The Post‐Modern Transcendental of Language in Science and Philosophy

In this chapter I discuss the deep mutations occurring today in our society and in our culture, the natural and mathematical sciences included, from the standpoint of the “transcendental of language”, and of the primacy of language over knowledge. That is, from the standpoint of the “completion of the linguistic turn” in the foundations of logic and mathematics using Peirce’s algebra of relations. This evolved during the last century till the development of the Category Theory as universal language for mathematics, in many senses wider than set theory. Therefore, starting from the fundamental M. Stone’s representation theorem for Boolean algebras, computer scientists developed a coalgebraic first-order semantics defined on Stone’s spaces, for Boolean algebras, till arriving to the definition of a non-Turing paradigm of coalgebraic universality in computation. Independently, theoretical physicists developed a coalgebraic modelling of dissipative quantum systems in quantum field theory, interpreted as a thermo-field dynamics. The deep connection between these two coalgebraic constructions is the fact that the topologies of Stone spaces in computer science are the same of the C*-algebras of quantum physics. This allows the development of a new class of quantum computers based on coalgebras. This suggests also an intriguing explanation of why one of the most successful experimental applications of this coalgebraic modelling of dissipative quantum systems is just in cognitive neuroscience

Generalized hydrodynamics of a class of integrable quantum field theories with non-diagonal scattering

In questo lavoro di tesi abbiamo analizzato alcuni modelli conformi con perturbazioni integrabili, in particolare il modello di Ising tri-critico e i successivi modelli minimali. Abbiamo costruito un protocollo che realizza questi modelli in un regime fuori dall'equilibrio termodinamico. Questo sistema è stato ottenuto connettendo due sistemi semi-infiniti termalizzati a due diverse temperature. In tempi e spazi grandi ci si aspetta che questo sistema evolva verso uno stato stazionario indipendente dal tempo. Le quantità fisiche di nostro interesse sono le correnti stazionarie generate in tale situazione. Per studiare questo sistema abbiamo utilizzato strumenti di integrabilità come il Bethe ansatz termodinamico, concetti di idrodinamica generalizzata e l'insieme di Gibbs generalizzato. Finora questo schema è stato formulato per le teorie di campo con un'interazione tra le particelle data da una matrice S diagonale, ovvero per i modelli con lo spettro di quasi-particelle prive di gradi di libertà interni. In questa tesi abbiamo proposto un'estensione di questo metodo a un modello dotato di uno spettro contenente quasi-particelle organizzate in multipletti di simmetrie e quindi dotate di gradi di libertà interni detti magnoni con processi d'urto descritti da matrici S non diagonali. Abbiamo quindi risolto numericamente le equazioni differenziali che descrivono il sistema di non equilibrio e abbiamo discusso questi risultati

Probing many-body physics with multiorbital quantum gases

This thesis reports on two experiments employing ultracold atoms to realize many-body physics in the presence of an orbital degree of freedom. In particular, we develop the experimental techniques to probe the Fermi polaron problem across an orbital Feshbach resonance and examine the relaxation dynamics in the one-dimensional mass-imbalanced Fermi-Hubbard model. Quasiparticles like the Fermi polaron constitute an elementary part of Landau's Fermi liquid theory and find extensive application in the description of interacting electron systems. In the first part of this thesis, we exploit the recently observed orbital Feshbach resonance in ytterbium to produce multiorbital Fermi polarons in mixtures of ground state and clock state atoms. To this end, we employ clock-line spectroscopy and identify the repulsive as well as attractive polaron in the many-body spectrum of the two-dimensional impurity-bath system. We also determine other important quasiparticle properties, namely, the residue and lifetime. Our measurement results agree well with a tailored many-body theory, thereby confirming the relevance of orbital interactions for the Fermi polaron problem. In the second experiment, we study the mass-imbalanced Fermi-Hubbard model with ytterbium atoms trapped in a state-dependent optical lattice for the ground and metastable clock state. Atomic populations are prepared in both of these states and correspond to heavy and light particles exhibiting vastly different dynamical time scales. Recently, such models have been extensively explored in the context of localization and thermalization in isolated quantum many-body systems. To probe non-equilibrium dynamics in our system, we record the density of the light species after adjusting the external trapping potential. In this way, we identify a strong suppression of transport at early times and slow relaxation at late times, with a significant dependence on the dynamical time scale and interaction strength of both species. Our results demonstrate the emergence of metastability and extremely slow thermalization due to dynamical constraints. The implementations of multiorbital many-body physics established within this thesis pave the way for quantum simulators that could shed light on open questions in condensed-matter theory.Diese Arbeit präsentiert zwei Experimente, welche für die Realisierung von Vielteilchenphysik mit einem orbitalen Freiheitsgrad ultrakalte Atome verwenden. Insbesondere werden im Rahmen dieser Arbeit experimentelle Techniken entwickelt, um das Fermi-Polaron-Problem in der Nähe einer orbitalen Feshbach-Resonanz zu untersuchen und die Relaxationsdynamik im eindimensionalen Fermi-Hubbard-Modell mit ungleichen Massen zu analysieren. Quasiteilchen wie das Fermi-Polaron sind ein elementarer Bestandteil von Landaus Fermi-Flüssigkeits-Theorie und finden umfangreiche Anwendung bei der Beschreibung wechselwirkender Elektronensysteme. Im ersten Teil dieser Arbeit benutzen wir die kürzlich entdeckte orbitale Feshbach-Resonanz in Ytterbium, um multiorbitale Fermi-Polaronen in Mischungen aus Atomen im Grundzustand und metastabilen Uhrenzustand zu erzeugen. Zu diesem Zweck setzen wir spektroskopische Messungen auf dem Uhrenübergang ein und identifizieren das attraktive als auch das repulsive Polaron im Vielteilchenspektrum des zweidimensionalen Teilchen-Bad-Systems. Außerdem bestimmen wir weitere wichtige Eigenschaften dieses Quasiteilchens—nämlich das Residuum und die Lebensdauer. Die Resultate unserer Messungen stimmen gut mit einer spezifischen Vielteilchentheorie überein und bestätigen damit die Bedeutung orbitaler Wechselwirkungen für das Fermi-Polaron-Problem. Im zweiten Experiment untersuchen wir das Fermi-Hubbard-Modell für ungleiche Massen mit Ytterbium-Atomen, die in einem zustandsabhängigen optischen Gitter für den Grundzustand und metastabilen Uhrenzustand gefangen sind. In diesen beiden Zuständen werden Atome präpariert und entsprechen dabei schweren und leichten Teilchen, die sehr unterschiedliche dynamische Zeitskalen aufweisen. Zuletzt wurden solche Modelle ausführlich im Zusammenhang von Lokalisierungs- und Thermalisierungsprozessen in isolierten Quanten-Vielteilchen-Systemen erforscht. Um die Nicht-Gleichgewichtsdynamik in unserem System zu untersuchen, zeichnen wir die Dichte der leichten Spezies auf, nachdem das externe Fallenpotential geändert wurde. Auf diese Weise identifizieren wir eine starke Unterdrückung des Transports zu frühen Zeiten und eine langsame Relaxation zu späten Zeiten mit signifikanter Abhängigkeit von der dynamischen Zeitskala und der Wechselwirkungsstärke beider Spezies. Unsere Ergebnisse zeigen, dass Metastabilität und extrem langsame Thermalisierung aufgrund dynamischer Einschränkungen auftreten können. Die in dieser Arbeit entwickelten Experimente zu multiorbitaler Vielkörperphysik ebnen den Weg für Quantensimulatoren, die offene Fragen zu Theorien kondensierter Materie beantworten könnten

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation