We would want to find a description for ultracold atoms (bosons, possibly extendable to fermions) that are injected and transported along a lattice. Starting from the Bose-Hubbard model coupled to one lead (or eventually more than one), equations of motion should be derived for correlation functions of mode creation and annihilation operators. With appropriate approximations these equation may be brought into a closed form. While this first part is purely analytic, the obtained equations of motions can be solved only in special cases (e.g. without atom-atom interactions) and numerical integration methods must be applied in general. A first step is the understanding of a method already introduced and applied to open quantum systems. This BBGKY hierarchy expansion consists of dynamical equations for two, four, etc. point correlations functions, i.e. the expectation values of the two-, four-, etc. body reduced density matrices. The interaction term in the Hubbard-Hamiltonian then induces the coupling between these dynamical equations to higher orders. Typically, we truncate at the second order, approximating the six-point correlator by products of two- and four-point correlation functions. This allows us to arrive at a closed system of coupled equations, which we can subsequently solve. The complication arises from the additional expectation values containing the reservoir operators (the boundary terms), which have to be taken into account in addition. A second step may be the extension of the BBGKY hierarchy expansion from time-equal expectation values to different-time ones for the one-, two-, etc. particle reduced density matrix elements. With appropriate approximations (e.g. the truncation of the hierarchy equations for higher-order expectation values) this should again lead to a closed but much larger system of equations for C-numbers, which can be solved numerically in principle.

Many quantum systems burn down to idealized few level systems in some approximation. We propose to study the possibilities of fully controlling the coupling of quantum states and qubits. This includes the extension of quantum control protocols from two to three (or more) level systems and to coherent sequences of Landau-Zener (LZ) transitions. Having at hand such protocols would allow, for instance, perfect adiabaticity, optimal robustness and speed-up of LZ transitions. Direct experimental applications are in sight for quantum simulation and quantum chaos control in a wide range of systems, from molecular magnets to ultracold atoms.

The Bethe Lattice spin glass is a system with finite connectivity whose low temperature phase is believed to be described by full Replica Symmetry Breaking (RSB). The computation of the order parameter is a valid tool of investigation into the properties of the RSB phase. Although an analytical approach is only possible in a limited class of mean field systems, a numerical computation is still possible. We rely on a general formula which holds for systems in the RSB phase, which exploits the information coming from the probability distribution of the lowest lying states. The latter is computed numerically by applying a convenient perturbation to the hamiltonian and considering the distribution of the overlap between the original and the perturbed ground state.

Natural photosynthetic systems interact with different environments, which are a source of disorder but can also induce cooperative coherent effects, such as superabsorption of light and supertransfer of excitation. Both cooperativity and disorder are essential to achieve efficient energy transport in natural complexes and in bio-inspired quantum devices. Application of cooperative effects to design a bio-inspired light-harvesting system is studied in a model consisting of a ring of donors surrounding a central core absorber. The working principle of this device is based on three steps: i) super-absorption of light from high energy states, ii) thermal relaxation which drives the excitation to low energy states, iii) supertransfer of the excitation from low energy states to the central core absorber. While in many relevant natural complexes absorbing and transferring states are the same, such device is based on the decoupling of absorption and transfer. The proposed device is able to outperform natural complexes in the same range of parameters and its efficiency increases with the system size.

We considered the DNA as a symbolic sequence constituted by four letters A, C, G, T, corresponding to the four nitrogenous bases, and we analyzed the inderdistances probability distributions of all the possibile couples of letters inside the sequence. We first studied a set of 18 different organisms, finding that CG distribution greatly differs from all the others, especially among mammals. Therefore we decided to charaterize it, by fitting the data to four model functions: exponential distribution, which is typical of stochastic processes with a characteristic scale; double exponential distribution, which involves two characteristic scales; stretched exponential distribution, which is related to relaxation phenomena in complex condensed-matter systems, and gamma distribution, which is typical of critical phenomena in the presence of a finite size effect and stochastic processes with multiplicative noise. According to residuals analysis and a goodness-of-fit test based on resampling technique and Kuiper's statistic, we found that CG interdistances distribution was well described by a gamma distribution. In order to understand which process could give rise to such a difference between CG and non-CGs distributions, in mammals, we elaborated a null model which showed that, given a non-CG distribution, it is always possible to obtain a new distribution, similar to that of CG, by randomly changing a specfic number of non-CG dinucleotides into another. Finally, we decided to extend this analysis by fitting CG distributions of 4425 different organisms, belonging to 7 different categories, to a gamma distribution. We found that, plotting scale parameter as a function of shape parameter, it is possible to distinguish 7 different clusters, which correspond to the 7 considered categories. Therefore we believe that this method can provide new tools for organisms characterization and classification, such as taxonomy.

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasi-synchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics. [1] F. Pittorino, M. Ibanez-Berganza, M. di Volo, A. Vezzani and R. Burioni, Phys. Rev. Lett. 118 (2017), 098102-6

By means of active and frozen N-Body simulations we revise the role of discreteness effects and external noise in the dynamics of self gravitating systems and non-neutral plasmas. In particular, we show that the use of frozen N-body realization may, in certain cases, lead to misleading conclusions.

Effective interactions between particles immersed in a fluid have been the subject of extensive investigations in different regimes: from th Asakura-Oosawa short range attraction present in the ideal gas limit, to the oscillatory behavior induced by repulsive forces. These depletion interactions represent a particular limit of the more general concept of solvent mediated forces, which are known to drive several important phenomena in soft matter, leading either to clustering, colloidal aggregation or dynamical arrest. Solvent mediated forces undergo a significant change when long range correlations are present in the host fluid due to the proximity of a second order phase transition. The universal properties of critical phenomena reflect in the structure of the effective interactions which acquire a scaling form. [1] The transition between the depletion and the critical Casimir regimes is a particularly challenging problem from the theoretical point of view because it requires the accurate description of inhomogeneous critical fluids at a microscopic level. To achieve this goal, we developed a novel density functional technique based on the weighted density concept [2]. Coupling this approach with the hierarchical reference theory of fluids (HRT) [3], which provides a microscopic description of fluids accurate also in the critical region, we performed a detailed investigation of the effective interactions between two hard walls immersed in a Yukawa fluid by varying the thermodynamic state. The evolution of the effective potential as a function of temperature and density is discussed, emphasizing the smooth transition between the high temperature, entropy-dominated, limit and the critical regime. Furthermore this approach allows a direct investigation of the universal properties both in the critical and in the pre-critical regime and these results are compared with predictions obtained by numerical simulations [4]. References: [1] M. E. Fisher and P. G. De Gennes, Comptes rendus de l’Academie des sciences, Serie B 287, 207 (1978). [2] P. Anzini and A. Parola, Physical Review E 94, 052113 (2016). [3] A. Parola and L. Reatto, Advances in Physics 44, 211 (1995). [4] N. Gnan, E. Zaccarelli, P. Tartaglia, and F. Sciortino, Soft Matter 8, 1991 (2012).

Chromosomes have a complex architecture in the cell nucleus, which serves vital functional purposes, yet its structure and folding mechanisms remain still incompletely understood. We show that genome-wide chromatin architecture data, as mapped by Hi-C methods across mammalian cell types and chromosomes, are well described by classical scaling concepts of polymer physics, from the sub-Mb to chromosomal scales. Chromatin is a complex mixture of different regions, folded in the conformational classes predicted by polymer thermodynamics. The 3D structure of various loci, important to the genome functionality, are derived with high accuracy; for instance, the Sox9 locus self-assembles hierarchically in higher-order domains, involving abundant many-body contacts. Finally, the model predictions on the effects of mutations on folding are tested against experimental data. References: Chiariello et al. SciRep, 2016 Barbieri et al. Nat Struct Mol Biol 2017 Beagrie et al. Nature 2017 Annunziatella et al. PRE 2016 Fraser et al. Mol.Sys.Biol. 2015