Quantum statistics and locality

Richard Becker

Clinton Thompson, Gautam Vemuri, G. S. Agarwal

We report a theoretical study of Anderson localization of nonclassical light with emphasis on the quantum statistical aspects of localized light. We demonstrate, from the variance in mean intensity of localized light, as well as site-to-site correlations, that the localized light carries signatures of quantum statistics of input light. For comparison, we also present results for input light with coherent field statistics and thermal field statistics. Our results show that there is an enhancement in fluctuations of localized light due to the medium's disorder. We also find superbunching of the localized light, which may be useful for enhancing the interaction between radiation and matter. Another important consequence of sub-Poissonian statistics of the incoming light is to quench the total fluctuations at the output. Finally, we compare the effects of Gaussian and Rectangular distributions for the disorder, and show that Gaussian disorder accelerates the localization of light.

Joseph E. Mayer

CHRISTOF WETTERICH

We formulate incomplete classical statistics for situations where the knowledge about the probability distribution outside a local region is limited. The information needed to compute expectation values of local observables can be collected in a quantum mechanical state vector, whereas further statistical information about the probability distribution outside the local region becomes irrelevant. The translation of the available information between neighboring local regions is expressed by a Hamilton operator. A quantum mechanical operator can be associated to each local observable, such that expectation values of ``classical'' observables can be computed by the usual quantum mechanical rules. The requirement that correlation functions should respect equivalence relations for local obeservables induces a non-commutative product in classical statistics, in complete correspondence to the quantum mechanical operator product. We also discuss the issue of interference and the complex structure of quantum mechanics within our classical statistical setting.

Bruno Bertini, Pavel Kos, Tomaž Prosen

Since the seminal work of Anderson, localization has been recognized as a standard mechanism allowing quantum many-body systems to escape ergodicity. This idea has acquired even more prominence in the last decade as it has been argued that localization---dubbed many-body localization (MBL) in this context---can sometimes survive local interactions in the presence of sufficiently strong disorder. A conventional signature of localization is in the statistical properties of the spectrum---spectral statistics---which differ qualitatively from those in the ergodic phase. Although features of the spectral statistics are routinely used as numerical diagnostics for localization, their derivation from first principles in the presence of nontrivial interactions has been lacking. Here we provide the example of a simple class of quantum many-body systems---which we dub strongly localized quantum circuits---that are interacting and localized and where the spectral statistics can be characterized exactly. Furthermore, we show that these systems exhibit a cascade of three different regimes for spectral correlations depending on the energy scale: at small, intermediate, and large scales they behave as disconnected patches of three decreasing sizes. We argue that these features appear in generic MBL systems, with the difference that only at the smallest scale do they become Poissonian.

John D. McGervey