The Friedel sum rule at Fano resonances

Area of Science:

• Quantum mechanics
• Mesoscopic physics
• Condensed matter theory

Background:

• Thermodynamic and transport properties of mesoscopic systems are crucial for understanding quantum phenomena.
• In non-chaotic or non-ergodic systems, these properties are independent of the impurity-averaged density of states.
• Traditional methods often require detailed knowledge of the quantum mechanical potential and interior wavefunctions.

Purpose of the Study:

• To demonstrate that partial and total density of states can be precisely calculated from asymptotic wavefunctions.
• To show that experimental determination of these properties is possible without knowledge of the system's interior.
• To establish novel relations for determining system properties.

Main Methods:

• Utilizing the asymptotic wavefunction or scattering matrix at resonances.
• Applying derived counterintuitive relations.
• Focusing on systems that are non-chaotic or non-ergodic.

Main Results:

• Exact determination of the partial density of states for a given impurity configuration.
• Exact determination of the density of states from asymptotic wavefunctions.
• Experimental accessibility of asymptotic wavefunctions without interior system knowledge.

Conclusions:

• The study provides a novel method for characterizing mesoscopic systems.
• It simplifies the experimental determination of thermodynamic and transport properties.
• The findings offer new insights into the behavior of non-chaotic and non-ergodic quantum systems.