Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials

We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- A nd two-particle systems, we derive the analogous results for the many-particle case in the presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamiltonian is shown to be integrable too. We determine the micromotion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wave packet and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coefficient strength of the linear potential on a time period is nonvanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model

The SURPRISE demonstrator: a super-resolved compressive instrument in the visible and medium infrared for Earth Observation

While Earth Observation (EO) data has become ever more vital to understanding the planet and addressing societal challenges, applications are still limited by revisit time and spatial resolution. Though low Earth orbit missions can achieve resolutions better than 100 m, their revisit time typically stands at several days, limiting capacity to monitor dynamic events. Geostationary (GEO) missions instead typically provide data on an hour-basis but with spatial resolution limited to 1 km, which is insufficient to understand local phenomena. In this paper, we present the SURPRISE project - recently funded in the frame of the H2020 programme – that gathers the expertise from eight partners across Europe to implement a demonstrator of a super-spectral EO payload - working in the visible (VIS) - Near Infrared (NIR) and in the Medium InfraRed (MIR) and conceived to operate from GEO platform -with enhanced performance in terms of at-ground spatial resolution, and featuring innovative on-board data processing and encryption functionalities. This goal will be achieved by using Compressive Sensing (CS) technology implemented via Spatial Light Modulators (SLM). SLM-based CS technology will be used to devise a super-resolution configuration that will be exploited to increase the at-ground spatial resolution of the payload, without increasing the number of detector’s sensing elements at the image plane. The CS approach will offer further advantages for handling large amounts of data, as is the case of superspectral payloads with wide spectral and spatial coverage. It will enable fast on-board processing of acquired data for information extraction, as well as native data encryption on top of native compression. SURPRISE develops two disruptive technologies: Compressive Sensing (CS) and Spatial Light Modulator (SLM). CS optimises data acquisition (e.g. reduced storage and transmission bandwidth requirements) and enables novel onboard processing and encryption functionalities. SLM here implements the CS paradigm and achieves a super-resolution architecture. SLM technology, at the core of the CS architecture, is addressed by: reworking and testing off-the-shelf parts in relevant environment; developing roadmap for a European SLM, micromirror array-type, with electronics suitable for space qualification. By introducing for the first time the concept of a payload with medium spatial resolution (few hundreds of meters) and near continuous revisit (hourly), SURPRISE can lead to a EO major breakthrough and complement existing operational services. CS will address the challenge of large data collection, whilst onboard processing will improve timeliness, shortening time needed to extract information from images and possibly generate alarms. Impact is relevant to industrial competitiveness, with potential for market penetration of the demonstrator and its components

Finite temperature off-diagonal long-range order for interacting bosons

Characterizing the scaling with the total particle number (N) of the largest eigenvalue of the one-body density matrix (++0) provides information on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting ++0Gê+NC0, then C0=1 corresponds in ODLRO. The intermediate case, 0<1, corresponds in translational invariant systems to the power-law decaying of (nonconnected) correlation functions and it can be seen as identifying quasi-long-range order. The goal of the present paper is to characterize the ODLRO properties encoded in C0 (and in the corresponding quantities CkGëá0 for excited natural orbitals) exhibited by homogeneous interacting bosonic systems at finite temperature for different dimensions in presence of short-range repulsive potentials. We show that CkGëá0=0 in the thermodynamic limit. In one dimension it is C0=0 for nonvanishing temperature, while in three dimensions it is C0=1 (C0=0) for temperatures smaller (larger) than the Bose-Einstein critical temperature. We then focus our attention to D=2, studying the XY and the Villain models, and the weakly interacting Bose gas. The universal value of C0 near the Berezinskii-Kosterlitz-Thouless temperature TBKT is 7/8. The dependence of C0 on temperatures between T=0 (at which C0=1) and TBKT is studied in the different models. An estimate for the (nonperturbative) parameter +¦ entering the equation of state of the two-dimensional Bose gases is obtained using low-temperature expansions and compared with the Monte Carlo result. We finally discuss a "double jump"behavior for C0, and correspondingly of the anomalous dimension ++, right below TBKT in the limit of vanishing interactions

Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials

We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- A nd two-particle systems, we derive the analogous results for the many-particle case in the presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamiltonian is shown to be integrable too. We determine the micromotion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wave packet and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coefficient strength of the linear potential on a time period is nonvanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model

Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas

An integrable model subjected to a periodic driving gives rise generally to a nonintegrable Floquet Hamiltonian. Here we show that the Floquet Hamiltonian of the integrable Lieb-Liniger model in the presence of a linear potential with a periodic time-dependent strength is instead integrable and its quasienergies can be determined using the Bethe ansatz approach. We discuss various aspects of the dynamics of the system at stroboscopic times and we also propose a possible experimental realization of the periodically driven tilting in terms of a shaken rotated ring potential

Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas

The scaling of the largest eigenvalue \u3bb0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation \u3bb0 3cBNC. The case C=1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well-known result also confirmed by bosonization gives instead C=1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V. We argue that the value C=1/2 characterizes the hard-core system independently of the nature of the potential V. We then define the exponents \u3b3 and \u3b2, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to \u3bb0, respectively, and we derive the scaling relation \u3b3+2\u3b2=C. Taking as a specific case the power-law potential V(x)2n, we give analytical formulas for \u3b3 and \u3b2 as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent

Finite temperature off-diagonal long-range order for interacting bosons

Characterizing the scaling with the total particle number (N) of the largest eigenvalue of the one-body density matrix (++0) provides information on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting ++0G\uea+NC0, then C0=1 corresponds in ODLRO. The intermediate case, 0<1, corresponds in translational invariant systems to the power-law decaying of (nonconnected) correlation functions and it can be seen as identifying quasi-long-range order. The goal of the present paper is to characterize the ODLRO properties encoded in C0 (and in the corresponding quantities CkG\ueb\ue10 for excited natural orbitals) exhibited by homogeneous interacting bosonic systems at finite temperature for different dimensions in presence of short-range repulsive potentials. We show that CkG\ueb\ue10=0 in the thermodynamic limit. In one dimension it is C0=0 for nonvanishing temperature, while in three dimensions it is C0=1 (C0=0) for temperatures smaller (larger) than the Bose-Einstein critical temperature. We then focus our attention to D=2, studying the XY and the Villain models, and the weakly interacting Bose gas. The universal value of C0 near the Berezinskii-Kosterlitz-Thouless temperature TBKT is 7/8. The dependence of C0 on temperatures between T=0 (at which C0=1) and TBKT is studied in the different models. An estimate for the (nonperturbative) parameter +\ua6 entering the equation of state of the two-dimensional Bose gases is obtained using low-temperature expansions and compared with the Monte Carlo result. We finally discuss a "double jump"behavior for C0, and correspondingly of the anomalous dimension ++, right below TBKT in the limit of vanishing interactions

Third Country National

This chapter analyses the individual status of a Third Country National (TCN) from a standpoint which highlights the creation and the conditioning of this status by European institutions and laws. It is divided into two sections. The first discusses TCNs under European Union (EU) law to determine how this individual status has been established through the formation of the EU and is today formally recognised and regulated through EU law. The interplay between EU nationals’ and TCNs’ rights and freedoms is then examined further in the second section which focuses on TCNs’ right to marry in the member state of Malta. This section broadly addresses the clear tension between the universal character of human rights and the systems for their implementation and enforcement within member states; which are mainly national in character and addressed to citizens and this notwithstanding the EU’s accession to the European Convention of Human Rights (ECHR). More specifically, the interrelationship between TCNs’ rights to marry and to exercise freedom of movement within member states, as well as the constraints which condition their access to such rights, provide a deeper understanding of the juridical implications of the individual status of TCN within the EU

Deviations from off-diagonal long-range order in one-dimensional quantum systems

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue \u3bb0 of the one-body-density matrix scales as \u3bb0 3c N, where N is the total number of particles. Putting \u3bb0 3c NC to define the scaling exponent C, then C = 1 corresponds to ODLRO and C = 0 to the single-particle occupation of the density matrix orbitals. When 0 < C <1, C can be used to quantify deviations from ODLRO. In this paper we study the exponent C in a variety of one-dimensional bosonic and anyonic quantum systems at T = 0. For the 1D Lieb-Liniger Bose gas we find that for small interactions C is close to 1, implying a mesoscopic condensation, i.e., a value of the zero temperature "condensate" fraction \u3bb0/N appreciable at finite values of N (as the ones in experiments with 1D ultracold atoms). 1D anyons provide the possibility to fully interpolate between C = 1 and 0. The behaviour of C for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter

Effects of central and peripheral inflammation on hippocampal synaptic plasticity

The central nervous system (CNS) and the immune system are known to be engaged in an intense bidirectional crosstalk. In particular, the immune system has the potential to influence the induction of brain plastic phenomena and neuronal networks functioning. During direct CNS inflammation, as well as during systemic, peripheral, inflammation, the modulation exerted by neuroinflammatory mediators on synaptic plasticity might negatively influence brain neuronal networks functioning. The aim of the present study was to investigate, by using electrophysiological techniques, the ability of hippocampal excitatory synapses to undergo synaptic plasticity during the initial clinical phase of an experimental model of CNS (experimental autoimmune encephalomyelitis, EAE) as well as following a systemic inflammatory trigger. Moreover, we compared the morphologic, synaptic and molecular consequences of central neuroinflammation with those accompanying peripheral inflammation. Hippocampal long-term potentiation (LTP) has been studied by extracellular field potential recordings in the CA1 region. Immunohistochemistry was performed to investigate microglia activation. Western blot and ELISA assays have been performed to assess changes in the subunit composition of the synaptic glutamate NMDA receptor and the concentration of pro-inflammatory cytokines in the hippocampus. Significant microglial activation together with an impairment of CA1 LTP was present in the hippocampus of mice with central as well as peripheral inflammation. Interestingly, exclusively during EAE but not during systemic inflammation, the impairment of hippocampal LTP was paralleled by a selective reduction of the NMDA receptor NR2B subunit levels and a selective increase of interleukin-1\u3b2 (IL1\u3b2) levels. Both central and peripheral inflammation-triggered mechanisms can activate CNS microglia and influence the function of CNS synapses. During direct CNS inflammation these events are accompanied by detectable changes in synaptic glutamate receptors subunit composition and in the levels of the pro-inflammatory cytokine IL1\u3b2