Program

Registration

Andrea Montanari
Sampling from the Sherringtong Kirkpatrick measure in the high-temperature phase

Ivan Amelio
Temporal coherence of out-of-equilibrium 1d quasi-condensates (Online)

Lasing in 1D arrays of resonators or polariton wires provides an example of an out-of-equilibrium quasi-condensate. We will discuss the spatio-temporal coherence properties of these systems by highlighting the interplay between Kardar-Parisi-Zhang (KPZ) universality and Bogoliubov-Schawlow-Townes phase diffusion [1]: the linewidth of a laser is a finite size effect. In particular, the lack of long-range order determines an important broadening of the linewidth of the emission spectrum, with exponents related to KPZ. Remarkably, the optimal coherence time is achieved for intermediate optical nonlinearity.

[1] I Amelio, I Carusotto, Physical Review X 10 (4), 041060

Coffee break

Giuseppe Mussardo
A Random Walk in Number Theory

The random walk is a crucial concept in statistical physics and plays an important role in shading new light and understanding of a famous conjecture in analytic number theory, i.e. the one posed by Bernhard Riemann in 1859 on the alignment of the zeros of a function deeply related to prime numbers.

Giuliano Giudici
Topological quantum matter and Rydberg atom arrays

Topological quantum matter represents the holy grail for quantum scientists as it stands out for its exotic properties and numerous applications in quantum computation. In this talk, I will review the most recent achievements and discuss novel research directions in quantum simulations of topological spin liquids with Rydberg atom arrays.

Lunch break

Alessio Lerose
Influence matrix approach to quantum many-body dynamics

In this talk I will introduce a new approach to study the out-of-equilibrium dynamics of extended isolated quantum many-body systems and their ergodic properties. While conventional signatures of quantum thermalization are associated with statistical properties of energy spectra and eigenstates ("eigenstate thermalization hypothesis"), this approach is inspired by the Feynman-Vernon influence functional theory. I will describe the evolution of a local subsystem in terms of an influence matrix (IM) - an operator acting on the space of temporal trajectories of the subsystem. The IM fully encodes the effects of the many-body system on its subsystems, and thus characterizes its ability (or failure) to behave as an efficient self-generated thermal bath. I will show that this complementary angle of attack on quantum many-body dynamics offers many advantages, both conceptually and practically. I will introduce the notion of temporal entanglement and discuss preliminary evidence on its role in characterizing universality classes of quantum many-body dynamics and computational efficiency.

Hubert Saleur
The O(n) conformal field theory in two dimensions (Online)

I will summarize some interesting aspects of the recent complete solution of the O(n) CFT in 2D based, in part, on the bootstrap technique

Coffee break

Pietro Menotti
Sergio Caracciolo: pupil, collaborator, scientist and friend

Personal recollection

Social dinner

Ettore Vicari
Coherent and dissipative dynamics at quantum phase transitions

The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit and at low energy. I present an overview of recent results of equilibrium and out-of-equilibrium phenomena at continuous and first-order quantum transitions, covering also some aspects related to the presence of dissipative mechanisms. These issues are mostly discussed within dynamic scaling frameworks, by extending the equilibrium quantum scaling laws that can be obtained by exploiting the quantum-to-classical mapping and the renormalization-group theory of critical phenomena.

https://arxiv.org/abs/2103.02626

Mauro Pastore
Effective bosonic theories for fermionc models on the lattice

In this contribution I will review some of the results we obtained in the context of lattice QFT, where we investigated the presence of bound states in the spectrum of certain fermionic relativistic models (’t Hooft, Gross-Neveu, Nambu-Jona Lasinio, etc.). To this aim, I will present a very general formalism devised by Caracciolo, Laliena, Palumbo et al. to obtain a theory of composite bosonic excitations above a non-perturbative vacuum state, starting from the underlying theory of fundamental fermions. The method consists in a Bogoliubov transformation in the Fermionic space of states, followed by a projection onto the space of composites, that will result in an effective action for the bosons, obtained from the elementary theory in a self-consistent way.

Coffee break

Maria Paola Lombardo
Universality and scaling of the QCD chiral transition (Online)

The nature of the high temperature chiral transition in QCD can be studied by exploting analogies with a magnetic system. The results from ab-initio lattice simulations are contrasted and compared with those of spin model in the appropriate universality class. We speculate that the boundary of the scaling window marks the crossover from strongly to weakly coupled plasma.

Andrea Di Gioacchino
Euclidean correlations in the statistical physics of the Traveling Salesman Problem

One of the first successes of the statistical physics of disordered systems has been its application to a number of combinatorial optimization problems, including the famous Traveling Salesman Problem (TSP). A limiting issue, however, has always been the difficulty to deal with the correlations introduced by the embedding of these problems in Euclidean space, and as a consequence most of the classical results are only valid in the infinite-dimension limit. I will discuss a series of papers [1, 2, 3] where we considered a variant of the TSP and managed to bypass this issue by focusing directly on the problem embedded in a low number of spatial dimensions. As I will show, our approach allowed us to successfully characterize some statistical properties of the solutions of the problem in 1 and 2 spatial dimensions.

[1] Caracciolo, Di Gioacchino, Gherardi, Malatesta, Solution for a bipartite Euclidean traveling-salesman problem in one dimension, Physical Review E , 97 (5), 052109 (2018).

[2] Caracciolo, Di Gioacchino, Malatesta, Molinari, Selberg integrals in 1D random Euclidean optimization problems, Journal of Statistical Mechanics: Theory and Experiment , 2019 (6), 063401 (2019).

[3] Capelli, Caracciolo, Di Gioacchino, Malatesta, Exact value for the average optimal cost of the bipartite traveling salesman and two-factor problems in two dimensions, Physical Review E , 98 (3), 030101 (2018)

Lunch break

Giorgio Parisi
Multiple Equilibra (Online)

Carlo Lucibello
Scaling hypothesis for the Euclidean bipartite matching problem

In this talk, I will present a work in collaboration with prof. Caracciolo and others appeared in 2014 on the optimal cost of random Euclidean bipartite matching problem. We propose a simple yet very predictive form, based on the Poisson’s equation, for the functional dependence of the cost on the density of points. This leads, for quadratic costs, to the analytic prediction of the large N limit of the average cost in dimension d = 1, 2 and of the subleading correction in higher dimension. A non-trivial scaling exponent, γd = (d−2) / d, which differs from the monopartite’s one, is found for the subleading correction. We argue that the same scaling holds true for a generic cost exponent in dimension d > 2.

Antonello Scardicchio
Localization and melting of interfaces in the two-dimensional quantum Ising model

I will show how the melting of a smooth interface in the 2D Ising model in transverse and longitudinal field shows signs of localization. This is done by means of a "holographic" mapping to a 1D integrable model of fermions in the large ferromagnetic coupling J limit and after the systematic introduction of 1/J corrections.

Coffee break

Coffee break

Gesualdo Delfino
Exact results for quenched disorder at criticality

The study of systems with short range quenched disorder has notoriously been a challenging problem for the theory of critical phenomena, and analytical insight on random critical points has been limited to rare perturbative limits. We will explain how we recently gained exact access to random criticality in two dimensions through a new way of exploiting conformal invariance.

Giuseppe del Vecchio del Vecchio
Generalised hydrodynamics and correlation functions

While statistical mechanics at equilibrium is relatively well settled, out-of-equilibrium phenomena escape universal description and represent one of the main challenges of theoretical physics nowadays. In this directions, in the past couple of decades, integrable models have represented a major playground territory not only because integrability gives access to analytic predictions but mainly because standard laboratory practices can now put them under direct experimental scrutiny. The main consequence of integrability is the presence of infinitely many conservation laws which strongly constrain the dynamics making the equilibrium ensembles rather different than the ordinary Gibbs state observed in presence of generic interactions. Generalised hydrodynamics (GHD) is the theory capturing long wavelength and large spacetime universal behaviour of integrable models and in the past five years it has produced an incredible amount of results in the field of our-of-equilibrium physics. In this contribution I will introduce GHD and discuss how, in combination with large deviation theory, it gives access to exact Euler scale (and beyond) correlation functions. Applications to XX and XY spin chain spin-spin correlation function and calculation of Reny’s and entanglement entropy are presented.