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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Exploring quantum ergodicity of unitary evolution through the Krylov approach
Gastón F Scialchi1,2, Augusto J Roncaglia1,2, Carlos Pineda3
1Facultad de Ciencias Exactas y Naturales, Departamento de Física, Universidad de Buenos Aires, Buenos Aires 1428, Argentina.
Physical Review. E
|February 20, 2025
Summary
This study demonstrates how a new quantum ergodicity formulation robustly tracks the transition from integrability to chaos in quantum many-body systems, using examples from random matrix theory and spin chains.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- Characterizing quantum evolutions in many-body systems is crucial.
- Krylov complexity is a key tool for time-independent Hamiltonians.
- A new formulation based on the Arnoldi approach extends quantum ergodicity to unitary evolutions.
Purpose of the Study:
- To investigate the robustness of the Arnoldi-based formulation for quantum ergodicity.
- To demonstrate its capability in observing the transition from integrability to chaos.
- To apply this formulation to both autonomous and kicked quantum systems.
Main Methods:
- Utilizing an Arnoldi-based approach to define quantum ergodicity for unitary dynamics.
- Analyzing quantum many-body systems, including kicked systems and Trotterized dynamics.
- Applying the formulation to systems described by random matrix theory and spin chains.
Main Results:
- The Arnoldi-based formulation effectively captures the transition from integrability to chaos.
- This method proves robust for both autonomous and time-dependent (kicked) systems.
- Demonstrated applicability across diverse physical models.
Conclusions:
- The proposed formulation offers a powerful and robust tool for studying quantum chaos.
- It provides new insights into quantum ergodicity in interacting many-body systems.
- The findings are relevant for understanding complex quantum dynamics.
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