Related papers: Quantum transfer operators and chaotic scattering
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…
Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties…
Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of…
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…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
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 connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has…
Future quantum computers may serve as a tool to access non-perturbative real-time correlation functions. In this talk, we discuss the prospects of using these to study Compton scattering for arbitrary kinematics. The restriction to a…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…
We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…