Time reversal and charge echo in an electron gas

Area of Science:

• Physics
• Quantum Mechanics
• Thermodynamics

Background:

• Basic laws of physics exhibit time-reversal invariance, except for subtle CP symmetry violations.
• The macroscopic world demonstrates a distinct arrow of time, seemingly contradicting time-reversal invariant dynamics.
• The direction of time in closed systems is typically attributed to boundary or initial conditions.

Purpose of the Study:

• To investigate the theoretical possibility of reversing time evolution in physical systems.
• To identify conditions under which a system's dynamics could be made to evolve backward in time.
• To explore the potential for observing an electronic phenomenon analogous to the spin echo, termed a 'charge echo'.

Main Methods:

• Theoretical analysis of systems with time-reversal invariant Hamiltonians.
• Examination of the property THT(-1)=-H for a unitary transformation T.
• Utilizing calculations for a single-band tight-binding model.

Main Results:

• A system's Hamiltonian (H) possessing the property THT(-1)=-H under a unitary transformation (T) allows for backward time evolution in principle.
• The spin echo serves as a prototype for this time-reversed behavior.
• Calculations indicate the potential observation of a 'charge echo' in electronic systems.

Conclusions:

• The arrow of time, while evident macroscopically, may not be an absolute constraint on microscopic system dynamics.
• Systems with specific Hamiltonian properties can, in theory, be manipulated to evolve backward in time.
• The concept of a 'charge echo' presents a novel avenue for experimental investigation in condensed matter physics.