Investigating finite-size effects in random matrices by counting resonances

Anton Kutlin, Carlo Vanoni
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)
2024-02-15 00:00:00
Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the notion of resonance is ill-defined, and the `number of resonances' does not have a direct mapping to any commonly used physical observable like the participation entropy, the fractal dimensions, or the gap ratios (r-parameter), restricting the method's predictive power to the thermodynamic limit only where it can be used for locating the Anderson localization transition. In this work, we reevaluate the notion of resonances and relate it to measurable quantities, building a foundation for the future application of the method to finite-size systems.
PDF: Investigating finite-size effects in random matrices by counting resonances.pdf
Empowered by ChatGPT