University of Washington
May 6 - 31, 2013
Fluctuations of macroscopic physical quantities in systems with large numbers of particles usually obey a normal distribution; however in many interesting cases, physical phenomena correspond to atypical and non-gaussian fluctuations. Non-gaussian statistics are ubiquitous in a wide variety of quantum systems, including conventional condensed matter, trapped atoms, quantum optics, as well as Monte Carlo simulations of many-body systems in nuclear and particle physics, and are the subject of active research, both theoretical and experimental. This program will provide the first opportunity to bring together researchers in these disparate fields to explore to what extent these nongaussian statistics observed in physical systems and their theoretical treatment share universal properties and common features. The exchange of expertise and scientific ideas between the communities of condensed matter, atomic, and nuclear physicists specializing in noise and nongaussian statistics is a central goal of this INT program.
a. Quantum and mesoscopic noise in condensed matter systems. Statistics of rare events have been extensively studied in disordered electron systems over the last two decades. Much progress has been achieved in understanding mesoscopic fluctuations in weakly disordered (metallic) systems in the absence electron-electron interactions. Examples include statistics of inverse participation ratios, anomalously localized states (and the ensuing anomalously long electron dwell times) in disordered metals. On the other hand, statistics of mesoscopic fluctuations near the Anderson metal-insulator transition, where the wave functions are believed to exhibit multifractal behavior remain an area of active research. Another set of outstanding issues is related to the role of electron-electron interactions and randomness in transport properties on mesoscopic scale. The questions range from fundamental to applied ones. The former group is exemplified by the effect of many-body localization on particle and energy transport and by the conductance fluctuations in mesoscopic spin glasses. In the case of spin glasses, atypical fluctuations are responsible for key features of glassy behavior, such as aging. Magnetic flux fluctuations limiting the coherence of superconducting qubits provide an example of the latter group of questions.
b. Quantum noise in optics and cold atoms. Similarly, understanding of photon fluctuations is at the heart of modern quantum optics, where measurement of full distribution functions of photons are relatively straightforward. Recently, much theoretical and experimental interest was focused on extending this analysis to cold atoms, with the aim of understanding many-body quantum correlations and their manifestations in shot-to-shot noise intrinsic to measurements performed on these systems. Since transport measurements with cold atoms are difficult, noise correlations and full distribution functions of fluctuations provide unique tools to characterize correlations, and non-gaussian fluctuations play a key role here. The increasing experimental control in cold atom systems and other quantum systems studied in condensed matter physics is envisioned to lead to rapid progress in this area.
c. Quantum noise in many-body simulations. There is growing evidence that there exist connections between noisy quantum systems in nature, and the noise and sign problems encountered in the Monte Carlo simulations commonly used in lattice QCD as well as many-body simulations of nuclear and atomic systems. A typical Monte Carlo computation requires measuring correlation functions for particles in a stochastic background field (for example, a quark in a gluon field, or a nucleon or atom in an auxiliary Hubbard-Stratonovich field). Averaging the correlation functions over the ensemble of background fields can provide a decent estimate of the true quantum expectation value for this operator, provided the values obtained are peaked around the mean. However, for certain observables -- often associated with fermion sign problems -- the distribution of values of the correlator over the ensemble of background fields is found to be very noisy, making a determination of the true average computionally expensive or impossible. These difficulties can sometimes be traced to heavy tailed, non-gaussian distributions, for which the most likely value is far from the mean value. Theoretical investigations of how these non-gaussian distributions arise in Monte Carlo computations bear a strong resemblance to the study of non-gaussian fluctuations in glassy and disordered condensed matter systems. There are hints that a better understanding of the statistical distributions in Monte Carlo simulations might provide the means to greatly improve many-body computations, and that theoretical tools used in the condensed matter literature could be very helpful to this theory community.