Assistant Professor CHEW Lock Yue
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PAP 521: Nonlinear Dynamics

Course Instructor

Assistant Professor CHEW Lock Yue
Emal: lockyue@ntu.edu.sg
Office: SBS B3 N-10
Tel: 6316-2968
webpage: http://www.ntu.edu.sg/home/lockyue/

Course Description

This module provides students with concepts and theories on nonlinear dynamical systems both in the classical and the quantum domain. 

Through this course, the student will come to appreciate the beautiful parallels between methods in nonlinear dynamics and thermodynamics; and gain a new perspective on quantum mechanics by studying quantum systems that correspond to classically chaotic systems.

By working on a term project, the students will acquire the skills to investigate into interesting problems within the area of nonlinear science, and to formulate and answer questions that are of both theoretical and practical importance.

Aims and Objectives

1) To provide a good understanding of theoretical approaches employed in the studies of nonlinear dynamical systems.

2) To build a firm foundation for more advanced study and research in the area of nonlinear science and complex systems.

3) To apply the advanced concepts learnt to further understand and create novel mesoscopic and nanoscopic structures.

Syllabus

1) Essentials of nonlinear dynamics: nonlinear mappings and their dynamical properties; probability measure in chaotic systems; symbolic dynamics; chaos and stochastic processes; Brownian diffusion versus deterministic diffusion.

2) Thermodynamics of chaotic systems: information measures; generalized canonical distributions; escort distributions; multifractals; the Rényi entropies; Lyapunov exponents.

3) Hamiltonian chaos: Hamilton-Jacobi theory; perturbation of integrable systems; KAM tori; strongly chaotic systems; the succession of increasingly random systems.

4) Quantum chaos: Semiclassical physics; quantization of classically chaotic systems; Gutzwiller trace formula; dynamical zeta function; quantum chaos in mesoscopic and nanoscopic structures, e.g. quantum dot billiards, antidot lattices.
Appointment by Email.


Schedule of Lectures


Day Time Location
Tuesday 10:30 - 12:30 SBS B3 N-19
Thursday 12:30 - 14:30 SBS B3 N-19

Pre-requisites

PAP 352 Chaotic Dynamical Systems and PAP 441 Advanced Quantum Mechanics, or Division Approval.

Assessment

Tutorial assessment 20%, term project 70%, presentation 10%.

Textbook and References

1) Edward Ott, "Chaos in Dynamical Systems", Cambridge University Press (2002).

2) Christian Beck and Friedrich Schlögl, "Thermodynamics of chaotic systems: an introduction", Cambridge University Press (1995).

3) Martin C. Gutzwiller, "Chaos in classical and quantum mechanics" Springer (1991).

4) Predrag Cvitanović et al., "Classical and quamtum chaos: A cyclist treatise", http://www.nbi.dk/ChaosBook/.

5) Hans-Jürgen Stöckmann, "Quantum chaos:an introduction", Cambridge University Press (1999).

6) Kathleen T. Alligood, Tim D. Sauer and James A. Yorke, "Chaos: An Introduction to Dynamical Systems", Springer-Verlag (1996).

7) Steven H. Strogatz, "Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering", Addison-Wesley (1994).

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