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Spectral behavior of contractive noise.
Gabriel G Carlo1, Alejandro M F Rivas, María E Spina
1Departamento de Física, CNEA, Libertador 8250, C1429BNP Buenos Aires, Argentina.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
We investigated quantum systems with contractive noise, finding that long-lived resonances increase with a power law. This growth surprisingly lacks correlation with the classical attractor
Area of Science:
- Quantum mechanics
- Quantum chaos
- Spectral analysis
Background:
- Investigating quantum systems under environmental influence is crucial for understanding open quantum systems.
- Contractive noise conserves total probability while reducing accessible phase space.
- Previous theories, like the fractal Weyl law, predict relationships for open systems with probability loss.
Purpose of the Study:
- To analyze the spectral behavior of quantum systems subjected to contractive noise.
- To determine the relationship between long-lived resonances and system parameters under such noise.
- To compare findings with existing theories, specifically the fractal Weyl law.
Main Methods:
- Spectral analysis of quantum systems.
- Modeling systems under contractive noise conditions.
- Comparison with classical attractors and fractal dimensions.
Main Results:
- The number of long-lived resonances exhibits power-law growth with parameter 'h'.
- A surprising lack of correlation was found between the power-law exponent and the fractal dimension of the classical attractor.
- This finding contradicts predictions from the fractal Weyl law for open systems.
Conclusions:
- Contractive noise leads to a distinct behavior of spectral resonances compared to systems with probability loss.
- The fractal Weyl law's applicability is limited, particularly under conditions of conserved total probability.
- Further theoretical development is needed to explain resonance behavior in systems with contractive noise.
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