相关论文: Quasiclassical Calculations in Beam Dynamics

The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (WPs) which originate from polynomial splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs…

The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave…

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…

The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…

The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…

In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…

We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…

In this thesis concrete quantum systems are investigated in the framework of the environment induced decoherence. The focus is on the dynamics of highly nonclassical quantum states, the Wigner function of which are negative over some…

The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…

A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…

We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then…

In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in…

To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the…

A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…

We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the…