Relevance of classical solutions to quantum theories

2005 ◽  
pp. 263-315
Author(s):  
J. L. Gervais
Keyword(s):  
Classical Solutions ◽  
Quantum Theories

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Strong coupling: resonant effects

2017 ◽  
Author(s):  
Alexey V. Kavokin ◽  
Jeremy J. Baumberg ◽  
Guillaume Malpuech ◽  
Fabrice P. Laussy
Keyword(s):  
Strong Coupling ◽  
Experimental Studies ◽  
Strong Coupling Regime ◽  
Theoretical Studies ◽  
Stimulated Scattering ◽  
Quantum Theories ◽  
Pump Probe ◽  
Exciton Polaritons ◽  
Linear Optical Properties ◽  
Experimental And Theoretical Studies

This chapter presents experimental studies performed on planar semiconductor microcavities in the strong-coupling regime. The first section reviews linear experiments performed in the 1990s that evidence the linear optical properties of cavity exciton-polaritons. The chapter is then focused on experimental and theoretical studies of resonantly excited microcavity emission. We mainly describe experimental configuations in which stimulated scattering was observed due to formation of a dynamical condensate of polaritons. Pump-probe and cw experiments are described in addition. Dressing of the polariton dispersion and bistability of the polariton system due to inter-condensate interactions are discussed. The semiclassical and the quantum theories of these effects are presented and their results analysed. The potential for realization of devices is also discussed.

scholarly journals Global classical solutions to the elastodynamic equations with damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mengmeng Liu ◽  
Xueyun Lin
Keyword(s):  
Initial Data ◽  
Periodic Boundary ◽  
Energy Estimate ◽  
Periodic Boundary Conditions ◽  
Deformation Tensor ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Weighted Energy ◽  
Global Classical Solutions ◽  
Weighted Energy Estimate

AbstractIn this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach is based on a time-weighted energy estimate, under the assumptions that the initial deformation tensor is a small perturbation around an equilibrium state and the initial data have some symmetry.

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

scholarly journals Generalised Kochen–Specker Theorem in Three Dimensions

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Václav Voráček ◽  
Mirko Navara
Keyword(s):  
Unit Sphere ◽  
Hidden Variables ◽  
Three Dimensions ◽  
Quantum Theories

AbstractWe show that there is no non-constant assignment of zeros and ones to points of a unit sphere in $$\mathbb{R}^3$$ R 3 such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.

scholarly journals FREQUENCY OF SEEING FUNCTIONS FOR INTENSITY DISCRIMINATION AT VARIOUS LEVELS OF ADAPTING INTENSITY

1951 ◽  
Vol 34 (4) ◽  
pp. 463-474 ◽  
Author(s):  
Conrad G. Mueller
Keyword(s):  
Human Subject ◽  
Intensity Discrimination ◽  
Quantum Theories ◽  
Foveal Stimulation

1. The percentage of times a human subject detects an increment (ΔI) in intensity was determined as a function of the magnitude of the increment and the magnitude of the stimulus (I) to which the increment is added. 2. Foveal stimulation was used, and five frequency of seeing curves were obtained at each of nine values of adapting intensity covering the range from –1.45 to 4.45 log photons. Each frequency of seeing curve shows the percentage of times an increment in intensity is detected as a function of the logarithm of the increment. 3. The slope of the frequency of seeing curve increases slightly with an increase in I and finally becomes independent of I at medium to high intensities. 4. The implications of the results for quantum theories of visual excitation are considered.

scholarly journals Spin and Dynamics in Relativistic Quantum Theories

2014 ◽  
Vol 56 (6-9) ◽  
pp. 395-399 ◽  
Author(s):  
W. N. Polyzou ◽  
W. Glöckle ◽  
H. Witała
Keyword(s):  
Relativistic Quantum ◽  
Quantum Theories
Sign in / Sign up

Export Citation Format

Share Document