Related papers: Equilibrium of disordered systems : constructing t…
In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled $n$-component $|\varphi|^4$ model under periodic boundary conditions in dimension $d \ge 4$. Both short-range and long-range interactions with…
The discontinuous Galerkin finite element method (DGFEM) developed by Rhebergen et al. (2008) offers a robust method for solving systems of nonconservative hyperbolic partial differential equations but, as we show here, does not…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller…
Flow equation methods, more generally known as Similarity Renormalization Group (SRG) techniques, were developed to address multiscale problems where multiple length or energy scales contribute simultaneously. In this Thesis, we formulate…
While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local…
The Ma-Dasgupta real-space renormalization methods allow to study disordered systems which are governed by strong disorder fixed points. After a general introduction to the qualitative ideas and to the quantitative renormalization rules, we…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal…
We describe a large disorder renormalization group (LDRG) method for the Anderson model of localization in one dimension which decimates eigenstates based on the size of their wavefunctions rather than their energy. We show that our LDRG…
To avoid the complicated topology of surviving clusters induced by standard Strong Disorder RG in dimension $d>1$, we introduce a modified procedure called 'Boundary Strong Disorder RG' where the order of decimations is chosen a priori. We…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice…
\textbf{Background} The reach of \textit{ab initio} theory has greatly increased in recent decades. However, predicting the location of the drip lines remains challenging due to uncertainties in nuclear forces and difficulties in describing…
We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension, such disordered anyon…
Symmetries are a key tool in understanding quantum systems, and, among many other things, can be exploited to increase the efficiency of numerical simulations of quantum dynamics. Disordered systems usually feature reduced symmetries and…
We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
The unrolling method has been investigated for learning variational models in X-ray computed tomography. However, it has been observed that directly unrolling the regularization model through gradient descent does not produce satisfactory…
This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of…