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Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…
We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential -- a theory with a…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
A novel procedure is presented which allows the construction of all axial vector fields on Riemannian two-spheres. Using these axial vector fields and the centre-of-mass unit sphere reference systems, a constructive definition of…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
The multilayer multiconfiguration time-dependent Hartree method is employed to study vibrationally coupled charge transport in models of single molecule junctions. To increase the efficiency of the simulation method, a representation of the…
We propose a scalar-tensor representation of $f(R)$ theories with use of conformal transformations. In this representation, the model takes the form of the Brans-Dicke model with a potential function and a non-zero kinetic term for the…
We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of…
It has been found that a model of extended electrons is more suited to describe theoretical simulations and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are easily incorporated,…
Some relevant transport properties of solids do not depend only on the spectrum of the electronic Hamiltonian, but on finer properties preserved only by unitary equivalence, the most striking example being the conductance. When interested…
This paper presents a group-theoretical vector space model (VSM) that extends the VSM with a group action on a vector space of the VSM. We use group and its representation theory to represent a dynamic transformation of information objects,…
The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…
This lecture will introduce the Support Vector algorithms for classification and regression. They are an application of the so called kernel trick, which allows the extension of a certain class of linear algorithms to the non linear case.…
Matrix models and related Spin-Calogero-Sutherland models are of major relevance in a variety of subjects, ranging from condensed matter physics to QCD and low dimensional string theory. They are characterized by integrability and exact…
This work contains the teleparallel version of the stationary axisymmetric solutions. We obtain the tetrad and the torsion fields representing these solutions. The tensor, vector and axial-vector parts of the torsion tensor are evaluated.…
The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ…
By using the plane-wave expansion for the electromagnetic-field vector potential, transition matrix elements between the relativistic bound and unbound states of hydrogenic atoms were expressed explicitly in terms of finite series made of…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
Recent advances in machine-learned interatomic potentials largely benefit from the atomistic representation and locally invariant many-body descriptors. It was however recently argued that including three- (or even four-) body features is…