Tag Eva-Maria Graefe

Entries 12 Total

On complexified mechanics and coquaternions

Dec 6, ’10 12:49 PM

Dorje C Brody, Eva-Maria Graefe

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and coquaternionic (split-signature analogue of quaternions) extensions of Hamiltonian mechanics are introduced, and are shown to offer a unifying framework for complexified classical and quantum mechanics. In particular, quantum theories characterised by complex Hamiltonians invariant under space-time reflection are shown to be equivalent to certain coquaternionic extensions of Hermitian quantum theories. One of the interesting consequences is that the space-time dimension of these systems is six, not four, on account of the structures of coquaternionic quantum mechanics.

http://arxiv.org/abs/1012.0757
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

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Wave packet evolution in non-Hermitian quantum systems

Oct 23, ’10 8:41 PM

Eva-Maria Graefe, Roman Schubert

Time evolution of the exact Wigner function at t=4The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase space metric—a phenomenon having no analogue in Hermitian theories. Furthermore, example studies show that the anti-Hermitian term can improve the accuracy of the classical approximation.

http://arxiv.org/abs/1010.4557
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

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