Fixed points of the dissipative Hofstadter model

Area of Science:

• Condensed matter physics
• Statistical mechanics

Background:

• Dissipative particle dynamics in periodic potentials are fundamental to understanding various physical phenomena.
• The influence of magnetic fields on such systems can lead to complex behaviors.

Purpose of the Study:

• To investigate the phase diagram of a dissipative particle in a periodic potential and magnetic field.
• To characterize the system's behavior in the weak barrier and tight binding regimes.

Main Methods:

• Analysis of the phase diagram in specific limits (weak barrier, tight binding).
• Investigation of the system's behavior at half flux per plaquette.
• Utilizing a combination of exact and variational methods.

Main Results:

• The system's physics is governed by a nontrivial fixed point across a broad range of dissipation values.
• An intermediate energy scale was identified, separating different physical regimes.
• The fixed point was characterized using combined analytical techniques.

Conclusions:

• The study reveals a robust fixed point dictating system behavior under specific conditions.
• The identified energy scale provides insight into the transition between weak coupling and tight binding physics.
• The findings contribute to the understanding of driven-dissipative quantum systems.