Classical to quantum correspondence in dissipative directed transport

Area of Science:

• Quantum mechanics
• Statistical physics
• Nonlinear dynamics

Background:

• Dissipative systems exhibit complex behaviors organized by (quantum) isoperiodic stable structures.
• Previous studies focused on mean currents and asymptotic distributions, leaving spectral properties less explored.

Purpose of the Study:

• To compare quantum and classical properties of dissipative systems, specifically the dissipative modified kicked rotator.
• To investigate the spectral behavior of classical and quantum operators and uncover a correspondence mechanism.

Main Methods:

• Analysis of classical Perron-Frobenius operators with thermal noise.
• Study of quantum superoperators without thermal noise for small effective Planck's constant (ℏeff) values.
• Characterization of eigenvectors using Weyl-Wigner distributions.

Main Results:

• A remarkable similarity was found between the classical and quantum spectra.
• A classical-to-quantum correspondence mechanism was unveiled, despite differences in noise types.
• This correspondence holds for both simple and chaotic attractors, extending beyond asymptotic distributions.

Conclusions:

• The study demonstrates a universal classical-to-quantum correspondence mechanism in dissipative systems.
• Eigenvector analysis via Weyl-Wigner distributions aids in identifying similarities and differences.
• The findings suggest this mechanism is a general feature of dissipative systems.