Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog.

Area of Science:

• Quantum Mechanics
• Theoretical Ecology
• Statistical Physics

Background:

• The Lotka-Volterra (LV) model describes predator-prey population dynamics.
• Classical Hamiltonian mechanics is often used to study LV dynamics.
• Understanding quantum effects in biological systems is an emerging area.

Purpose of the Study:

• To investigate LV dynamics within an extended Weyl-Wigner (WW) quantum mechanics framework.
• To explore the coexistence of classical and quantum evolution.
• To quantify quantum analog effects on ecological models.

Main Methods:

• Utilizing the Heisenberg-Weyl noncommutative algebra ([x,k]=i).
• Interpreting canonical variables in terms of LV variables (y=e^{-x}, z=e^{-k}).
• Analyzing Wigner currents for thermodynamic and Gaussian quantum ensembles.

Main Results:

• The WW framework allows for the identification of classical and quantum evolution coexistence.
• Quantum features introduce corrections to the classical phase-space patterns of LV dynamics.
• Wigner flow precisely profiles quantum modifications for Gaussian ensembles, enabling comparison of quantum and classical regimes.

Conclusions:

• The developed WW framework provides a method for studying quantumlike effects in competitive biosystems.
• Gaussian quantum ensembles serve as a suitable configuration for comparing quantum and classical dynamics.
• This approach extends the understanding of quantum influences on microscopic biological interactions.