Related papers: Fixed-node and fixed-phase approximations and thei…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the…
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a…
On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…
Observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many-body physics. Here we further explore a computational scheme [Y. Tang and A. W.…
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction…
We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view…
Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
We present numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with a general non-local in space-time interaction. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the…
A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…
In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schr\"odinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic…
Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a…
Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
An one-parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended…