Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains

We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale $\tau$ . The time evolution of the entanglement entropy displays different regimes depending on the value of $\tau$, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of entanglement entropy and Schmidt gap.Comment: Accepted for publication in Phys. Rev.

Synthetic gauge fields in synthetic dimensions: interactions and chiral edge modes

Synthetic ladders realized with one-dimensional alkaline-earth(-like) fermionic gases and subject to a gauge field represent a promising environment for the investigation of quantum Hall physics with ultracold atoms. Using density-matrix renormalization group calculations, we study how the quantum Hall-like chiral edge currents are affected by repulsive atom-atom interactions. We relate the properties of such currents to the asymmetry of the spin resolved momentum distribution function, a quantity which is easily addressable in state-of-art experiments. We show that repulsive interactions significantly enhance the chiral currents. Our numerical simulations are performed for atoms with two and three internal spin states

PRESERVATION OF QUATERNARY SEDIMENTS IN DSGSD ENVIRONMENTS: THE MONT FALLÈRE CASE STUDY (AOSTA VALLEY, NW ITALY)

Deep seated gravitational slope deformations (DSGSD) in the Western Alps, which usually affect glacial valleys, produce strong deformation in both bedrock and Quaternary cover, generally favouring erosion. This research, which examines a DSGSD along the Mont Fallère southern slope in the Aosta Valley, suggests that DSGSD can also locally favour the formation and preservation of the Quaternary stratigraphic successionns for the following reasons: - the development of transversal elongated depressions, which are essentially connected with the onset of gravitational structures (trenches, minor scarps, and counterscarps) and filled by differentiated Quaternary successions; - the occurrence of closed depressions along the slope, which originate from the gradual evolution of gravitational structures (trenches or minor scarps and associated counterscarps) and are occupied by lakes that are progressively filled by lacustrine and palustrine sequences; - the occurrence of wide, flat, irregular surfaces that are characterized by lower erosional phenomena with respect to the surrounding steep slopes and preserve various Quaternary stratigraphic successions; - the development of rounded reliefs and associated wide depressions, both of which exhibit topographic surfaces that hang over torrential incisions that are located along the main fractures; this morphology favours the preservation of glacial, outwash, lacustrine and palustrine sediments; - wide colluvial and debris cover that buries and partially preserves older Quaternary sediments; - the local occurrence of a travertine cover and carbonatie-cemented sediments, which preserve the older Quaternary sediments. These morphological conditions are favourable to prehistoric human settlements, resulting in archaeological mountain sites that also provide a chronological reference for the evolution of DSGSD

Entanglement Entropies in One-Dimensional Systems

In the thesis, we discuss some aspects of 1D quantum systems related to entanglement entropies; in particular, we develop a new numerical method for the detection of crossovers in Luttinger liquids, and we discuss the behaviour of Rényi entropies in open conformal systems, when the boundary conditions preserve their conformal invariance

A Low-Cost GNSS Prototype for Tracking Runners in RTK Mode: Comparison with Running Watch Performance

GNSS positioning is widely use in every kind of application. Nowadays, low-cost GNSS modules are becoming available to apply the Real-Time Kinematic mode in those applications in which a centimeter-level accuracy would be appreciated for a precise positioning. In this work, we developed a prototype for collecting data in RTK mode with a single-frequency multi-constellation device during some physical tests performed by a professional runner. Prior to do this, we assessed the accuracy in estimating the distance actually covered during a walking on a signalized line. Also, we verified the capability to detect short sprints of about 12–15 s. Finally, we compared the results of our prototype with a Polar M430 running watch during three Cooper tests and a Kosmin test. The comparison highlighted that the running watch overestimated the total distance systematically and did not describe the performance of the athlete accurately in time. The distance overestimation was +4.7% on average using the running watch, whereas our prototype system exhibited an error level of about 0.1%