Symmetry operations and critical behavior in classical to quantum stochastic processes.

Area of Science:

• Quantum physics
• Statistical mechanics
• Complex systems

Background:

• Classical stochastic processes can be modeled using quantum analogs.
• Quantum processes often exhibit simultaneous coherence generation and destruction.
• Markov chains are fundamental in modeling systems with memoryless transitions.

Purpose of the Study:

• To generate quantum extensions of classical Markov chains using symmetry operations.
• To investigate the distinct relaxation dynamics of these quantum extensions.
• To analyze the relationship between coherence and relaxation speed.

Main Methods:

• Constructing quantum analogs of classical stochastic processes via superpositions.
• Employing symmetry operations to create diverse quantum Markov chain extensions.
• Monitoring coherence, equilibrium probability, domain wall decay, and purity.

Main Results:

• Quantum extensions exhibit significantly different relaxation processes.
• Coherence, equilibrium probability, domain wall decay, and purity vary across extensions.
• A relationship is found between L1 norm coherence and relaxation speed.
• Finite-size scaling exists for coherence, with distinct critical exponents for short and long times.

Conclusions:

• Quantum extensions of Markov chains offer rich and varied dynamical behaviors.
• Coherence plays a crucial role in the relaxation dynamics of these quantum systems.
• The study provides insights into quantum information processing and condensed matter physics.