1,720,998 research outputs found
Ferromagnetism in a repulsive atomic Fermi gas with correlated disorder
Full text linkWe investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas in the presence of a correlated random field that represents an optical speckle pattern. The density is tuned so that the (noninteracting) Fermi energy is close to the mobility edge of the Anderson localization transition. We employ quantum Monte Carlo simulations to determine various ground-state properties, including the equation of state, the magnetic susceptibility, and the energy of an impurity immersed in a polarized Fermi gas (repulsive polaron). In the weakly interacting limit, the magnetic susceptibility is found to be suppressed by disorder. However, it rapidly increases with the interaction strength, and it diverges at a much weaker interaction strength compared to the clean gas. Both the transition from the paramagnetic phase to the partially ferromagnetic phase, and the one from the partially to the fully ferromagnetic phase, are strongly favored by disorder, indicating a case of order induced by disorder
Localization of interacting Fermi gases in quasiperiodic potentials
Full text linkWe investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasiperiodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low-energy) Anderson localized and (high-energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasiperiodic potential. To discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point
Kohn's localization in disordered fermionic systems with and without interactions
Full text linkUnderstanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper, we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First, we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-Andre Hamiltonian and its modification including next-nearest-neighbor hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localization tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then, we investigate the effect of weak repulsive interactions in the Aubry-Andre Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximatio
Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning
Full text linkAdiabatic quantum computers, such as the quantum annealers commercialized by
D-Wave Systems Inc., are routinely used to tackle combinatorial optimization
problems. In this article, we show how to exploit them to accelerate
equilibrium Markov chain Monte Carlo simulations of computationally challenging
spin-glass models at low but finite temperatures. This is achieved by training
generative neural networks on data produced by a D-Wave quantum annealer, and
then using them to generate smart proposals for the Metropolis-Hastings
algorithm. In particular, we explore hybrid schemes by combining single
spin-flip and neural proposals, as well as D-Wave and classical Monte Carlo
training data. The hybrid algorithm outperforms the single spin-flip
Metropolis-Hastings algorithm. It is competitive with parallel tempering in
terms of correlation times, with the significant benefit of a much shorter
equilibration time.Comment: 24 pages, 7 figure
Few-boson localization in a continuum with speckle disorder
Full text linkThe disorder-induced localization of few bosons interacting via a contact potential is investigated through the
analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in
a continuum and describes one-dimensional bosonic atoms exposed to the spatially correlated disorder due to an
optical speckle field. First, we identify the speckle-field intensity required to observe, in the single-particle case,
the Poisson level-spacing statistics, which is characteristic of localized quantum systems, in a computationally
and experimentally feasible system size. Then, we analyze the two-body and the three-body systems, exploring
a broad interaction range, from the noninteracting limit up to moderately strong interactions. Our main result is
that the contact potential does not induce a shift towards the Wigner-Dyson level-spacing statistics, which would
indicate the emergence of an ergodic chaotic state, indicating that localization can occur also in interacting
few-body systems in a continuum. We also analyze how the ground-state energy evolves as a function of the
interaction strength
Out-of-equilibrium dynamics of repulsive Fermi gases in quasiperiodic potentials: A density functional theory study
Full text linkThe dynamics of a one-dimensional two-component Fermi gas in the presence of a quasiperiodic optical lattice (OL) is investigated by means of a density functional theory approach. Inspired by the protocol implemented in recent cold-atom experiments—designed to identify the many-body localization transition—we analyze the relaxation of an initially prepared imbalance between the occupation number of odd and of even sites. For quasidisorder strength beyond the Anderson localization transition, the imbalance survives for long times, indicating the inability of the system to reach local equilibrium. The late-time value of the imbalance diminishes for increasing interaction strength. Close to the critical quasidisorder strength corresponding to the noninteracting (Anderson) transition, the interacting system displays an extremely slow relaxation dynamics, consistent with subdiffusive behavior. The amplitude of the imbalance fluctuations around its running average is found to decrease with time, and such damping is more effective with increasing interaction strengths. While our study addresses the setup with two equally intense OLs, very similar effects due to interactions have been observed also in recent cold-atom experiments performed in the tight-binding regime, i.e., where one of the two OLs is very deep and the other is much weaker
Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena
Full text linkWe benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via density functional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks–Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries
Applicazione del machine learning ai learning analytics della piattaforma Moodle per creare gruppi eterogenei nei corsi on-line
Full text linkIn university courses to promote collaborative activities among students, on-line learningenvironments such as e-learning platforms are used. Effective collaborative activitiesinvolve the creation of heterogeneous groups of 4 or 5 students. In the university contextthe formation of groups is difficult due to the high number of students. Groups are oftenunbalanced and not very functional if chosen randomly. Some e-learning platforms, suchas Moodle, lack an intelligent mechanism that allows the automatic creation of heterogeneousgroups of students. We applied clustering algorithms on Moodle learning analytics(LA) that allowed to build groupings that identify the different characteristics ofstudents based on their behaviors kept on the platform. Therefore we have developedan intelligent numerical tool which, using clusters obtained from Machine Learning onthe LA, generates heterogeneous groups. These groups are made available on the platformfor the teacher. The project will conclude with the development of a Moodle pluginto automate the exchange of data and information between the Machine Learning algorithmand the Moodle platform.Nei percorsi universitari, per favorire le attività collaborative tra gli studenti, vengono utilizzatiambienti di apprendimento on-line come le piattaforme e-learning. Attività collaborativeefficaci prevedono la creazione di gruppi eterogenei di 4 o 5 studenti. Nelcontesto universitario la formazione dei gruppi è difficile per l’elevato numero di studenti.Se scelti in maniera casuale, spesso i gruppi risultano sbilanciati e poco funzionali. Alcunepiattaforme e-learning, ad esempio Moodle, mancano di un meccanismo “intelligente”che permetta di creare in automatico gruppi eterogenei di studenti. Il nostro lavoro consistenel realizzare un software in Python in grado di creare gruppi eterogenei di studenti,utilizzando tecniche di Machine Learning con i dati estratti da Moodle. Abbiamo applicato algoritmi di clustering sui learning analytics (LA) di Moodle che hanno permesso di costruiredei raggruppamenti che identificano le caratteristiche degli studenti in base ai lorocomportamenti in piattaforma. Abbiamo quindi sviluppato uno strumento numerico “intelligente”che, utilizzando i cluster ottenuti dal Machine Learning sui LA, genera gruppieterogenei. Questi gruppi vengono messi a disposizione in piattaforma per il docente. Ilprogetto si concluderà con lo sviluppo di un plugin di Moodle per automatizzare lo scambiodi dati e informazioni tra l’algoritmo di Machine Learning e la piattaforma Moodle
Quantum Monte Carlo study of the role of p-wave interactions in ultracold repulsive Fermi gases
Full text linkSingle-component ultracold atomic Fermi gases are usually described using
noninteracting many-fermion models. However, recent experiments reached a
regime where -wave interactions among identical fermionic atoms are
important. In this paper, we employ variational and fixed-node diffusion Monte
Carlo simulations to investigate the ground-state properties of
single-component Fermi gases with short-range repulsive interactions. We
determine the zero-temperature equation of state, and elucidate the roles
played by the -wave scattering volume and the -wave effective range. A
comparison against recently derived second-order perturbative results shows
good agreement in a broad range of interaction strength. We also compute the
quasiparticle effective mass, and we confirm the perturbative prediction of a
linear contribution in the -wave scattering volume, while we find
significant deviations from the beyond-mean-field perturbative result, already
for moderate interaction strengths. Finally, we determine ground-state energies
for two-component unpolarized Fermi gases with both interspecies and
intraspecies hard-sphere interactions, finding remarkable agreement with a
recently derived fourth-order expansion that includes -wave contributions.Comment: 9 pages, 4 figures. Extended data for the effective mass and changed
title. Post-print versio
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