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Integrable dissipative exclusion process: Correlation functions and physical properties.

N Crampe1, E Ragoucy2, V Rittenberg3

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Summary
This summary is machine-generated.

We introduce a generalized exclusion process with particle creation and annihilation. This integrable model, driven by boundary reservoirs, allows exact calculation of its steady state and currents.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Integrable Systems

Background:

  • The symmetric simple exclusion process (SSEP) is a fundamental model in statistical mechanics.
  • Generalizations of SSEP are crucial for understanding complex driven systems.
  • Investigating non-equilibrium dynamics with particle creation/annihilation is key to new physical insights.

Purpose of the Study:

  • To study a one-parameter generalization of the SSEP on a 1D lattice.
  • To incorporate pair creation and annihilation dynamics alongside standard hopping.
  • To analyze the system's behavior under non-equilibrium conditions driven by boundary reservoirs.

Main Methods:

  • The model is shown to be integrable, related to the open XXZ spin chain via gauge transformation.
  • Bethe equations are employed to compute the full spectrum of the Markov matrix.
  • Matrix product form is used to express the stationary state.

Main Results:

  • Exact computation of the Markov matrix spectrum.
  • Derivation of multipoint correlation functions from the stationary state.
  • Calculation of lattice and creation-annihilation currents, and their variances.

Conclusions:

  • The generalized exclusion process remains integrable despite added complexity.
  • The stationary state allows for exact calculation of transport properties.
  • Finite-size variance of the lattice current converges to macroscopic fluctuation theory predictions in the thermodynamic limit.