Related papers: Equilibrium of disordered systems : constructing t…
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
There are several known constructions of equilibrium states for H\"older continuous potentials in the context of both subshifts of finite type and uniformly hyperbolic systems. In this article we present another method of building such…
The equilibrium properties of allocation algorithms for networks with a large number of nodes with finite capacity are investigated. Every node is receiving a flow of requests and when a request arrives at a saturated node, i.e. a node…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
The density-matrix renormalization-group (DMRG) algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the…
Polymer systems in slab geometries are studied on the basis of the recently presented Gaussian Ellipsoid Model [J. Chem. Phys. 114, 7655 (2001)].The potential of the confining walls has an exponential shape. For homogeneous systems in…
This paper introduces a deep learning-based super-resolution (SR) framework specifically developed for accurately reconstructing high-resolution velocity fields in two-way coupled particle-laden turbulent flows. Leveraging conditional…
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…
This paper originates from lectures delivered at the summer school "Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost)…
In this paper, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines the CDG framework with the sparse grid approach, with the aim…
One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization.…
Recently a novel real-space RG algorithm was introduced, identifying the relevant degrees of freedom of a system by maximizing an information-theoretic quantity, the real-space mutual information (RSMI), with machine learning methods.…
In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some…