Stohastična deformacija pravila 54

Koterle, Matija (author), Prosen, Tomaž (mentor)

V delu se osredotočimo na numerične metode za raziskovanje enodimenzionalnih mnogodelčnih sitemov v obliki matrično produktnih stanj. Model, ki ga obravnavamo v nalogi je t.i. celični avtomat pravilo 54, ki je v zadnjih letih postal popularen mikroskopski model, saj je zanj mogoče točno izračunati mnogo paradigem statistične mehanike. Iz preliminarnih rezultatov se zdi, da so zaradi posebnih integrabilnostnih lastnosti raziskovalno zanimive t.i. deformacije pravila 54, ki dovolijo dodatne procese. Posebej se posvetimo matrično produktni formulaciji neravovesnih stacionarnih stanj pravila 54 in njegovih deformacij, ki jih raziskujemo s pomočjo numeričnih metod za časovni razvoj mnogodelčnih sistemov (algoritem TEBD).

• Language: Slovenian
• Keywords: celični avtomati, neravnovesna stacionarna stanja, matrično produktna stanja, algoritem TEBD
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-148493
• COBISS.SI-ID: 165119235
• Publication date in RUL: 25.08.2023

KOTERLE, Matija, 2023, Stohastična deformacija pravila 54 [online]. Master’s thesis. [Accessed 25 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=148493

Secondary language

• Language: English
• Title: Stochastic deformations of Rule 54

Abstract

In this work we focus on numerical methods used for studying one-dimensional many-body systems as matrix product states. We begin by considering the recently popular microscopic model, the reversible cellular automaton Rule 54, for which many paradigms of statistical mechanics may be solved exactly. Preliminary results show that rule 54 may be deformed by addition of new rules in a stochastic manner whilst preserving integrability of the model. We study the non-equilibrium steady states of rule 54 and primarily its stochastic deformations in the matrix product formulation by use of numerical methods such as time evolving block decimation.

• Keywords: cellular automata, non-equilibrium steady state, matrix product states, TEBD