Towards quantization Conway Game of Life

Krzysztof Pomorski; Dariusz Kotula

Home/Archive/arXiv

arXiv · 2306.15151

Towards quantization Conway Game of Life

Krzysztof Pomorski·Dariusz Kotula

View original source ↗Read source document ↗Export metadata ↓

Abstract

Classical stochastic Conway Game of Life is expressed by the dissipative Schr\"odinger equation and dissipative tight-binding model. This is conducted at the prize of usage of time dependent anomalous non-Hermitian Hamiltonians as with occurrence of complex value potential that do not preserve the normalization of wave-function and thus allows for mimicking creationism or annihilationism of cellular automaton. Simply saying time-dependent complex value eigenenergies are similar to complex values of resonant frequencies in electromagnetic resonant cavities reflecting presence of dissipation that reflects energy leaving the system or being pumped into the system. At the same time various aspects of thermodynamics were observed in cellular automata that can be later reformulated by quantum mechanical pictures. The usage of Shannon entropy and mass equivalence to energy points definition of cellular automata temperature. Contrary to intuitive statement the system dynamical equilibrium is always reflected by negative temperatures. Diffusion of mass, energy and temperature as well as phase of proposed wave function is reported and can be directly linked with second thermodynamics law approximately valid for the system, where neither mass nor energy is conserved. The concept of complex-valued mass mimics wave-function behavior. Equivalence an anomalous second Fick law and dissipative Schr\"odinger equation is given. Dissipative Conway Game of Life tight-binding Hamiltonian is given using phenomenological justification.

Explore related subjects

cond-mat.dis-nn cond-mat.mes-hall nlin.CG

Keep this discovery

BibTeX RIS

Krzysztof Pomorski, Dariusz Kotula. 2023-06-27. Towards quantization Conway Game of Life. https://arxiv.org/abs/2306.15151

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2026

Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions

In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct $ \{p,q\} $ tilings reveals one-parameter scaling collapses with a common critical exponent $ \nu\simeq1 $ within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.

cond-mat.dis-nn↗

arXiv2026

Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices

We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form $\mathbf{A}(\mathbf{I}+\mathbf{T})$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix, $\mathbf{T}$ is a finite-rank normal perturbation, and $\mathbf{I}$ denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--P\'ech\'e framework.

cond-mat.dis-nn↗