9:009:30  iscrizioni 
9:309:50  Andreas Komnik — Universität Heidelberg
Quantum transport in contacted molecules
Electrically contacted molecules are considered to be the ultimate current switches. Their typical dimensions of about 1
nm would allow to design the smallest possible transistor units. However, contrary to solid state circuitry their
conductance properties can be decisively influenced by the harmonic degrees of freedom (local phonons).
Surprisingly, there are parameter regimes, in which the presence of such seemingly disturbing effects might in fact
become an advantage making such a device intrinsically bistable. We discuss these possibilities using analytical as well
as numerical techniques and make predictions for the transport properties of contacted molecules in the relevant regimes
and make contact to such fundamental multiparticle phenomena as Kondo effect.
References: J. Klatt, L. Mühlbacher, and A. Komnik, submitted to PRB (2015) K.F. Albrecht, H. Wang, L. Mühlbacher, M. Thoss, and A. Komnik Phys. Rev. B 86, 081412(R) (2012) S. Maier, T. L. Schmidt, and A. Komnik, Phys. Rev. B 83, 085401 (2011) 
9:5010:10  Boris Fine — Skolkovo Institute of Science and Technology
Reversing Chaos
One of the ways to manipulate artificially created quantum systems is to reverse their dynamics. Our
ability to do this is limited by the phenomenon of chaos. In classical systems, chaos implies exponential
sensitivity to small perturbations. It is to be shown in this presentation that nonintegrable lattices of
spins 1/2, which are often considered to be chaotic, are not exponentially sensitive to small
perturbations [1]. This result is obtained by comparing the responses of chaotic lattices of classical
spins and nonintegrable lattices of spins 1/2 to imperfect reversal of spin dynamics known as Loschmidt
echo. In the classical case, Loschmidt echoes exhibit exponential sensitivity to small perturbations
characterized by twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2,
Loschmidt echoes are only powerlaw sensitive to small perturbations. Our findings imply that it is
impossible to define Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At the
same time, the above absence of exponential sensitivity to small perturbations is an encouraging news for
the efforts to create quantum simulators. The powerlaw sensitivity of spin 1/2 lattices to small
perturbations is predicted to measurable in nuclear magnetic resonance experiments.
[1] B. V. Fine, T. A. Elsayed, C. M. Kropf and A. S. de Wijn, Phys. Rev. E 89, 012923 (2014). 
10:1010:30  Andrea Tomadin — NESTCNR & SNS Pisa
Transport and optical properties of an electron gas in a Sierpinski carpet
Recent progress in the design and fabrication of artificial twodimensional (2D) materials paves the way for the
experimental realization of electron systems moving on plane fractals. In this work, we present the results of
computer simulations for the conductance and optical absorption spectrum of a 2D electron gas roaming on a
Sierpinski carpet, i.e. a plane fractal with Hausdorff dimension intermediate between one and two. We find that the
conductance is sensitive to the spatial location of the leads and that it displays fractal fluctuations whose
dimension is compatible with the Hausdorff dimension of the sample. Very interestingly, electrons in this fractal
display a broadband optical absorption spectrum, which possesses sharp "molecular" peaks at low photon energies.

10:3010:50  Maurizio Rossi — Università di Padova
The challenge of the unitary Bose gas
We investigate the zerotemperature properties of a diluted homogeneous Bose gas made of \(N\)
particles interacting via a twobody squarewell potential by performing Monte Carlo simulations.
We tune the interaction strength to achieve arbitrary positive values of the scattering length and
compute by Monte Carlo quadrature the energy per particle $E/N$ and the condensate fraction \(N_0/N\)
of this system by using a Jastrow ansatz for the manybody wave function which avoids the formation
of the selfbound groundstate and describes instead a (metastable) gaseous state with uniform
density. In the unitarity limit, where the scattering length diverges while the range of the interatomic potential is much smaller than the average distance between atoms, we find a finite energy per particle (\(E/N=0.70\ \hbar^2(6\pi^2n)^{2/3}/2m\), with \(n\) the number density) and a quite large condensate fraction (\(N_0/N=0.83\)) [1]. Starting from the obtained equation of state we study also the frequencies of the monopole and quadrupole oscillations of the gas trapped in a isotropic harmonic potential within Density Functional Theory in the Local Density approximation. We include also the damping effect of threebody losses on such modes [2]. Prompted by the very recent experimental data of \(^{85}\)Rb atoms at unitarity [3] we focus on the momentum distribution as a function of time. Our results suggest that at unitarity, a quasistationary momentum distribution is reached at low momenta after a long transient, contrary to what found experimentally for large momenta which equilibrate on a time scale shorter than the one for three body losses [4]. References 1. M. Rossi, L. Salasnich, F. Ancilotto and F. Toigo, Phys. Rev. A 89, 041602(R) (2014) 2. M. Rossi, F. Ancilotto, L. Salasnich and F. Toigo, arXiv:1408.3945 (accepted in EPJ) 3. P. Makotyn, C.E. Klauss, D.L. Goldberger, E.A. Cornell and D.S. Jin, Nature Phys. 10, 116 (2014) 4. F. Ancilotto, M. Rossi, L. Salasnich and F. Toigo, arXiv:1501.05491 (accepted in FBSY) 
10:5011:20  pausa caffè  affissione poster 
11:2012:00  Luca Leuzzi — NANOTECCNR Roma
The glassy random laser: replica symmetry breaking in the intensity fluctuations of laser emission spectra
The behavior of a recently introduced overlap parameter is
analyzed, measuring the correlation between intensity
fluctuations of waves in random media in different physical regimes,
with varying amount of disorder and nonlinearity. Its relationship
is established to the standard Parisi overlap order parameter in the
replica theory for spinglasses. In the recently introduced complex spherical
spinglass model, describing the onset and behavior of random
lasers, replica symmetry breaking in the intensity fluctuation
overlap is shown to occur at high pumping or low temperature.
This order parameter identifies the laser transition in random media
and describes its glassy nature in terms of emission spectra data,
the only data so far accessible in random laser measurements.
The theoretical analysis is, eventually, compared to recent spectroscopy
measurements demonstrating the validity of the theory and providing a
straightforward interpretation of different spectral behaviors in
different kinds of random lasers.

12:0012:20  Andrea Gabrielli — Università di Roma "La Sapienza"
Finite\(N\) corrections to Vlasov dynamics and the range of pair interactions
We explore [1] the conditions on a pair interaction for the
validity of the Vlasov equation to describe the dynamics of an interacting \(N\) particle system in the large \(N\)
limit. Using a coarsegraining in phase space of the exact Klimontovich equation for such a system, we evaluate
the scalings with \(N\) of the terms describing the corrections to the Vlasov equation for the coarsegrained one
particle phase space density. Considering an interaction with radial pair force \(F(r)\sim1/ra\), regulated to a
bounded behavior below a "softening" scale \(l\), we find that there is an essential qualitative difference between
the cases \( a < d \) (i.e. the spatial dimension) and \(a > d\) , i.e., depending on the the integrability at large
distances of \(F(r)\). For \( a < d \) the corrections to the Vlasov dynamics for a given coarsegrained scale
are essentially insensitive to the softening parameter \(l\), while for \(a>d\) the corrections are directly
regulated by \(l\), i.e. by the small scale properties of the interaction, in agreement with the Chandrasekhar
approach [2]. This gives a simple physical criterion for a basic distinction between longrange (\( a < d \)) and short
range (\(a>d\)) interactions, different from the thermodynamic one (\( a < d1 \) or \( a > d1 \)).
This alternative classification, based purely on
dynamical arguments, is relevant notably to understanding the conditions for the existence of socalled
quasistationary states in longrange interacting systems. [1] A. Gabrielli et al., Phys. Rev. E, 90, 062910 (2014). [2] A. Gabrielli et al., Phys. Rev. Lett., 115, 210602 (2010). 
12:2012:40  Paolo Politi — ISCCNR Firenze
Dynamics of confined membranes
The dynamics of a onedimensional membrane confined between two walls is derived from an hydrodynamic model.
The main ingredients of the evolution equation are the adhesion potential with the confining walls and the bending
rigidity of the membrane. The resulting dynamics is frozen, with the membrane decomposing in adhesion patches on the two
walls. If the system is strongly perturbed, a transition from frozen dynamics to coarsening may be observed.
In collaboration with Thomas Le Goff and Olivier PierreLouis (CNRSLyon). 
12:4013:00  Ugo Marzolino — University of Ljubljana
Computational complexity of matrix product states and matrix product operators
I study matrix product states (MPS) and matrix product operators (MPO) from the point of view of
computational complexity. MPS are pure states whose coefficients in an orthonormal tensor basis are
transition amplitudes in an auxiliary, virtual Hilbert space, while MPO are operators with coefficients in
an orthonormal operator tensor basis being represented as trantion amplitudes in an auxiliary Hilbert
space. In particular, I show that measuring transition amplitudes of MPS or expectations of local
operators of density matrices described by a MPO allows to encode, in the auxiliary space, quantum
circuits with the additional power of general linear operators, and thus solve very hard computational
problems. I will exemplify the above result with cluster state (MPS) and steady states of boundary
dissipated quantum spin chains (MPO). This result deepens the knowledge of hardly implementable quantum
problems. As a byproduct of the above construction and after a very short introduction to complexity
classes, I prove an important result of computational complexity. The latter states that quantum Turing
machine with postselection and bounded error probability with subroutines, that exactly solve problems
probabilistically solvable by the same type of machine, can be simulated without the exact subroutines.
This result, together with the equivalence between quantum Turing machine with postselection and bounded
error probability and probabilistic Turing machines with unbounded error probability, implies the collapse
of a hierarchy of classical computational classes that was not yet proven.

13:0014:30  pausa pranzo 
14:3015:30  sessione poster 
15:3015:50  Angelo Carollo — Università di Palermo
Decoherenceinduced topological phase transition in 1D fermion model.
The 1D Kitaev chain is a prototypical example of a system which shows topological order, signalled by the
presence of an odd number of spatially separated Majorana zero modes. Depending on the Hamiltonian
parameters, such a system undergoes a transition from a topologically trivial to a nontrivial phase. We
show that a suitably engineered decoherence may indeed enact a similar transition to a topologically
nontrivial phase, starting from an otherwise trivial one. Such a phenomenon is the result of the
interplay between Hamiltonian and dissipative interactions. These findings are relevant to applications in
solid state physics as well as in the context of coldatoms.
In collaboration with Fabio Anzà, Davide Valenti, Bernardo Spagnolo 
15:5016:10  Antonio Scala — ISCCNR Roma
Self Healing Percolation
We present a model of percolation mimicking the
selfhealing dynamics of a smart grid. While in the case of random graphs it is possible to work out an
analytic solution, in the case of two dimensional networks we must resort to numerical simulations. Our
findings hint that for planar lattices duality plays a key role yet to be understood. Finally, by to tackling
the problem of being connected to a source node, we find the existence of two separate solutions that we study
by applying cavity methods and recursive equations.

16:1016:30  Marco Zamparo — Politecnico di Torino
A solvable example of nonstrictlyconvex large deviation principle in statistical mechanics
We develop a rigorous large deviation theory for random vectors within
an exactly solvable lattice gas model. The rate function is completely
characterized. The occurrence of discontinuous phase transitions leads
to a rate function which is affine on part of its domain.

16:3017:00  pausa caffè 
17:0017:20  Alessandro Codello — CP3Origins Odense (DK)
Approximating the Ising model on fractal lattices of dimension below two
We construct an approximation to the free energy of the Ising model on fractal lattices of
dimension smaller than two, in the case of zero external magnetic field. The result is obtained as the limit of
the exact free energies of the Ising model on periodic approximations. The free energies are computed using a
generalization of the combinatorial method of Feynman and Vodvickenko.
As a first application, we compute estimates to the critical temperature for many different Sierpinski carpets and we compare the results with known Monte Carlo estimates. The results show that our method is capable of determining the critical temperature with, possibly, arbitrary accuracy and paves the way to determine \(T_c\) for any fractal of dimension below two. The singularity of the free energy is logarithmic at the critical point, thus \(\alpha = 0\), for any periodic approximation. We also compute the correlation length as a function of the temperature and extract the relative critical exponent, we find \(\nu=1\) for all periodic approximation, as expected from Universality. 
17:2017:40  Nicolò Defenu — SISSA Trieste
Fixed Points Structure & Effective Fractional Dimension for \(O(N)\) Models with LongRange Interactions
We study \(O(N)\) models with powerlaw interactions by using functional renormalization group methods: we
show that both in Local Potential Approximation (LPA) and in LPA' their critical exponents can be computed
from the ones of the corresponding shortrange \(O(N)\) models at an effective fractional dimension. In LPA
such effective dimension is given by \(D_{\rm eff}=2d/\sigma\), where \(d\) is the spatial dimension and
\(d+\sigma\) is the exponent
of the powerlaw decay of the interactions. In LPA' the prediction by Sak [Phys. Rev. B 8, 1 (1973)] for
the critical exponent \(\eta\) is retrieved and an effective fractional dimension \(D'_{\rm eff}\) is obtained.
Using these results we determine the existence of multicritical universality classes of longrange \(O(N)\)
models and we present analytical predictions for the critical exponent \(\nu\) as a function of \(\sigma\) and
\(N\): explicit results in 2 and 3 dimensions are given. Finally, we propose an improved LPA" approximation to describe the full theory
space of the models where both shortrange and longrange interactions are present and competing: a
longrange fixed point is found to branch from the shortrange fixed point at the critical value \(\sigma_∗=2−\eta_{\rm SR} \)
(where \(\eta_{\rm SR}\) is the anomalous dimension of the shortrange model), and to subsequently control the critical
behavior of the system for \(\sigma <\sigma_∗\).

17:4018:00  Enrico Ubaldi — Università di Parma
Memory in Time Varying Networks
In many social and information systems, the network of the interactions is
generated by the agents activity. The temporal evolution of the
connectivity pattern and the dynamics taking place on the network might be
strictly coupled, as they evolve on the same time scales (information
diffusion, sexual transmitted diseases etc.). Besides, most of these
systems manifest memory effect on the agent dynamics. Given these
difficulties, the description of the processes behind the networks
evolution is a challenging task that we can now tackle using large, high
definition datasets. We present a generalized version of the model found in Karsai et al. [Sci. Rep. 4 2014]: here, the temporal evolution of the single agent’s egocentric network is encoded in a reinforcement process where the creation of new edges by an active agent is discouraged. We propose an analytical approach to the problem and provide an asymptotic solution for the evolving degree distribution and for the average degree of the network as a function of the memory parameters. The introduced model is tested against numerical simulations and several timeresolved datasets: a striking agreement between the model predictions and both the numerical and real data is found. 
18:0018:20  Giulio Cimini — ISCCNR Roma
Estimating topological properties of weighted networks from limited information
A problem typically encountered when studying complex systems is the limitedness of the information available
on their topology, which hinders our understanding of their structure and of the dynamical processes taking
place on them. A paramount example is provided by financial networks, whose data are privacyprotected: banks
publicly disclose only their aggregate exposure towards other banks, keeping individual exposures towards each
single bank secret. Yet, the estimation of systemic risk strongly depends on the detailed structure of the
interbank network. The resulting challenge is that of using aggregate information to statistically reconstruct
a network and correctly predict its higherorder properties. Standard approaches either generate
unrealistically dense networks, or fail to reproduce the observed topology by assigning homogeneous link
weights. Here we develop an improved reconstruction method based on statistical mechanics concepts, that makes
use of the empirical link density in a highly nontrivial way. Technically, the novelty of our approach lies in
the preliminary estimation of node degrees from empirical node strengths and link density, followed by a
maximumentropy inference based on the combination of empirical strengths and estimated degrees. Our method is
successfully tested on the international trade network and the interbank money market, and represents a
valuable tool for gaining insights on privacyprotected or partiallyaccessible systems.
