Related papers: opbasis -- a Python package to derive minimal oper…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
The software project kdotpy provides a Python application for simulating electronic band structures of semiconductor devices with $\mathbf{k}\cdot\mathbf{p}$ theory on a lattice. The application implements the widely used Kane model,…
We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying…
Symmetry under time-reversal appears in the microscopic description of many physical systems. In a quantum mechanical setting it acts as an anti-unitary operator, so does not fall under general analyses based on unitary symmetries. In…
Starting from the operator algebra of the (1+1)D Ising model on a spatial lattice, this paper explicitly constructs a subalgebra of smooth operators that are natural candidates for continuum fields in the scaling limit. At the critical…
Mathematica offers, by way of the package Combinatorics, many useful functions to work on graphs and ordered structures, but none of these functions was specific enough to meet the needs of our research group. Moreover, the existing…
Probability density functions form a specific class of functional data objects with intrinsic properties of scale invariance and relative scale characterized by the unit integral constraint. The Bayes spaces methodology respects their…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
The study of complex many-body systems via analysis of the trajectories of the units that dynamically move and interact within them is a non-trivial task. The workflow for extracting meaningful information from the raw trajectory data is…
An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction…
At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to…
Parameter-efficient fine-tuning (PEFT) allows model builders to capture the task-specific parameters into adapters, which are a fraction of the size of the original base model. Popularity of PEFT technique for fine-tuning has led to the…
This paper demonstrates the application of semidefinite programming to lattice field theories, showcasing spin chains and lattice scalar field theory. Requiring expectation values of manifestly positive semi-definite operators to be…
Python's dynamic type system, while offering significant flexibility and expressiveness, poses substantial challenges for static analysis and automated tooling, particularly in unannotated or partially annotated codebases. Existing type…
We develop an effective field theory for the description of high energetic or hard photons, the on-shell effective theory (OSEFT). The OSEFT describes the so called eikonal or semi-classical optical limit, allowing for corrections organized…
We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…
It is common in classical mechanics to encounter systems whose Hamiltonian $H$ is the sum of an often exactly integrable Hamiltonian $H_0$ and a small perturbation $\epsilon H_1$ with $\epsilon\ll1$. Such near-integrability can be exploited…
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…