arXiv subjects

Matija Koterle

Publications and source records attributed to Matija Koterle.

3 recordsLinked to original sources

arXiv2026

Effective field theories of nonlinear fluctuating hydrodynamics in one dimension

Describing emergent macroscopic phenomena in low spatial dimensions is known to be notoriously challenging, primarily due to strong interactions that render perturbative approaches inapplicable. On the other hand, low-dimensional systems host a wealth of unorthodox phenomena. A prominent example is the emergence of superdiffusive transport in one-dimensional interacting systems, traditionally studied in the framework of nonlinear fluctuating hydrodynamics. After identifying and discussing internal inconsistencies in the previous formulations, in this work we develop a general and systematic approach for constructing effective field theories of one-dimensional hydrodynamic systems in the form of coupled stochastic Langevin-type equations compatible with the physical requirements of local equilibrium states such as the thermodynamic Maxwell relation and fluctuation-dissipation symmetry. We implemented a general numerical integration scheme and exemplified our construction on a simple model of two interacting hydrodynamic modes with a non-Gaussian stationary equilibrium measure.

cond-mat.stat-mech↗

arXiv2026

Ergodic behaviors in reversible 3-state cellular automata

Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of ergodic behavior, we perform a systematic study of three-state cellular automata (with a stable `vacuum' state and `particles' with $\pm$ charges). The classification is aided by the automata's different transformation properties under discrete symmetries: charge conjugation, spatial parity and time reversal. In particular, we propose a simple classification that distinguishes between types and levels of ergodic behavior in such system as quantified by the following observables: the mean return time, the number of conserved quantities, and the scaling of correlation functions. In each of the physically distinct classes, we present examples and discuss some of their phenomenology. This includes chaotic or ergodic dynamics, phase-space fragmentation, Ruelle-Pollicott resonances, existence of quasilocal charges, and anomalous transport with a variety of dynamical exponents.

cond-mat.stat-mech↗

arXiv2026

Anomalous transport in non-integrable classical field theories

Anomalous KPZ spin transport is well established in integrable non-Abelian lattice models but has not been investigated in continuum field theories as discretization in numerics generally break the continuum theory's integrability. We show that finite temperature acts as a regulator that can restore anomalous transport over a broad time window. In a family of spin field theories labeled by integer $n$, the $n = 1$ case is the Landau-Lifshitz model, whose numerical data shows spin superdiffusion with Kardar-Parisi-Zhang (KPZ) scaling and, at lower temperature ballistic energy transport, whereas both observables are diffusive at high temperature. The non-integrable $n = 2$ case shows the same crossover. While Lyapunov analysis confirms the model's non-integrability, the structure of spin-density space-time profiles suggests that long-lived soliton-like trajectories exist at low temperature.

cond-mat.stat-mech↗