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Updated: Jun 8, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Universality of spectra for interacting quantum chaotic systems
Wojciech Bruzda1, Marek Smaczyński, Valerio Cappellini
1Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, 30-059 Kraków, Poland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Quantum systems undergoing periodic measurements exhibit universal spectral behavior. Eigenvalues reveal convergence to a stable state, dependent on measurement complexity and system dimension.
Area of Science:
- Quantum dynamics
- Quantum information theory
- Statistical mechanics
Background:
- Quantum systems are susceptible to environmental interactions, leading to decoherence.
- Quantum measurements can be modeled as periodic interactions with a measurement device.
- Classical chaos and strong decoherence significantly influence quantum system evolution.
Purpose of the Study:
- To analyze the spectral properties of a quantum dynamical system under periodic environmental interaction.
- To understand the universal behavior of quantum system spectra under strong chaos and decoherence.
- To connect spectral properties to the convergence rate of quantum states.
Main Methods:
- Analysis of a model quantum dynamical system.
- Investigation of the evolution operator's spectra.
- Mathematical modeling using random quantum maps and random Ginibre matrices.
- Asymptotic analysis in the limit of large dimensions.
Main Results:
- Universal spectral behavior observed under strong chaos and decoherence.
- A single eigenvalue of unity corresponds to the invariant state.
- Other eigenvalues form a disk in the complex plane, determining convergence speed.
- Spectral properties are characteristic of random quantum maps and real random Ginibre matrices.
Conclusions:
- The spectral properties provide insights into quantum measurement processes.
- The convergence rate to the invariant state is quantifiable and depends on measurement operators.
- The study establishes a connection between quantum dynamics, random matrix theory, and quantum information.
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