Related papers: Time-Varying Spectrum of the Random String

In this paper, we present an exact formalism for transient current-current correlations and transient noise spectra. The exact solution of transient current correlations in both the time domain and the frequency domain are obtained. Without…

We generalize the Lewis-Riesenfeld technique of solving the time-dependent Schrodinger equation to cases where the invariant has continuous eigenvalues. An explicit formula for a generalized Lewis-Riesenfeld phase is derived in terms of the…

We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…

We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency,…

A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…

This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…

The generation of a streaking spectrogram is based on energy absorption from the streaking laser. Investigating this absorption we show rigorously under which condition the measured time shift is independent of properties of the streaking…

Spectrum sensing is a fundamental operation in cognitive radio environment. It gives information about spectrum availability by scanning the bands. Usually a fixed amount of time is given to scan individual bands. Most of the times,…

We construct a time-dependent solution in vacuum string field theory and investigate whether the solution can be regarded as a rolling tachyon solution. First, compactifying one space direction on a circle of radius R, we construct a…

The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.

We study the evolution, the transverse spreading and the subsequent thermalization of string states in the Weyl static axisymmetric spacetime. This possesses a singular event horizon on the symmetry axis and a naked singularity along the…

In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…

In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…

We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We…

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…

Based on the eigenvalue idea and the time-varying weighted vector norm in state space we construct here the lower and upper bounds on the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the…

Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…