Scaling at the chaos threshold for interacting electrons in a quantum Dot

Area of Science:

• Quantum mechanics
• Many-body physics
• Statistical mechanics

Background:

• Investigates the complex behavior of many-electron Fock states within confined geometries.
• Focuses on the phenomenon of chaotic mixing driven by random two-body interactions.

Purpose of the Study:

• To distinguish between different regimes of Fock state mixing based on interaction strength, excitation energy, and level spacing.
• To characterize the transition to chaotic mixing and identify the governing scaling parameter.

Main Methods:

• Analysis of Fock state mixing in a confined system.
• Distinguishing between two primary regimes based on system parameters.
• Examination of scaling functions and their dependence on excitation energy.

Main Results:

• Identified two distinct regimes in the dependence of Fock state mixing on interaction strength (V), excitation energy (ε), and level spacing (Δ).
• Observed large-scale delocalization in Fock space across both regimes.
• Characterized the crossover region by a pronounced maximum in a scaling function, particularly with increasing excitation energy.
• Determined the scaling parameter governing the transition as (εV/Δ²)ln(Δ/V).

Conclusions:

• The study distinguishes between general Fock state delocalization and true chaotic mixing, which occurs only at high interaction strengths.
• The crossover region exhibits unique scaling behavior, highlighting the role of excitation energy.
• The identified scaling parameter provides a quantitative measure for the transition to chaos in these quantum systems.