Related papers: A Geometrical Interpretation of Frequency
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…
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…
A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
In this note the noncommutative geometry is interpreted as a functor, whose range is a family of the operator algebras. Some examples are given and a program is sketched.
For particles in an anharmonic potential, classical mechanics asserts that there is a renormalization of the bare frequency of the oscillatory motion, and statistical mechanics claims that the anharmonicity causes a correction to the heat…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies…
We present here an explicit form of the random spectral measure element, what allows us to express a stationary random field as a stochastic integral explicitly depending on its power spectrum and a spectral tensor if the field is a vector…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…
The basic notions related to coherence phenomena are formulated. Two types of coherence are described, state coherence and transition coherence. Useful characteristics for quantifying coherence are defined, such as coherence functions,…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
The semi-velocity is defined as an exponential function of the rapidity. Physically the semi-velocity is interpreted as the relativistic analogue of the phase velocity, a geometrical interpretation done within the framework of…
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
Coherent fraction is a concept widely used in the synchrotron radiation community. Here I discuss the meaning of coherent fraction, an accurate way to define it, and the different formulations found in literature to calculate it. After…
Pulse filtering through a medium with infinite periodic structure in transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose widths of transmitting and…
The paper proposes a novel general definition of coherency among power system devices of any type. The proposed approach is thus not limited to synchronous machines. With this aim, the paper shows that coherency can be formally based on the…