Startling magnetic effects have been reported, in the last decade or so, when structural glasses (multi-silicates, but also amorphous glycerol) are studied at low and ultra-low (mK) temperatures. The heat capacity and dielectric constant of glasses, dominated by tunneling systems at these temperatures, ought to display universal features and to be oblivious to the magnetic field. Instead, small non-monotonic deviations have been observed in the dielectric constant (real part and loss) when the glasses are immersed in weak magnetic fields (10 mT up to 1 T). Moreover significant deviations have been reported for the heat capacity and also for the amplitude of the dipole or polarization echo. We have developed a theory able to explain quantitatively the magnetic effects in the heat capacity, and present our best results for the dielectric constant and loss in a magnetic field. Also, we have solved the problem of the astonishing magnetic effects reported on the echo amplitude, and using the very same model. We present our explanation, for ALL of the magnetic effects, in terms of special tunneling systems coupled orbitally to the magnetic field and residing in ``crystal embrios'' (nano-crystals or smaller) within the otherwise homogeneously disordered solid. This theory shows that the glass transition is more likely to be associated to the formation of crystal droplets around Tg than to frustration as is the case in the spin-glasses. The ``magnetic'' tunneling systems become therefore a viable probe to study these crystal embryos when other spectroscopies would fail.

We present accurate results based on Quantum Monte Carlo simulations of two-component bosonic systems on a square lattice and in the presence of an external harmonic confinement. Starting from hopping parameters and interaction strenght which stabilize the Ising antiferromagnetic phase in the homogeneous case and at half filing factor, we study how the presence of the harmonic confinement challenge the ralization of such phase. We consider realistic trapping frequencies and number of particle, and establish under which conditions, i.e. total number of particles and unbalance between the two component, the antiferromagnetic phase can be observed in the trap.

Recent developments in cooling and controlling ultracold gases of magnetic atoms and polar molecules open a new perspective on many-body physics of ultracold gases, which was previously strongly related to contact interactions. We will present a theoretical analysis of bosonic and fermionic gases confined in 1D and quasi-1D geometries, combining analytical approaches based on the Tomonaga-Luttinger liquid formalism with numerical DMRG calculations. Several phenomena are investigated, from the formation of a staircase of insulating phases to the emergence of exotic pairing instabilities which are stable even in standard experimental setups.

The repulsive one-dimensional Hubbard model with bond-charge interaction (HBC) in the superconducting regime is mapped onto the spin-1/2 XY model with transverse field, after assuming short-ranged antiferromagnetic correlations between electrons. We calculate density correlations and phase boundaries, realizing an excellent agreement with numerical results. The critical line for the superconducting transition is shown to coincide with the analytical factorization line identifying the commensurate-incommensurate transition in the XY model.

It is already known that by suitably designing the coupling coefficient of a nearest neighbour hopping Hamiltonian it is possible to achieve perfect quantum state transfer in a spin chain, in the absence of errors. I will present here an encoding-decoding strategy which allows a perfect recovery of the state transfer in the presence of broad class of systematic errors.

We discuss the properties of ultracold gases with two hyperfine levels in non-abelian potentials, showing that it is possible to have ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the non-abelian part of the vector potential makes the Landau levels non-degenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-abelian quantum Hall states appear: these ground states, including deformed Moore-Read states (characterized by Ising anyons as quasi-holes), are studied for both fermionic and bosonic gases.

We consider correlated Lévy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter α, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a single-long jump approximation, we analytically determine the long-time asymptotic behaviour of the moments of the probability distribution, as a function of α and of the dynamic exponent z associated to the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated Lévy-walk models.

arxiv:1104.1817

We have considered a variation of the graph-coloring problem. The optimisation goal is to color the vertices of a graph with a fixed number of colours, in a way to maximise the number of different colors present in the set of nearest neighbors of each given vertex. This problem, which we have pictorially called "palette-coloring", has been recently addressed as a basic example of combinatorial optimization problem arising in the context of distributed data storage. Even though it has not been proved to be NP-complete, random search algorithms find the problem hard to solve, whereas heuristics based on belief propagation turn out to exhibit noticeable performances.

In a celebrated paper, Julian Schnakenberg proposed a general theory of fluxes of information and conservation laws on a network, identifying the macroscopic external observables which keep a system out of equilibrium. In this talk we show that his observables are indeed the correct constraints to be imposed to Prigogine's minimum entropy production principle. Speculation about the possible quantum version of Schnakenberg's theory leads to the identification of SU(2) spin networks as an useful mathematical instrument -the very same spin networks that have been used by Rasetti in a quantum information perspective to engineer a model of a quantum Turing machine.

Irreversible propagation processes are responsible of important phenomena observed in real-world networks, from the spread of influence and viral marketing to financial contagion, liquidity-shock propagation and cascading failures. Motivated by recent literature in computer science, I will consider these dynamical processes from the inverse point of view of optimization over the initial conditions. A prototypical example is the algorithmic problem of finding the smallest set of initial seeds that maximizes the final outcome of a threshold dynamics. For this problem, efficient algorithms can be derived using a cavity approach. I will discuss some numerical results, possible applications and limitations of the method.