Related papers: Uncertainty principle for the two-sided quaternion…
The nondecimated or translation-invariant wavelet transform (NDWT) is a central tool in classical multiscale signal analysis, valued for its stability, redundancy, and shift invariance. This paper develops two complementary quantum…
Wiener-Khinchin theorem, the fact that the autocorrelation function of a time process has a spectral decomposition given by its power spectrum intensity, can be used in many disciplines. However, the applications based on a quantum…
This article develops a duality principle for non-linear elasticity. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation is concave. Moreover,…
Quaternionic Linear Canonical Transforms (QLCTs) are a family of integral transforms, which generalized the quaternionic Fourier transform and quaternionic fractional Fourier transform. In this paper, we extend the energy concentration…
Using the worldline quantum field theory (WQFT) formalism for classical scattering, we study the deflection of light by a heavy massive spinless/spinning object. WQFT requires the use of the worldline dressed propagator of a photon in a…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our…
Quantum fluctuations are fundamental in quantum technologies, affecting computing, sensing, cryptography, and thermodynamics. These include fluctuations in the variation of energy, charge, and other observables driven by interactions with…
We review the implementation of two QKD protocols (BB84 and B92) keeping in mind that their implementations do not easily satisfy the requirement of use of single photons. We argue that current models do not take into account issues raised…
In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_{\alpha}\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(\alpha \notin \pi \mathbb{Z}\). We demonstrate that…
The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a…
This paper presents quasilinear theory (QLT) for classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic, and gravitational effects are subsumed. A…
This study investigates uncertainty quantification (UQ) using quantum-classical hybrid machine learning (ML) models for applications in complex and dynamic fields, such as attaining resiliency in supply chain digital twins and financial…
We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincar\'e symmetry (with all 10 generators), as proposed in ref. [7]. This allows to formulate…
We investigate coherent backscattering of light by two harmonically trapped atoms in the light of quantitative quantum duality. Including recoil and Doppler shift close to an optical resonance, we calculate the interference visibility as…
In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules…
A two-mode optical parity-time (PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation.…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…