Related papers: Operator Spreading in Quantum Maps
We study operator scrambling in quantum circuits built from `super-Clifford' gates. For such circuits it was established in arXiv:2002.12824 that the time evolution of operator entanglement for a large class of many-body operators can be…
Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an…
In this study, we explore the interplay between $\mathcal{PT}$-symmetry and quantum chaos in a non-Hermitian dynamical system. We consider an extension of the standard diagnostics of quantum chaos, namely the complex level spacing ratio and…
Understanding how and whether local perturbations can affect the entire quantum system is a fundamental step in understanding non-equilibrium phenomena such as thermalization. This knowledge of non-equilibrium phenomena is applicable for…
According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that…
Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is…
The operator wavefunction provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature this wavefunction can acquire a phase that…
Boundary time crystals (BTCs) are prominent examples of continuous time crystals in collective spin systems governed by Lindbladian evolution. To date, their analysis has mostly relied on semiclassical and numerical approaches. Here, we…
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined…
Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of…
We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Out-of-time-ordered correlators (OTOC) have been extensively used as a major tool for exploring quantum chaos and also recently, there has been a classical analogue. Studies have been limited to closed systems. In this work, we probe an…
For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper we analyse the…
We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give…
The question of thermalization in quantum many-body systems has long been studied through the properties of matrix elements of operators corresponding to local observables. More recently, the focus has shifted to the dynamics of operators,…
The Floquet operator, defined as the time-evolution operator over one period, plays a central role in the work presented in this thesis on periodically perturbed quantum systems. Knowledge of the spectral nature of the Floquet operator…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
We analyze a randomly perturbed quantum version of the baker's transformation, a prototype of an area-conserving chaotic map. By numerically simulating the perturbed evolution, we estimate the information needed to follow a perturbed…
We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical stochastic process. Thus we are able to study many dynamical properties at finite…