| ESPERIMENTO FI11, RESPONSABILE: Andrea Cappelli
L'attivita' di ricerca di questa iniziativa e` centrata sui metodi non
perturbativi in teoria quantistica dei campi e sulle loro applicazioni ai
sistemi della meccanica statistica. Negli ultimi anni si e' assistito ad una
rimarchevole convergenza di tecniche, provenienti in special modo dalle
teorie conformi e dai modelli integrabili, che ha fornito una importante
sorgente di nuove idee e di risultati esatti da confrontare con
esperimenti e simulazioni numeriche. Il controllo di diversi
effetti fisici passa per il calcolo analitico di funzioni di correlazione,
l'identificazione del contenuto operatoriale e dello spettro di massa delle
teorie, lo studio del limite continuo di modelli di reticolo, l'uso degli
sviluppi di taglia finita e lo studio delle condizioni bordo.
Altri campi di ricerca rilevanti di questa iniziativa sono lo
studio della teoria del trasporto e dell'approccio
all'equilibrio termodinamico in sistemi di bassa dimensionalita' e
con interazioni a lungo raggio che presentano comportamenti
speciali ed effetti non-perturbativi.
Meccanica statistica, Teoria quantistica dei campi, Invarianza conforme,
Metodi non perturbativi, Sistemi Integrabili, Teoria del trasporto,
Sistemi fuori dall'equilibrio termodinamico, Interazioni a lungo raggio,
Effetti di bordo e di volume finito
Statistical mechanics, Quantum field theory, Conformal Invariance,
Non-perturbative methods, Integrable systems, Transport theory,
Systems out of thermal equilibrium, Long-range interactions,
Boundary and finite-volume effects.
| OBIETTIVI DELL'ESPERIMENTO FI11
|This INFN Initiative involves research activity in the interdisciplinary area between Quantum Field Theory, Condensed Matter Theory and Statistical Physics, especially in low dimension. This domain developed considerably in the last twenty years, with the discovery of new and remarkable physical phenomena due to strong interactions. Such results led to introduce concepts and methods going beyond the ranges of established disciplines.
The main theme is the study of exactly solvable models in two dimensions, namely conformal field theories, integrable systems and perturbations thereof, together with their application to statistical mechanics and condensed matter problems. Exact solutions provide the tools to understand the physics of low-dimensional systems, that are characterized by non-perturbative effects.
The lure of low dimensional systems has attracted theoretical and experimental physicists, and with each advance towards this realm of Flatland, new, exciting and rich physics has emerged. From a theoretical point of view, the advent of Conformal Field Theory in 1984 has opened up an exact approach to massless low-dimensional systems and since then, the field has grown explosively in several directions, including the string theory of fundamental interactions, the statistical mechanics of phase transitions and growth phenomena, and new approaches for strongly-interacting systems. In the same period, one has also witnessed a parallel development in many subjects of mathematics, such as infinite dimensional Lie algebras, integrable equations, random matrices and probability. This blend of mathematical and physical ideas is at the root of the scientific elegance and extraordinary effectiveness that characterize the theoretical results in this area. Among them, let us mention the exact field theory computation of quantum Ising model correlators that has found a direct confirmation by neutron scattering experiments, and the solution of several problems involving transport and strong interactions, as e.g. in the quantum Hall effect, by applying conformal field theory and Bethe ansatz techniques.
Since there is a rather broad spectrum of problems in statistical mechanics and condensed matter, there are, accordingly, several research lines in this INFN Initiative. Let us mention the study of the quantum Hall effect and in general the strongly-interacting electron systems, the one and two-dimensional spin systems, and the quantum integrable statistical systems with meta-stable vacua. Let us also remark the relation between two-dimensional (exactly solvable) field theories and string theory: fruitful interchanges of methods and physical analogies between the two domains have occurred several times in the past and continue nowadays. Three connections that have been recently investigated in this initiative are: i) the matrix gauge theories of D0 branes applied to the fractional quantum Hall effect; ii) the use of integrable spin chains and Bethe Ansatz solutions to obtain the spectrum of anomalous dimensions in N=4 supersymmetric Yang-Mills theory in 4 dimensions; iii) the use of entanglement entropy for characterizing T=0 condensed matter systems and black-hole geometries. Last but not least, the possibility of realizing relativistic fermions in the (2+1) and (3+1) dimensions in graphene, cold atoms and topological insulators.
Quantum field theories or other quantum systems with infinite degrees of freedom are intensively analyzed when subjected to an abrupt change of their coupling constants (quantum quench). A particular important case is given by quantum integrable systems, i.e. with an infinite number of conserved quantities, whose long-time asymptotic behavior is not fully understood: they might thermalize or not and their asymptotic behaviour could be described by generalized Gibbs ensembles.
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