We consider heat transport in one-dimensional harmonic chains with isotopic disorder, focusing our attention on how disorder correlations affect heat conduction. Our approach reveals that long-range correlations can change the number of low-frequency extended states. As a result, with a proper choice of correlations one can control how the conductivity scales with the chain length \(N\). We present a detailed analysis of the role of specific long-range correlations for which a size-independent conductivity is exactly recovered in the case of fixed boundary conditions. As for free boundary conditions, we show that disorder correlations can lead to a conductivity slowly dependent on \(N\), so that normal conduction is almost recovered even in this case.

Quantum transport of excitations or particles across network like structures provides a general framework for a broad class of problems in complex quantum dynamics - from photonic circuitry to photosynthetic light harvesting. Furthermore, advanced experimental control of network structure and particle number allows to think anew about fundamental and non-trivial issues in many particle quantum dynamics. For example, what distinguishes quantum statistical from bona fide many particle interference effects? How can we unambiguously characterize the many particle wave function in a many particle quantum walk, in a statistically robust and computationally tractable manner? How do symmetries and disorder affect characteristic transport properties? The talk will present selected examples of recently debated, complex quantum transport phenomena on network-like structures, and elaborate on the basic principles which determine the rather rich phenomenology.

The understanding of the underlying dynamical mechanisms which determines the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of such mechanism may also lead to potentially interesting applications based on the possibility to control the heat flow. Indeed, a model of thermal rectifier has been recently proposed in which heat can flow preferentially in one direction. In particular we discuss here the possibility to increase the rectifying factor by orders of magnitude.
We then discuss a new approach, which is rooted in nonlinear dynamical systems, for increasing the efficiency of thermoelectric machines. The main focus will be on the physical mechanisms, unveiled by these dynamical models, which lead to high thermoelectric efficiency, approaching the Carnot limit. The role of conservation laws and symmetry breaking will be emphasized.

There has been a lot of interest in recent years in disordered photonic media in which the spatial arrangement of scattering elements goes beyond a simple Gaussian distribution. Examples include photonic quasi-crystals, hyper-uniform structures, and structures in which the distribution is inhomogeneous [1]. We will discuss recent developments in the field and in particular go into the case of self-similar random systems and Lévy flights. We will discuss optical super-diffusion and show how dynamic optical measurements can be used to determine the fractal dimension of an optical random walk [2].

References

[1] D.S. Wiersma, Disordered Photonics, Nature Photon. 7, 188 (2013).
[2] R. Savo, M. Burresi, T. Svensson, K. Vynck, and D.S. Wiersma, Measuring the fractal dimension of an optical random walk, arXiv:1312.5962v1 [physics.optics] 20 Dec 2013.

In collaboration with R. Savo, M. Burresi, T. Svensson and K. Vynck

It ia proved through a KAM procedure the pure point nature of the Floquet spectrum of the weakly forced quantum harmonic oscillator under no-resonance conditions, Explciti estimates are worked out on the amplitude of the forcing term and on the ratios between the diophantine constants of the frequencies.

Anderson localization is a universal phenomenon affecting quantum particles in a disordered environment. In three spatial dimensions, theory predicts a quantum phase transition from localization to diffusion at a critical energy, the mobility edge, which depends on the disorder strength. Although it has been recognized already long ago as a prominent feature of disordered systems, so far the mobility edge could not be measured in any physical system.
I will report on the measurement of the mobility edge for ultracold atoms in a disordered potential created by laser speckles. We are able to measure the mobility edge in a range of disorder strengths sufficiently large to explore both regimes where the spatial correlations of the disorder are relevant or not relevant. The precise control over the atomic system allows now a close experiment-theory comparison, and is a prerequisite to study the even more challenging problem of disorder and interactions.

Cold ions can be confined to chains. As the density is increased above a certain value a transition between the chain and zigzag phases takes place. It belongs to the Ising Universality class and was studied in the framework of Classical and Quantum Statistical Mechanics.

TBA

Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this talk, I will describe the model from a different point of view, emphasizing the equilibrium and nonequilibrium aspects of its dynamics from a statistical physics perspective. I will discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise.