Quantum Theory

Hamiltonian systems: chaos and quantization by Alfredo M. Ozorio de Almeida

By Alfredo M. Ozorio de Almeida

This advent to the idea of Hamiltonian chaos outlines the most ends up in the sphere, and is going directly to ponder implications for quantum mechanics. The examine of nonlinear dynamics, and specifically of chaotic structures, is likely one of the quickest transforming into and best components in physics and utilized arithmetic. In its first six chapters, this well timed publication introduces the speculation of classical Hamiltonian structures. the purpose isn't to be entire yet, particularly, to supply a mathematical trunk from which the reader might be in a position to department out. the focus is on periodic orbits and their neighbourhood, as this method is mainly compatible as an creation to the consequences of the speculation of chaos in quantum mechanics, that are mentioned within the final 3 chapters.

Show description

Read Online or Download Hamiltonian systems: chaos and quantization PDF

Best quantum theory books

Reading Bohr: Physics and Philosophy (Fundamental Theories of Physics 152)

Examining Bohr: Physics and Philosophy bargains a brand new viewpoint on Niels Bohr's interpretation of quantum mechanics as complementarity, and at the relationships among physics and philosophy in Bohr's paintings, which has had momentous importance for our figuring out of quantum thought and of the character of data regularly.

Mathematical Methods in Physics

Physics has lengthy been considered as a wellspring of mathematical difficulties. Mathematical tools in Physics is a self-contained presentation, pushed via historical motivations, very good examples, particular proofs, and a spotlight on these elements of arithmetic which are wanted in additional formidable classes on quantum mechanics and classical and quantum box conception.

The Quantum Theory of Measurement

The superb accuracy in verifying quantum results experimentally has lately renewed curiosity in quantum mechanical size concept. during this ebook the authors provide in the Hilbert area formula of quantum mechanics a scientific exposition of the quantum conception of size. Their procedure contains the thoughts of unsharp objectification and of nonunitary variations wanted for a unifying description of varied specified investigations.

Motion Mountain – The Adventure of Physics. The quantum of change

A latest creation to physics,captivating, basic, with many color photos, animations and flicks, riddles and demanding situations. It covers mechanics, thermodynamics, relativity, quantum physics and glossy makes an attempt at unification.

Extra resources for Hamiltonian systems: chaos and quantization

Example text

23d) which substituting Eq. 23e) s in agreement with Eq. 23a). 24a) and the corresponding trace dynamics equation of motion of Eq. 15b). Thus, for Weyl-ordered Hamiltonians formed with c-number coefficients, we conclude that the trace dynamics equations of motion generated by H agree with the Heisenberg picture equations of motion generated by H , on an initial time slice on which the phase space variables are canonical. It is also evident that on this time slice [H, i] = 0. 24b) But since Eq. 24b) guarantees that the Heisenberg picture equations of motion preserve the canonical algebra on the next time slice, integrating forward in time step by step then implies that trace dynamics agrees with Heisenberg picture dynamics at all subsequent times, and therefore can be extended to a unitary dynamics in this case.

The example of Eq. 20c) required the use of two pairs of canonical variables q1,2 , p1,2 ; using our Weyl-ordering result, we shall now show that any trace dynamics for a single 36 Trace dynamics pair of bosonic variables q, p, when extended to the canonical algebra [q, p] = i, always can be represented as a unitary Heisenberg evolution. We shall proceed by induction, and assume that the result has been proved for any trace dynamics generated by a trace Hamiltonian H = TrH of degree n or less in p and q.

We conclude that as of this writing the localization model is favored, both because the assumptions needed to derive it within our framework are more robust, and because there are unresolved problems with the mechanisms that have been proposed to explain reduction in the energy-driven model. Finally, in Chapter 7 we indicate how our proposal for an emergent quantum theory addresses the motivational questions raised above in Section 3, and discuss some of the issues that will be relevant for future developments.

Download PDF sample

Rated 4.75 of 5 – based on 20 votes