Related papers: Application of a renormalization group algorithm t…
Motivated by recent progress in the experimental development of quantum simulators based on Rydberg atoms, we introduce and investigate the dynamics of a class of $(1+1)$-dimensional quantum cellular automata. These non-equilibrium…
In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's "coupling from the past" approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
We design an optimal group boarding method using a stochastic cellular automata model for passenger movements, which is extended by a virus transmission approach. Furthermore, a new mathematical model is developed to determine an…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical…
We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
We consider a probabilistic cellular automaton to analyze the stochastic dynamics of a predator-prey system. The local rules are Markovian and are based in the Lotka-Volterra model. The individuals of each species reside on the sites of a…
Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from…
We propose a new concept upon the renormalization group (RG) procedure for an interacting many-electron correlated system in the framework of natural orbitals, and formulate an algorithm for this RG approach. To demonstrate its…
Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
We review the renormalization group method applied to non-equilibrium dynamics by tracing the way how the hydrodynamic equations can be derived as reduced dynamics of the Boltzmann equation as a typical example.