Open quantum systems and Random Matrix Theory

Abstract

A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the ${\Delta }_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and ${\Delta }_3(L)$ statistic exhibit the signatures of missed levels.

15 pages, 9 figures

References in corpus (12)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering
• Missing levels in correlated spectra
• Superradiance Transition in Transport Through Nanosystems
• S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances
• Nuclear Structure, Random Interactions and Mesoscopic Physics
• Geometric chaoticity leads to ordered spectra for randomly interacting fermions
• Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
• Interplay of superradiance and disorder in the Anderson Model
• Resonance width distribution for open quantum systems
• A maximum likelihood method to correct for missed levels based on the ${\Delta }_3(L)$ statistic

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• Test of the Porter-Thomas distribution with the total cross section autocorrelation function