Classical and Quantum Conway Game of Life - Methodologies and Applications

Explore the classical and quantum aspects of Conway's Game of Life in this 42-minute HyperComplex Seminar presentation. Delve into the mathematical foundations of cellular automata, examining stochastic variations and their quantum mechanical interpretations. Discover how the dissipative Schrödinger equation and tight-binding models can describe the game's dynamics, and investigate the thermodynamic properties emerging from these systems. Learn about complex-valued potentials, anomalous non-Hermitian Hamiltonians, and their role in mimicking the creation and annihilation processes in cellular automata. Analyze the diffusion of mass, energy, and temperature in the context of the second law of thermodynamics, and explore the concept of complex-valued mass. Gain insights into the equivalence between anomalous Fick's law and the dissipative Schrödinger equation. Study various methodologies for describing both classical and quantum versions of the Game of Life, including statistical physics approaches and functional data analysis techniques. Examine the evolution of probability distributions in one-dimensional systems and the mapping of stochastic processes to quantum mechanical frameworks. Investigate the determination of effective complex potentials and the parameterization of tight-binding Hamiltonians in the context of Conway's Game of Life.

Methodologies in description Classical and Quantum Conway Game of Life
Structures in the Classical Conway Game of Life (generated in the created simulator)
Rules of the Stochastic Conway Game of Life
Life expectancy of the population depending on the level of probability
Generalization of the Stochastic Conway Game of Life to the case of N species of cellular automata
Four competing cellular automata
Description of the dynamics of the Stochastic Gam of Life by using statistical physics methodology
Diffusion dynamics for a two-barrier system with two small holes in each barrier
Evolution of the probability distribution over time in a system with two sinusoidally moving barriers
The Complex Stochastic Game of Life as the prototype of the Quantum Game of Life (one-dimensional case)
Evolution of the probability distribution over time in the one-dimensional Complex Game of life
Mapping the Stochastic Game of Life to Quantum Mechanics methodology as an example of functional data analysis
Mapping the Stochastic Game of Life using quantum mechanics methodology (step 2)
Determination of the effective complex potential from the Schrödinger equation derived from the probability density occurring in a classical stochastic process (e.g. Stochastic Game of Life)
Determination of the effective complex potential of the Complex Game of Life using the Schrödinger equation
Tight-binding model in single-electron device
Parametrization of tight-binding Hamiltonian
Anomalous features of tight-binding model reproducing the behavior of Conway Game of Life
Summary of the obtained analytical and numerical results
Literature