Related papers: Complex Frequency as Generalized Eigenvalue
We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP),…
We completely characterize the conditions under which a complex unitary number is an eigenvalue of the non-backtracking matrix of an undirected graph. Further, we provide a closed formula to compute its geometric multiplicity and describe…
Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
Quaternion-valued signals along with quaternion Fourier transforms (QFT)provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
In the complex plane, the frequency response of a univariate polynomial is the set of values taken by the polynomial when evaluated along the imaginary axis. This is an algebraic curve partitioning the plane into several connected…
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…
The invariance principle, through which the steady-state behavior of nonlinear systems was introduced by Isidori and Byrnes, is leveraged in this article to bring forth a unifying characterization of the frequency response of nonlinear…
Rabi frequencies for multiphoton absorption by atoms or molecules that can be characterized as two- or three-level systems are obtained in the cases of single and double laser perturbations. If the ambiguity in the origin of absolute energy…
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…
Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The…
A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of…