Spatial-field correlation: the building block of mesoscopic fluctuations

Area of Science:

• Condensed matter physics
• Wave phenomena in disordered systems

Background:

• Mesoscopic systems often lack self-averaging, a property where system properties become independent of microscopic details.
• This absence is linked to complex correlations within the system's intensity patterns.

Purpose of the Study:

• To investigate the nature of long-range intensity correlations in mesoscopic systems.
• To elucidate the mathematical structure of the correlation function governing the absence of self-averaging.

Main Methods:

• Utilized microwave measurements to probe intensity correlations.
• Performed diagrammatic calculations to theoretically confirm and analyze the correlation function.

Main Results:

• The correlation function of normalized intensity was expressed as a sum of three distinct terms.
• Each term depends on the square of the field correlation function, F(E), and spatial displacements (ΔR, Δr).
• The leading term is the product F(ΔR)F(Δr), followed by terms proportional to the sum and a combination of products and sums.

Conclusions:

• Confirmed that long-range intensity correlations are responsible for the lack of self-averaging in mesoscopic systems.
• Provided a detailed mathematical framework for understanding these correlations and their impact on system behavior.