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4
votes
2answers
357 views

How and why can random matrices answer physical problems?

Random matrix theory pops up regularly in the context of dynamical systems. I was, however, so far not able to grasp the basic idea of this formalism. Could someone please provide an instructive ...
1
vote
2answers
236 views

Non-linear dynamics of classical hydrogen atom

I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell ...
7
votes
2answers
831 views

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics?

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
5
votes
6answers
802 views

Could the Schrödinger equation be nonlinear?

Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity (QG) be ...
5
votes
2answers
217 views

Does the logistic map have an attractor for a particular value of the parameter?

Background: Currently I am studying a course on non-linear dynamics. We have been studying about attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple ...
4
votes
3answers
236 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? ...
2
votes
1answer
498 views

What is the amplitude of the limit cycle of the van der Pol oscillator?

In the second edition of Classical dynamics of particles and systems by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where ...
2
votes
0answers
320 views

Nonlinear refraction index of vacuum above Schwinger limit

This question is more about trying to feel the waters in our current abilities to compute (or roughly estimate) the refraction index of vacuum, specifically when high numbers of electromagnetic quanta ...
2
votes
1answer
214 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ ...
1
vote
1answer
103 views

Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal ...