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From classical to quantum stochastic processes.

Gustavo Montes1,2,3, Soham Biswas1, Thomas Gorin1

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Summary
This summary is machine-generated.

This study introduces quantum analogs of classical stochastic processes by using path superpositions. These quantum analogs exhibit altered scaling behavior and can accelerate relaxation dynamics in systems like the Ising spin chain.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Classical stochastic processes govern systems with inherent randomness.
  • Understanding quantum effects on classical dynamics is crucial for developing new theories.
  • Ising spin chains are fundamental models in statistical mechanics.

Purpose of the Study:

  • To construct quantum analogs of classical stochastic processes.
  • To investigate the impact of quantum coherence on classical observables and dynamics.
  • To explore changes in relaxation and scaling behavior.

Main Methods:

  • Replacing random path choices in classical processes with quantum superpositions.
  • Analyzing nonunitary quantum evolution and coherence generation/destruction.
  • Applying the zero-temperature Glauber dynamics to a linear Ising spin chain.

Main Results:

  • Quantum analogs exhibit modified scaling behavior compared to classical counterparts.
  • Transient coherences can significantly alter observable scaling.
  • Quantum analogs of Glauber dynamics show different domain growth exponents.
  • In some cases, quantum analogs demonstrate faster relaxation than classical processes.

Conclusions:

  • Quantum analogs of stochastic processes can be constructed via path superpositions.
  • Quantum coherence, even transiently, influences classical system dynamics and scaling.
  • This approach offers new insights into quantum-classical transitions and relaxation phenomena.