Related papers: Dynamical Phase Transitions in a 2D Classical None…
We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of…
A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix".…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model.…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the…
The nonequilibrium dynamic phase transition in ferromagnetic systems is reviewed. Very recent results of dynamic transition in kinetic Ising model and that in Heisenberg ferromagnet is discussed.
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half-filling, long-time trajectories with a large enough imbalance…
Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…