer claimed the products to have a broad bactericidal action, regardless of the external conditions and completely independent from additional factor that would lead to the activation of the system, the efficacy of the informed drinking glass was tested using standardised, microbiological tests. Respecting the principle of a single-blind test for each of 5 samples of each type of the informed glass, growth reduction factor (RF) (difference log cfu/ml - colony per unit/ml of control glass and log cfu/ml of each informed glass) was determined after0,2,4,6 and 8 h in spring water experimentally contaminated with standardised ATCC strains of two types of bacteria and one yeast. The results showed a statistically significant bactericidal action of the blue informed glass with all strains - Enterococcus faecalis (RF 0.62/0.76), Salmonella enteritidis (RF 0.87/0.97), and Candida albicans (RF 0.5/0.60) - as opposed to the red and green glasses where this effect was negligible (RF < 0.1). However, when the tests were repeated in complete darkness, none of the three informed glasses showed any bactericidal action. The obtained results indicate a fraud: bactericidal effect is rather a result of photocatalytic action of a hidden component used on purpose in the production of glass or subsequently applied by the use of nanotechnology (possibly antimony trioxide or titanium oxide) than of the so-called‘‘orgon and hydronic technology’’.Key words: Nostrums, Water, Quackery, Complementary therapies, Health care fraud, Homeopathy, Self -caredoi: 10.4314/ajtcam.v8i4.

MVG Mechanism: Differential Privacy under Matrix-Valued Query

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.Comment: Appeared in CCS'1