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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Strong zero modes (SZMs) are conserved operators found in quantum spin chains.
  • SZMs contribute to long coherence times for edge spins in quantum systems.

Purpose of the Study:

  • To define and analyze classical stochastic analogues of strong zero modes.
  • To investigate the properties and implications of these operators in classical systems.

Main Methods:

  • Focus on one-dimensional classical stochastic systems with single occupancy and nearest-neighbor transitions.
  • Analysis of particle hopping, pair creation, and annihilation processes.
  • Determination of exact SZM operator forms for integrable parameters.

Main Results:

  • Identified and characterized strong zero modes in classical stochastic chains.
  • Demonstrated that stochastic SZMs are generally nondiagonal in the classical basis.
  • Discovered exact relations between time-correlation functions due to stochastic SZMs, absent in systems with periodic boundaries.

Conclusions:

  • Stochastic SZMs exhibit distinct dynamical consequences compared to their quantum counterparts.
  • The presence of stochastic SZMs leads to unique, conserved properties in classical stochastic systems.
  • These findings offer new insights into conserved quantities in classical statistical physics.