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We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two…
In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
We present a formalism for studying the behaviour of quantum systems coupled to nonequilibrium environments exhibiting nonGaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations,…
We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In…
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame potential," which is minimized by unitary $k$-designs and measures the $2$-norm…
Understanding quantum chaos is of profound theoretical interest and carries significant implications for various applications, from condensed matter physics to quantum error correction. Recently, out-of-time ordered correlators (OTOCs) have…
We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic…
Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…
Periodically kicked Floquet systems such as the kicked rotor are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics there are several diagnostic measures of the presence of (or the transition to)…
Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and…
Precise qubit control in the presence of spatio-temporally correlated noise is pivotal for transitioning to fault-tolerant quantum computing. Generically, such noise can also have non-Gaussian statistics, which hampers existing…
We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…
We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two…
It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…
We use two models of nuclear collective dynamics - the geometric collective model and the interacting boson model - to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further…
We investigate the role of quantum monitoring in the dynamical manifestations of Hamiltonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under…
We study the control problem of regulating the purity of a quantum harmonic oscillator in a Gaussian state via weak measurements. Specifically, we assume time-invariant Hamiltonian dynamics and that control is exerted via the back-action…
Quantum weak chaos is studied in a perturbed degenerate system --- a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is…