Related papers: Deep learning the Hohenberg-Kohn maps of Density F…
The electronic and magnetic properties of many strongly-correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the…
It is shown that the Hohenberg-Kohn lemma and theorem are direct consequences of the statement that the ground state energy (or free energy) of a system of interacting particles in an external field is a unique functional of the potential…
Time-dependent density functional theory is extended to include dissipative systems evolving under a master equation, providing a Hamiltonian treatment for molecular electronics. For weak electric fields, the isothermal conductivity is…
The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neuralnetwork approximation of this…
Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
We simulate scanning probe imaging of the local density of states related to scattering Fermi level wave functions inside a resonant cavity. We calculate potential landscape within the cavity taking into account the Coulomb charge of the…
We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show…
For a large class of feature maps we provide a tight asymptotic characterisation of the test error associated with learning the readout layer, in the high-dimensional limit where the input dimension, hidden layer widths, and number of…
Temporal-difference and Q-learning play a key role in deep reinforcement learning, where they are empowered by expressive nonlinear function approximators such as neural networks. At the core of their empirical successes is the learned…
We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly…
The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…
The electronic structure calculations based upon energy density functionals are highly successful and widely used both in solid state physics and quantum chemistry. Moreover, the Hohenberg-Kohn theorems and the Kohn-Sham method provide them…
We develop an effective field theory to describe the superfluid pairing in strongly interacting fermions with arbitrary short-range attractions, by extending Kaplan's idea of coupling fermions to a fictitious boson state in Nucl. Phys. B…
The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based…