Elusive phase transition in the replica limit of monitored systems

We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random direction. We make use of the replica trick to account for the Born's rule weighting of the measurement outcomes in the study of purification and other observables, with an exact description in the large-$N$ limit. We find that the nature of the phase transition strongly depends on the number $n$ of replicas used in the calculation, with the appearance of non-perturbative logarithmic corrections that destroy the disentangled/purifying phase in the relevant $n \rightarrow 1$ replica limit. Specifically, we observe that the purification time of a mixed state in the weak measurement phase is always exponentially long in the system size for arbitrary strong measurement rates.Comment: 7+16 pages, 3+4 figure

Spreading of a local excitation in a Quantum Hierarchical Model

We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. We provide analytical predictions for its time evolution, solving the single-particle dynamics on a hierarchical network. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times. Furthermore, a universal scaling among space and time is found related to the algebraic decay of the interactions as $r^{-1-\sigma}$. We compare our predictions to numerics, employing tensor network techniques, for large magnetic fields, discussing the robustness of the mechanism in the full many-body dynamics

Towards Relativistic Atomic Physics. I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field

A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. In the inertial rest frame the isolated system is seen as a decoupled non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass $M$ and the rest spin ${\vec {\bar S}}$ of the system) and an external realization of the Poincare' group. Then an isolated system of positive-energy charged scalar articles plus an arbitrary electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) are explicitly given. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem,at least at the classical level.Comment: Minor change

Analisi di un sistema PTES basato su cicli Brayton-Joule

L'obiettivo di questa Tesi, svolta in collaborazione con Enel S.p.A, è stato quello di effettuare un'analisi termodinamica di un sistema PTES basato su cicli Brayton-Joule al fine di valutarne l’efficienza energetica. In particolare, sono state analizzate due configurazioni differenti: il sistema con mezzo di accumulo solido e quello con mezzo di accumulo liquido. In entrambi i casi è stata condotta un’analisi di sensitività, con l’ausilio del software Matlab®, al fine di valutare l’influenza di alcuni parametri termodinamici ed elettrici sull’efficienza di round trip del sistema. Per quanto riguarda il caso con mezzo di accumulo liquido, sono state effettuate anche alcune valutazioni tecniche necessarie a verificare ulteriormente la fattibilità pratica del sistema proposto. The purpose of this thesis, carried out in collaboration with Enel S.p.A, has been to conduct a thermodynamic analysis of a PTES system based on Brayton-Joule cycles, in order to evaluate its energy efficiency. In detail, two different configurations were analyzed: the system with solid storage medium and the system with liquid storage medium. In both cases, a sensitivity analysis was conducted with the help of the Matlab® software, in order to evaluate the influence of some thermodynamic and electrical parameters on the system's round trip efficiency. Regarding the case with liquid storage medium, some technical evaluations have also been carried out to further verify the practical feasibility of the proposed system