Related papers: A Geometrical Interpretation of Frequency
The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
There are several common conventions in use by the gravitational-wave community to describe the amplitude of sources and the sensitivity of detectors. These are frequently confused. We outline the merits of and differences between the…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the…
This work introduces a geometrical method for analyzing transient gravitational waves recorded at interferometric observatories. This approach is intended to aid in assessing the performance and sensitivity of next-generation detector…
We describe the interaction of surface acoustic waves with electrons in an array of quantum wires, patterned out of a two dimensional electron gas. Two specific geometries are considered, in which the surface acoustic wave travels parallel,…
Complex eigenfrequencies of the exterior of a scatterer are considered as signatures of the scatterer's shape. A parameter characterizing the ratio of the maximum transverse and longitudinal dimensions of a body is found.
We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of…
An axiomatic theory of classical nondissipative waves is proposed that is constructed based on the definition of a wave as a multidimensional oscillator. Waves are represented as abstract vectors $|\psi\rangle$ in the appropriately defined…
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the…
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…