Related papers: Floquet operator dynamics and orthogonal polynomia…
We explore the connection between two seemingly distant fields: the set of cyclic functions $f$ in a Hilbert space of analytic functions over the unit disc $\D$, on the one hand, and the families of orthogonal polynomials for a weight on…
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces $L^2(\mu)$ with measures $\mu$ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics.…
We study the dynamics of atoms interacting periodically with a dissipative optical cavity and employ Floquet theory to analyze their low-frequency behavior. By means of an effective atom-only master equation, valid in the bad cavity regime,…
The spontaneous breaking of time translation symmetry in periodically driven Floquet systems can lead to a discrete time crystal. Here we study the occurrence of such dynamical phase in a driven-dissipative optomechanical system with two…
The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and…
We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the…
We explore the physics of scrambling in the moving mirror models, in which a two-dimensional CFT is subjected to a time-dependent boundary condition. It is well-known that by choosing an appropriate mirror profile, one can model quantum…
In this note, we present a well-known connection between the Sobolev-Slobodeckij spaces, also known as Fractional Sobolev spaces, and interpolation theory. We show how Sobolev spaces can be equivalently characterized as real and complex…
In this paper, we consider a new class of multi phase operators with variable exponents, which reflects the inhomogeneous characteristics of hardness changes when multiple different materials are combined together. We at first deal with the…
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
The theory of orthogonal polynomials on the unit circle (OPUC) dates back to Szeg\"o's work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his two-volume book [Si4], [Si5], the survey paper (or…
We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…
Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…
We study the radiative dynamics of coupled electric dipoles, modelled as Lorentz oscillators (LOs), in the presence of real-time mechanical oscillations. The dipoles are treated in a self-consistent way through a direct electromagnetic…
In this paper, we analyze the harmonically driven Jaynes-Cummings and Lipkin-Meshkov-Glick models using both numerical integration of time-dependent Hamiltonians and Floquet theory. For a separation of time-scales between the drive and…
This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the…
We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed…
We investigate the classical-quantum correspondence in the inverted harmonic oscillator (IHO) system. It is shown that the out-of-time-order correlators (OTOCs) which the initial states are located at any position in the IHO system possess…