Origin of the $1/f^{\alpha }$-Spectral-Noise in Chaotic and Regular Quantum Systems

Abstract

Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^{\alpha }$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving non-linear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent $\alpha$ takes the same value, $\alpha =2$, for both, fully chaotic and fully integrable systems.

5 pages, 2 figures

References in corpus (7)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Semiclassical propagator of the Wigner function
• Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems
• Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
• Spin dynamics of hopping electrons in quantum wires: algebraic decay and noise
• Time-domain scars: resolving the spectral form factor in phase space

Cited by in corpus (8)

• Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
• Signatures of a critical point in the many-body localization transition
• Power spectrum and form factor in random diagonal matrices and integrable billiards
• Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Correlated Dephasing Noise in Single-photon Scattering
• Power spectra and autocovariances of level spacings beyond the Dyson conjecture
• Multiclass classification of dephasing channels