Exact out-of-equilibrium central spin dynamics from integrability

We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schr\"odinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices of the time dependence of the coupling constants. Our method establishes a new link between this system and the SU(2) Wess-Zumino-Witten model, and sheds new light on the implications of integrability in out-of-equilibrium quantum physics. As an application, a driven four-spin system is studied in detail

Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions

We study quenches in integrable spin-1/2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit.Comment: 14 pages, 3 figures, including supplementary material [from v3: figures updated and corrected, author added

Quench action approach for releasing the N\'eel state into the spin-1/2 XXZ chain

The steady state after a quantum quench from the N\'eel state to the anisotropic Heisenberg model for spin chains is investigated. Two methods that aim to describe the postquench non-thermal equilibrium, the generalized Gibbs ensemble and the quench action approach, are discussed and contrasted. Using the recent implementation of the quench action approach for this N\'eel-to-XXZ quench, we obtain an exact description of the steady state in terms of Bethe root densities, for which we give explicit analytical expressions. Furthermore, by developing a systematic small-quench expansion around the antiferromagnetic Ising limit, we analytically investigate the differences between the predictions of the two methods in terms of densities and postquench equilibrium expectation values of local physical observables. Finally, we discuss the details of the quench action solution for the quench to the isotropic Heisenberg spin chain. For this case we validate the underlying assumptions of the quench action approach by studying the large-system-size behavior of the overlaps between Bethe states and the N\'eel state.Comment: 57 pages, 7 figures, v3: minor changes, references update

Quasi-soliton scattering in quantum spin chains

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The time evolved block decimation (TEBD) algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.Comment: 15 pages, 7 figures. (v2: citations added

Quantum Quenches in Integrable Field Theories

We study the non equilibrium time evolution of an integrable field theory in 1+1 dimensions after a sudden variation of a global parameter of the Hamiltonian. For a class of quenches defined in the text, we compute the long times limit of the one point function of a local operator as a series of form factors. Even if some subtleties force us to handle this result with care, there is a strong evidence that for long times the expectation value of any local operator can be described by a generalized Gibbs ensemble with a different effective temperature for each eigenmode

Cardiac injury and mortality in patients with Coronavirus disease 2019 (COVID-19): insights from a mediation analysis

Patients at greatest risk of severe clinical conditions from coronavirus disease 2019 (COVID-19) and death are elderly and comorbid patients. Increased levels of cardiac troponins identify patients with poor outcome. The present study aimed to describe the clinical characteristics and outcomes of a cohort of Italian inpatients, admitted to a medical COVID-19 Unit, and to investigate the relative role of cardiac injury on in-hospital mortality

Non-equilibrium dynamics of the Tavis-Cummings model

In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between near-integrable and chaotic systems. Here we propose to describe the off-equilibrium dynamics of the Tavis-Cummings model by an underlying classical Hamiltonian system, which can be analyzed using the powerful tools of classical theory of motion. We show that scattering in the classical phase space can drive the quantum model close to thermal equilibrium. Interestingly, this happens in the fully quantum regime, where physical observables do not show any dynamic chaotic behavior.Comment: 4 pages, 3 figure

Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points

Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench in the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g. by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder

Rivisitando i “Materiali resilienti”

L’articolo intende valorizzare l’esperienza del ciclo di conferenze “Materiali Resilienti”, organizzato dall’Archivio di Stato di Bologna e dal Chiostro dei Celestini. Obiettivo del contributo è mettere in risalto l’interazione tra lo sviluppo dei principali punti nodali affrontati sul tema donne e lavoro tra il medioevo e l'età contemporanea, con la lettura delle fonti archivistiche e bibliografiche eseguite dall'attrice Marinella Manicardi