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Integrable quantum systems of finite size are generically robust against weak enough integrability-breaking perturbations, but become quantum chaotic and thermalizing if the integrability-breaking is strong enough. We argue that the onset…
We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form…
Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging…
Using numerical simulations we investigate dynamical quantum chaos in isolated nuclear spin systems. We determine the structure of quantum states, investigate the validity of the Curie law for magnetic susceptibility and find the spectrum…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
The process tensor provides a general representation of a quantum system evolving under repeated interventions and is fundamental for numerical simulations of local many-body dynamics. In this work, we introduce the projected process…
Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body…
Quantum simulation elucidates properties of quantum many-body systems by mapping its Hamiltonian to a better-controlled system. Being less stringent than a universal quantum computer, noisy small- and intermediate-scale quantum simulators…
A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
The field of quantum chaos originated in the study of spectral statistics for interacting many-body systems, but this heritage was almost forgotten when single-particle systems moved into the focus. In recent years new interest emerged in…
Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not…
While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a…
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to…
Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit…
While traditionally regarded as an obstacle to quantum coherence, recent breakthroughs in quantum optics have shown that the dissipative interaction of a qubit with its environment can be leveraged to protect quantum states and synthesize…
We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Chaos makes isolated systems of many interacting particles quickly thermalize and forget about their past. Here, we show that quantum mechanics hinders chaos in many-body systems: although the quantum eigenstates are thermal and strongly…