Field-theoretic approach to metastability in the contact process

Area of Science:

• Statistical Physics
• Quantum Field Theory
• Network Dynamics

Background:

• The contact process is a fundamental model for phenomena like epidemic spread and population dynamics.
• Understanding its behavior on complex networks, especially in non-equilibrium steady states, is crucial.
• Mean-field approximations often fail to capture crucial network effects.

Purpose of the Study:

• To develop a quantum field-theoretic framework for the contact process on regular graphs.
• To investigate corrections to mean-field predictions using perturbation theory in 1/z.
• To compare theoretical predictions with numerical simulations on various lattice structures.

Main Methods:

• Introduction of a quantum field-theoretic formulation for the contact process dynamics.
• Perturbative expansion in powers of 1/z (inverse degree of the graph).
• Calculation of effective potentials and corrections to particle density distributions.
• Numerical simulations on D-dimensional hypercubic and Cayley lattices.

Main Results:

• A quantum field-theoretic approach successfully describes the contact process on regular graphs.
• Perturbative calculations yield corrections to the mean-field particle density in the out-of-equilibrium stationary state.
• The derived corrections accurately predict both typical properties (e.g., average density) and rare fluctuations (e.g., metastable state lifetime).

Conclusions:

• The quantum field-theoretic formulation provides a powerful tool for analyzing non-equilibrium systems on networks.
• The 1/z expansion offers a systematic way to improve upon mean-field approximations.
• Excellent agreement between theory and simulations validates the developed formalism for diverse lattice structures.