相关论文: Complexity Growth in Integrable and Chaotic Models
Chaotic instability in many-body systems is commonly quantified by the largest Lyapunov exponent, yet general constraints on its magnitude in classical interacting systems remain poorly understood. Here we establish explicit,…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…
The equational complexity function $\beta_\mathscr{V}:\mathbb{N}\to\mathbb{N}$ of an equational class of algebras $\mathscr{V}$ bounds the size of equation required to determine membership of $n$-element algebras in $\mathscr{V}$. Known…
In this dissertation we examine the relationships between the several hierarchies, including the complexity, $\mathrm{LUA}$ (Linearly Universal Avoidance), and shift complexity hierarchies, with an eye towards quantitative bounds on growth…
We consider a natural front evolution problem the East process on $\mathbb{Z}^d, d\ge 2,$ a well studied kinetically constrained model for which the facilitation mechanism is oriented along the coordinate directions, as the equilibrium…
A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief…
The Sachdev-Ye-Kitaev (SYK) model is a system of $N$ Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence…
Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Studies of random unitary circuits have shown that the calculation of Renyi entropies of entanglement can be mapped to classical statistical mechanics problems in spacetime. In this paper, we develop an analogous spacetime picture of…
We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model.…
One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to…
We investigate the conjugacy growth of finitely generated linear groups. We show that finitely generated non-virtually-solvable subgroups of GL_d have uniform exponential conjugacy growth and in fact that the number of distinct polynomials…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Non-uniform rates of morphological evolution and evolutionary increases in organismal complexity, captured in metaphors like "adaptive zones", "punctuated equilibrium" and "blunderbuss patterns", require more elaborate explanations than a…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…