Search results for "Level crossing"
showing 7 items of 7 documents
Level-crossing rate and average duration of fades of non-stationary multipath fading channels
2017
The level-crossing rate (LCR) and average duration of fades (ADF) are important statistical quantities describing the fading behaviour of mobile radio channels. To date, these quantities have only been analysed under the assumption that the mobile radio channel is wide-sense stationary, which is generally not the case in practice. In this paper, we propose a concept for the analysis of the LCR and ADF of non-stationary channels. Rice's standard formula for the derivation of the LCR of wide-sense stationary processes is extended to a more general formula enabling the computation of the instantaneous LCR of non-stationary processes. The application of the new concept results in closed-form ex…
Dynamics of a two-state system through a real level crossing
2015
The dynamics of a two-state system whose energies undergo a real crossing at some instant of time is studied. At this instant, both the coupling and the detuning vanish simultaneously, which leads to an exact degeneracy of the eigenenergies of the system. It is found that the dynamics of the system is primarily determined by the manner in which the degeneracy occurs. This interesting behavior is reminiscent of a symmetry breaking process, since the totally symmetric situation occurring at the crossing is significantly altered by infinitesimal quantities, which remove the degeneracy, with very important dynamical implications from there on. A very simple analytical formula is derived, which …
Neutrino conversions in a polarized medium
1997
Electron polarization induced by magnetic fields can modify the potentials relevant for describing neutrino conversions in media with magnetic fields. The magnitudes of polarization potentials are determined for different conditions. We show that variations of the electron polarization along the neutrino trajectory can induce resonant conversions in the active-sterile neutrino system, but cannot lead to level crossing in the active-active neutrino system. For neutrino flavour conversions the polarisation leads only to a shift of the standard MSW resonance. For polarizations $\lambda \lsim 0.04$ the direct modifications of the potential (density) due to the magnetic field pressure are smalle…
Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions
2006
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of \alpha_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a…
Inverse square root level-crossing quantum two-state model
2020
We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-root function of time. This is a member of one of the five families of bi-confluent Heun models. We prove that this is the only non-classical exactly solvable field configuration among the bi-confluent Heun classes, solvable in terms of finite sums of the Hermite functions. The general solution of the two-state problem for this model is written in terms of four Hermite functions of a shifted and scaled argument (each of the two fundamental solutions presents an irreducible combination of two Hermite functions). We pr…
An Exact Solution for the Level-Crossing Rate of Shadow Fading Processes Modelled by Using the Sum-of-Sinusoids Principle
2008
Published version of an article in the journal: Wireless Personal Communications. The original publication is available at Springerlink. http://dx.doi.org/10.1007/s11277-008-9512-3 The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed …
An Exact Solution for the Level-Crossing Rate and the Average Duration of Fades of the Envelope of Sum-of-Cisoids Processes
2012
Authors version of an article published in the journal: Procedia Technology. Also available from the publisher at: http://dx.doi.org/10.1016/j.protcy.2012.03.004 Sum-of-cisoids (SOC) processes provide a physically and numerically appealing framework for the modelling and simulation of a wide class of mobile radio channels. This paper is concerned with the problem of finding a general solution for the level-crossing rate (LCR) and the average duration of fades (ADF) of the envelope of SOC processes. Exact expressions are derived for the LCR and the ADF by taking into account that the inphase component, the quadrature component, and the time derivatives of the inphase and quadrature component…