Thermodynamics of rare events

Scaling laws of physics are derived from extreme value distributions. Small jump processes that comprise a compound Poisson distribution generate the asymptotic distributions of stable laws. These extreme value distributions, or their tails, can be expressed in terms of the entropy decrease. As an example, the scaling law for the radius of gyration of a polymer is derived which is comparable to Flory's formula. The entropy is identified by its property of concavity, which is shown to coincide with Boltzmann's probabilistic definition for first passage in a random walk. A more general definition is required for nonintegral dimensions. The relation to mean-field theory of the kinetic Weiss-Ising model is shown and this distribution of the order parameter is governed by an asymptotic distribution for the smallest value rather than a normal distribution. Finally, the logarithm of the sample size is shown to be the yardstick for the decrease in entropy.     

Theory and methods for rare events

This paper reviews the transition path theory (TPT) for activated events and summarizes a set of methods and algorithms to compute all relevant quantities of this theory: free energy, rate and mechanism of the event. We provide a set of examples to illustrate the applicability of the methods to problems in chemistry, biophysics and material science.     

Projective measurements via linear optics and photon detectors

The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state. The statement holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states. The text was submitted by the author in English.     

Optimizing searches via rare events

Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate in determining the final distribution of running times. As a by-product of our analysis we show how search algorithms are optimized by random restarts.     

Is there a photon excess or photon deficit in the cosmic events?

Summary Bjorken predicted in the recent past about the large excess emission of photons in high-energy collisions and this was subsequently corroborated by some experimentalists as well. Obviously, this phenomenon is just opposite in nature to pro-centauro events marked by the production of photonless hadrons. In this note we will try to trace the outlines of this confusing and contradictory situation, probe quantitatively into this excess emission of photons (called progammaisation events) and compare them mainly with Bjorken's disoriented-chiral-condensate (DCC) model.     

地球自转和倾角的实时测量

地球的自转旋转速度和自转轴取向,始终经历着行星内部、海洋和大气变化所带来的持续不断的涨落。德国研究人员最近报道了对这些微小涨落的第一次连续测量。这一实验设施的主体由埋在地下14 m深处的4个激光陀螺组合而成。新设施提供的数据对于保持GPS导航系统之即时精度非常重要。     

Non-commutative geometry and measurements of polarized two photon coincidence counts

Employing Maxwell’s equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy, and position are derived. The photon “Zitterbewegung” along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.     

Real-time observation of discrete Andreev tunneling events

We provide a direct proof of two-electron Andreev transitions in a superconductor-normal-metal tunnel junction by detecting them in a real-time electron counting experiment. Our results are consistent with ballistic Andreev transport with an order of magnitude higher rate than expected for a uniform barrier, suggesting that only part of the interface is effectively contributing to the transport. These findings are quantitatively supported by our direct current measurements in single-electron transistors with similar tunnel barriers.     

Effect of rare events on out-of-equilibrium relaxation

This Letter reports experimental and numerical results on particle dynamics in an out-of-equilibrium granular medium. We observed two distinct types of grain motion: the well known cage motion, during which a grain is always surrounded by the same neighbors, and low probability "jumps," during which a grain moves significantly more relative to the others. These observations are similar to the results obtained for other out-of-equilibrium systems (glasses, colloidal systems, etc.). Although such jumps are extremely rare, by inhibiting them in numerical simulations we demonstrate that they play a significant role in the relaxation of out-of-equilibrium systems.     

Analysis of rare events in heavy-ion experiments

Experiments in both high-and low-energy physics are planned so that physically interesting effects mathematically are rare (or small probability) events, compared to others, whose probabilities are not small. Correspondingly, the purpose of the paper was the development of the formalism for the treatment of rare events, which could be an inevitable alternative to methods requiring too much a priori information about the studied effect, in a situation when such information is absent, but, instead, background information is available, e.g., from calibration measurements. The main topics of the paper were as follows: (1) To what extent are the methods of Poisson time-event streams suitable for the goal declared? (2) What information can be extracted from the calibration measurement that detected zero interesting events? The method described is illustrated by the analysis of data registered in the experiment on the synthesis of element 114.     

Sampling rare switching events in biochemical networks

Bistable biochemical switches are widely found in gene regulatory networks and signal transduction pathways. Their switching dynamics are difficult to study, however, because switching events are rare, and the systems are out of equilibrium. We present a simulation method for predicting the rate and mechanism of the flipping of these switches. We apply it to a genetic switch and find that it is highly efficient. The path ensembles for the forward and reverse processes do not coincide. The method is widely applicable to rare events and nonequilibrium processes.     

Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance

One challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time. We present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, phenomena that lie outside of patterns of statistical regularity. We review evidence consistent with the possibility that such outliers may not exist. This possibility is supported by recent analysis of databases containing information about each trade of every stock.     

A cryogenic underground observatory for rare events: CUORE, an update

CUORE is a proposed tightly packed array of 1000 TeO₂ bolometers, each being a cube 5 cm on a side with a mass of 750 g. The array consists of 25 vertical towers, arranged in a square of 5 towers by 5 towers, each containing ten layers of four crystals. The design of the detector is optimized for ultralow-background searches for neutrinoless double beta decay of ¹³⁰Te (33.8% abundance), cold dark matter, solar axions, and rare nuclear decays. A preliminary experiment involving 20 crystals of various sizes (MIBETA) has been completed, and a single CUORE tower is being constructed as a smaller scale experiment called CUORICINO. The expected performance and sensitivity, based on Monte Carlo simulations and extrapolations of present results, are reported.     

Importance sampling of rare events in chaotic systems

The European Physical Journal B - A way to make financial models effective is by letting them to represent the so called “fat tails”, i.e., extreme changes in stock prices that are...     

Experimental evidence and consequences of rare events in quantum tunneling

Tiny spatial fluctuations of tunnel barrier parameters are shown to have dramatic consequences on the statistical properties of quantum tunneling. A direct experimental evidence is provided that the tunnel current through metal-oxide junctions, imaged at a nanometric scale, exhibits broad statistical distributions extending over more than 4 orders of magnitude. Striking effects of broad current distributions are shown: the total tunnel transmission is dominated by few highly transmitting sites and the typical current density varies strongly with the size of the junction. Moreover, self-averaging of the tunnel current fluctuations occurs only for unexpectedly large junction areas. Received 1 April 1999     

Search for new phenomena using single photon events at LEP1

Data are presented on the reaction e⁺e^? → γ + no other detected particle at centre-of-mass energies of 89.48, 91.26 and 93.08 GeV. The cross-section for this reaction is related directly to the number of light neutrino generations which couple to the Z° boson, and to several other possible phenomena such as the production of excited neutrinos, the production of any invisible ‘X’ particle, and the magnetic moment of the tau neutrino. Based on the observed number of single photon events, the number of light neutrinos that couple to the Z° is measured to be N_v = 2.89 ± 0.38. No evidence is found for anomalous production of energetic single photons, and upper limits at 95% confidence level are determined for excited neutrino production (BR < 4 ? 8 × 10^?6 depending on its mass), production of an invisible ‘X’ particle (σ, < 0.1 pb for masses below 60 GeV), and the magnetic moment of the tau neutrino (< 5.1 × 10^-6 μB).     

Harmonic measure for percolation and ising clusters including rare events

We obtain the harmonic measure of the hulls of critical percolation clusters and Ising-model Fortuin-Kastelyn clusters using a biased random-walk sampling technique which allows us to measure probabilities as small as 10{-300}. We find the multifractal D(q) spectrum including regions of small and negative q. Our results for external hulls agree with Duplantier's theoretical predictions for D(q) and his exponent -23/24 for the harmonic measure probability distribution for percolation. For the complete hull, we find the probability decays with an exponent of -1 for both systems.