TY - CHAP

T1 - Quantum Chaos

AU - Kam, Chon Fai

AU - Zhang, Wei Min

AU - Feng, Da Hsuan

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - In classical mechanics, chaos originates from nonlinearity and is extremely sensitive to initial conditions. For different but exceedingly close initial states could give rise to distinctly different states in the time evolution. It is in this sense that the results are nondeterministic. As linear quantum evolution includes classical physics as a limiting case, how chaos can be manifested in quantum dynamics thus becomes a puzzle. To this end, there are two ways of exploring quantum chaos. One is via the quantum-classical correspondence realization, and the other is the study of the universal level statistics of quantum systems whose classical counterparts are chaotic. In this chapter, we shall focus on the first approach as coherent states naturally connect quantum dynamics with classical mechanics. We shall discuss how a quantum system can be represented by the associated Lie group and spectral generating algebra, from which the concept of classical-like degrees of freedom can be defined, and the corresponding coset space of the coherent states can serve as the quantum counterpart of phase space. Meanwhile, quantum integrability can be defined via the concept of dynamical symmetry. Thus, the universal properties of quantum chaos associated with dynamical symmetry breaking are obtained within the framework of coherent state representation.

AB - In classical mechanics, chaos originates from nonlinearity and is extremely sensitive to initial conditions. For different but exceedingly close initial states could give rise to distinctly different states in the time evolution. It is in this sense that the results are nondeterministic. As linear quantum evolution includes classical physics as a limiting case, how chaos can be manifested in quantum dynamics thus becomes a puzzle. To this end, there are two ways of exploring quantum chaos. One is via the quantum-classical correspondence realization, and the other is the study of the universal level statistics of quantum systems whose classical counterparts are chaotic. In this chapter, we shall focus on the first approach as coherent states naturally connect quantum dynamics with classical mechanics. We shall discuss how a quantum system can be represented by the associated Lie group and spectral generating algebra, from which the concept of classical-like degrees of freedom can be defined, and the corresponding coset space of the coherent states can serve as the quantum counterpart of phase space. Meanwhile, quantum integrability can be defined via the concept of dynamical symmetry. Thus, the universal properties of quantum chaos associated with dynamical symmetry breaking are obtained within the framework of coherent state representation.

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U2 - 10.1007/978-3-031-20766-2_12

DO - 10.1007/978-3-031-20766-2_12

M3 - Chapter

AN - SCOPUS:85159956186

T3 - Lecture Notes in Physics

SP - 241

EP - 279

BT - Lecture Notes in Physics

PB - Springer Science and Business Media Deutschland GmbH

ER -