Related papers: A Unified Approach to Time-Frequency Representatio…
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is…
The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of…
We perform a Wigner analysis of Fourier integral operators (FIOs), whose main examples are Schr\"odinger propagators arising from quadratic Hamiltonians with bounded perturbations. The perturbation is given by a pseudodifferential operator…
The Wigner time delay, defined by the energy derivative of the total scattering phase shift, is an important spectral measure of an open quantum system characterising the duration of the scattering event. It is related to the trace of the…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
Quasicrystals are tempered distributions $\mu$ which satisfy symmetric conditions on $\mu$ and $\widehat \mu$. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In…
Wigner-type distributions have shown their effectiveness in classification problems of sonar and radar. We present an overview of applications where resonance features in echoes scattered from targets insonified or illuminated with short…
Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a…
In this note we study the properties of a sequence of approximate propagators for the Schr\"odinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a…
The integration of operator kernels with the Wigner distribution, first conceptualized by E. Wigner in 1932 and later extended by L. Cohen and others, has opened new avenues in time-frequency analysis and operator calculus. Despite…
We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2(\mathbb{R})$. To our knowledge, there is no other criterion…
The emergence of alternative multiplexing domains to the time-frequency domains, e.g., the delay-Doppler and chirp domains, offers a promising approach for addressing the challenges posed by complex propagation environments and…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many…
The Wigner-Smith (WS) time delay matrix relates a system's scattering matrix to its frequency derivative and gives rise to so-called WS modes that experience well-defined group delays when interacting with the system. For systems composed…
Moving detectors in relativistic quantum field theories reveal the fundamental entangled structure of the vacuum which manifests, for instance, through its thermal character when probed by a uniformly accelerated detector. In this paper, we…
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…
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.
The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…