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Spatiotemporally ordered patterns in a chain of coupled dissipative kicked rotors
Full text linkIn this work we consider the dynamics of a chain of many coupled kicked
rotors with dissipation. We map a rich phase diagram with many dynamical
regimes. We focus mainly on a regime where the system shows period doubling,
and forms patterns that are persistent and depend on the stroboscopic time with
period double than that of the driving: The system shows a form of
spatiotemporal ordering analogous to quantum Floquet time crystals.
Spatiotemporally ordered patterns can be understood by means of a
linear-stability analysis that predicts an instability region that contains the
spatiotemporally ordered regime. The boundary of the instability region
coincides with the lower boundary of the spatiotemporally ordered regime, and
the most unstable mode has length scale double than the lattice spacing, a
feature that we observe in the spatiotemporally ordered patterns: Period
doubling occurs both in time and space. We propose an implementation of this
model in an array of SQUID Josephson junctions with a pulsed time-periodic
flux.Comment: 15 pages, 13 figures, linear stability analysis adde
Periodic driving of a coherent quantum many body system and relaxation to the Floquet diagonal ensemble
Full text linkThe coherent dynamics of many body quantum system is nowadays an experimental reality: by means of the cold atoms in optical lattices, many Hamiltonians and time-dependent perturbations can be engineered. In this Thesis we discuss what happens in these systems when a periodic perturbation is applied. Thanks to Floquet theory, we can see that -- if the Floquet spectrum obeys certain continuity conditions possible in the thermodynamic limit-- dephasing among Floquet quasi-energies makes local observables relax to a periodic steady regime described by an effective density matrix: the Floquet diagonal ensemble (FDE). By means of numerical examples on the Quantum Ising Chain and the Lipkin model, we discuss the properties of the FDE focusing on the difference among ergodic and regular quantum dynamics and on how this reflects on the thermal properties () of the asymptotic condition. We verify thermalization in the classically ergodic Lipkin model and we demonstrate that this effect is induced by the Floquet states being delocalized and obeying Eigenstate Thermalization Hypothesis.We discuss also, in the Ising chain case, the work probability
distribution, whose asymptotic condition is not described by the form (Generalized Gibbs Ensemble) that FDE acquires for local obserbvables because of integrability. Dephasing makes some correlations invisible in the local observables, but they are still present in the system.
We consider also the linear response limit: when the amplitude of the perturbation is vanishingly small, the Floquet diagonal ensemble is not sufficient to describe the asymptotic condition given by LRT.
For every small but finite amplitude, there are quasi-degeneracies in the Floquet spectrum giving rise to pre-relaxation to the condition predicted by Linear Response; these phenomena are strictly related to energy absorption and boundedness of the spectrum
Erratum: Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian [Phys. Rev. B 105, 064305 (2022)]
Full text linkCorrection to https://dx.doi.org/10.1103/PhysRevB.105.064305
Floquet resonances close to the adiabatic limit and the effect of dissipation
No full textWe study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in cannot be given, because of the singularity of the zero frequency limit, we are able to describe this phenomenon by means of a mapping to an extended Hilbert space, in terms of resonances of an effective two-band Wannier-Stark ladder. Remarkably, the phenomenon survives in presence of dissipation towards an environment and can be therefore easily experimentally observed
Many-Body Synchronization in a Classical Hamiltonian System
Full text linkWe study synchronization between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with a period twice the driving period (synchronized regime) and a regime where the oscillations die after a finite transient (chaotic regime). We emphasize the peculiarity of our result, having been synchronization observed so far only in driven-dissipative systems. We discuss how our findings can be interpreted as a period-doubling time crystal and we show that synchronization can appear both for an overall regular and overall chaotic dynamics
Signatures of many-body localization in the dynamics of two-site entanglement
Full text linkWe are able to detect clear signatures of dephasing—a distinct trait of many-body localization (MBL)—via the dynamics of two-site entanglement, quantified through the concurrence. Using the protocol implemented by M. Schreiber et al. [Science 349, 842 (2015)], we show that in the MBL phase the average two-site entanglement decays in time as a power law, while in the Anderson localized phase it tends to a plateau. The power-law exponent is not universal and displays a clear dependence on the interaction strength. This behavior is also qualitatively different from the ergodic phase, where the two-site entanglement decays exponentially. All the results are obtained by means of time-dependent density matrix renormalization-group simulations and further corroborated by analytical calculations on an effective model. Two-site entanglement has been measured in cold atoms: our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase
Erratum: Asymptotic work statistics of periodically driven Ising chains (Journal of Statistical Mechanics: Theory and Experiment (2016))
No full textThe quantum Ising chain for beginners
Full text linkWe present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. In particular, we analyse the form of the ground state and excitations of the model, relating them to the symmetry-breaking physics, and illustrate aspects connected to calculating dynamical quantities, thermal averages, correlation functions and entanglement entropy. A few problems provide simple applications of the techniques
Thermalization propagation front and robustness against avalanches in localized systems
No full textWe investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a T=∞ thermal bath through its leftmost site. By analyzing local magnetizations we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower-bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance - a global quantity measuring localization - thermalizes over a timescale that is exponential both in disorder strength and system size is in agreement with these results
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