We survey the application of a relatively new branch of statistical physics--community detection-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of part
itioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.
Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become sharp when extrapolated
to high temperature within a classical liquid phase. In the current work, we suggest basic quantum bounds on relaxation (and thermalization) times, examine kinetic theory by taking into account such possible fundamental quantum time scales, find new general equalities connecting semi-classical dynamics and thermodynamics to Plancks constant, and compute current correlation functions. Our analysis suggests that, on average, the extrapolated high temperature dynamical viscosity of general liquids may tend to a value set by the product of the particle number density ${sf n}$ and Plancks constant $h$. We compare this theoretical result with experimental measurements of an ensemble of 23 metallic fluids where this seems to indeed be the case. The extrapolated high temperature viscosity of each of these liquids $eta$ divided (for each respective fluid by its value of ${sf n} h$) veers towards a Gaussian with an ensemble average value that is close to unity up to an error of size $0.6 %$. Inspired by the Eigenstate Thermalization Hypothesis, we suggest a relation between the lowest equilibration temperature to the melting or liquidus temperature and discuss a possible corollary concerning the absence of finite temperature ideal glass transitions. We suggest a general quantum mechanical derivation for the viscosity of glasses at general temperatures. We invoke similar ideas to discuss other transport properties and demonstrate how simple behaviors including resistivity saturation and linear $T$ resistivity may appear very naturally. Our approach suggests that minimal time lags may be present in fluid dynamics.
The range of the magnitude of the liquid viscosity as a function of the temperature (T) is one of the most impressive of any physical property, changing by approximately 17 orders of magnitude from its extrapolated value at infinite temperature to th
at at the glass transition. We present experimental measurements of containerlessly processed metallic liquids that reveal that the ratio of the viscosity to its extrapolated infinite temperature value follows a universal function of Tcoop/T. The temperature Tcoop corresponds to the onset of cooperative motion and is strongly correlated with the glass transition temperature. On average the extrapolated infinite temperature viscosity is found to be nh, where h is Plancks constant and n is the particle number density. A surprising universality in the viscosity of metallic liquids and its relation to the glass transition is demonstrated.
Decoherence effects at finite temperature (T) are examined for two manifestly quantum systems: (i) Casimir forces between parallel plates that conduct along different directions, and (ii) a topological Aharonov-Bohm (AB) type force between fluxons in
a superconductor. As we illustrate, standard path integral calculations suggest that thermal effects may remove the angular dependence of the Casimir force in case (i) with a decoherence time set by h/(k_{B} T) where h is Planks constant and k_{B} is the Boltzmann constant. This prediction may be tested. The effect in case (ii) is due a phase shift picked by unpaired electrons upon encircling an odd number of fluxons. In principle, this effect may lead to small modifications in Abrikosov lattices. While the AB forces exist at extremely low temperatures, we find that thermal decoherence may strongly suppress the topological force at experimentally pertinent finite temperatures. It is suggested that both cases (i) and (ii) (as well as other examples briefly sketched) are related to a quantum version of the fluctuation-dissipation theorem.
We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theo
ries and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of $Z_N$ models in the $Ntoinfty$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.
