Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks [PDF]
arXiv.org, 2022 As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.
Winfried Lotzsch +2 more
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Retarded time superposition principle and the relativistic collision operator [PDF]
, 1981 Hizanidis, K., Molvig, K., Swartz, K.
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Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion [PDF]
, 2002 We show that the effective diffusivity matrix $D(V^n)$ for the heat operator $\partial_t-(\Delta/2-\nabla V^n \nabla)$ in a periodic potential $V^n=\sum_{k=0}^n U_k(x/R_k)$ obtained as a superposition of Holder-continuous periodic potentials $U_k$ (of ...
Ben-Arous, Gérard, Owhadi, Houman
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Weighted superposition operators on Fock spaces [PDF]
RACSAM, 2022 We characterize all pairs of entire functions (u,ψ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}
Tesfa Mengestie
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Quantum state engineering by a coherent superposition of photon subtraction and addition [PDF]
, 2010 We study a coherent superposition of field annihilation and creation operator acting on continuous variable systems and propose its application for quantum state engineering.
Lee, Su-Yong, Nha, Hyunchul
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Intertwiner entanglement excitation and holonomy operator [PDF]
Classical and quantum gravity, 2022 In the loop quantum gravity framework, spin network states carry entanglement between quantum excitations of the geometry at different space points.
Qiang Chen, E. Livine
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Coherent and incoherent superposition of transition matrix elements of the squeezing operator
New Journal of Physics, 2022 We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation).
Sándor Varró
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Coulomb solutions from improper pseudo-unitary free gauge field operator translations [PDF]
, 2014 Fundamental problems of quantum field theory related to the representation problem of canonical commutation relations are discussed within a gauge field version of a van Hove-type model.
Aste, Andreas
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Demonstratio Mathematica, 2014 We prove that if a superposition operator maps a subset of the space of all metric-vector-space-valued-functions of bounded n-dimensional Φ-variation into another such space, and is uniformly continuous, then the generating function of the operator is an
Bracamonte Mireya +3 more
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Does gravity induce wavefunction collapse? An examination of Penrose's conjecture [PDF]
, 2013 According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g.
Gao, Shan
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