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2018 | OriginalPaper | Chapter

Nonlinear Quantum Mechanics

Author : Björn Birnir

Published in: Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

Publisher: Springer International Publishing

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Abstract

We show that the nonlinear bifurcations found by simulations in single quantum wells in the terahertz regime [5, 6, 25] also occur in semiconductor superlattices (SSLs) in the gigahertz range [2, 3, 11]. The only exception is the second Hopf bifurcation to quasi-periodic orbits on a torus. The advantage of experiments on SSLs in the gigahertz range is that the experiments can be conducted at room temperature and a chaotic oscillator due to the random dressing of a period two-orbit has already been measured [31, 32]. We determine [42] that the route to chaos for SSLs in the sequential tunneling regime is the period doubling cascade. Shorter (10-period) superlattices are observed to exhibit faster oscillations compared with longer (50-period) ones. Two plateaus are observed as functions of the voltage bias, and intrinsically chaotic dynamics on the second plateau are possible only for shorter SSLs, while the dynamics in the first plateau contain intrinsic chaos only for longer (N > 50) SSLs [21].

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next chapter Chaotic Current Self-oscillations in Doped, Weakly Coupled Semiconductor Superlattices for True Random Number Generation
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Metadata
Title
Nonlinear Quantum Mechanics
Author
Björn Birnir
Copyright Year
2018
Book
Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

Print ISBN: 978-3-319-76598-3

Electronic ISBN: 978-3-319-76599-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-76599-0_1

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