[Paper Review] Intrinsic Decoherence and Irreversibility in the Quasiperiodic Kicked Rotor

A. C. Sicardi Shifino, G. Abal+3 more|ArXiv.org|Aug 28, 2003

Quantum chaos and dynamical systems3 citations

TL;DR

This paper demonstrates that the quasiperiodic kicked rotor exhibits intrinsic decoherence and time irreversibility without coupling to an external environment, due to its dense frequency response spectrum. By perturbing the expectation value of quantum observables, the system displays exponential sensitivity to initial conditions—mirroring classical chaos—while maintaining unitary evolution, revealing a quantum mechanism for irreversibility distinct from environmental decoherence.

ABSTRACT

We show that some classically chaotic quantum systems uncoupled from noisy environments may generate intrinsic decoherence with all its associated effects. In particular, we have observed time irreversibility and high sensitivity to small perturbations in the initial conditions in a quasiperiodic version of the kicked rotor. The existence of simple quantum systems with intrinsic decoherence clarifies the quantum--classical correspondence in chaotic systems.

Motivation & Objective

• To investigate whether quantum systems can exhibit decoherence-like effects without coupling to an external noisy environment.
• To explore the emergence of time irreversibility and sensitivity to initial conditions in a quantum system with a dense frequency spectrum.
• To clarify the quantum-classical correspondence in chaotic systems by identifying intrinsic mechanisms for decoherence.
• To determine whether a dense quasienergy spectrum is necessary for intrinsic decoherence in classically chaotic quantum systems.

Proposed method

• The quasiperiodic kicked rotor is modeled with two incommensurate kick periods, leading to a time-dependent Hamiltonian with a dense frequency response spectrum.
• The system's dynamics are analyzed using a quantum map that evolves the wavefunction coefficients in angular momentum space via Bessel functions.
• Time reversal is simulated by evolving the system backward from a perturbed state, with perturbations applied to the expectation value of observables rather than the wavefunction directly.
• Sensitivity to perturbations is quantified by measuring the threshold perturbation size ε_th ≈ 1/ℓ_max, which decreases as ℓ_max increases with time.
• The evolution of the second moment ⟨n²⟩ is tracked to observe diffusion and reversibility, with time reversal applied at different evolution times to assess sensitivity.
• The comparison with the periodically kicked rotor—characterized by a discrete spectrum and dynamical localization—highlights the role of spectral density in enabling intrinsic decoherence.

Experimental results

Research questions

• RQ1 Can a quantum system isolated from its environment exhibit intrinsic decoherence and time irreversibility?
• RQ2 Is the dense frequency response spectrum of the quasiperiodic kicked rotor responsible for enabling intrinsic decoherence?
• RQ3 How does perturbing the expectation value of a quantum observable lead to large-scale wavefunction changes, mimicking classical chaos?
• RQ4 What is the role of dynamical localization in suppressing sensitivity to perturbations in systems with discrete spectra?
• RQ5 Does intrinsic decoherence in the quasiperiodic kicked rotor lead to irreversible dynamics similar to environment-induced decoherence?

Key findings

• The quasiperiodic kicked rotor exhibits persistent diffusion in angular momentum space due to its dense frequency response spectrum, preventing dynamical localization.
• Time reversal in the system leads to irreversible behavior when small perturbations are applied to the expectation value of observables, with the threshold perturbation size decreasing as ℓ_max increases over time.
• The system shows exponential sensitivity to initial condition perturbations when the perturbation is applied to the mean value of an observable, even though the wavefunction evolution remains unitary.
• The threshold perturbation ε_th ≈ 1/ℓ_max decreases with time, indicating increasing sensitivity as higher angular momentum modes become populated.
• In contrast, the periodically kicked rotor exhibits a fixed ε_th after localization, showing that a discrete spectrum suppresses long-term sensitivity.
• The results support the conjecture that a dense spectrum is necessary for intrinsic decoherence and irreversible dynamics in quantum chaotic systems.