相关论文: A minimal and universal representation of fermioni…

We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…

Permutation-invariant, -equivariant, and -covariant functions and anti-symmetric functions are important in quantum physics, computer vision, and other disciplines. Applications often require most or all of the following properties: (a) a…

Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…

Composite fermion wavefuctions have been used to describe electrons in a strong magnetic field. We show that the polynomial part of these wavefunctions can be obtained by applying a normal ordered product of suitably defined annihilation…

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite…

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…

Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas and Myrheim proposed how a fermionic wave function can be represented as a function of…

Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…

We introduce a new fermionic variational wavefunction, generalizing the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from…

A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…

This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We…

Recent neural networks demonstrated impressively accurate approximations of electronic ground-state wave functions. Such neural networks typically consist of a permutation-equivariant neural network followed by a permutation-antisymmetric…

A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion…

We examine the interplay of symmetry and topological order in $2+1$ dimensional fermionic topological phases of matter. We define fermionic topological symmetries acting on the emergent topological effective theory described using braided…

In this paper we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their…

In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge…

We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations,…

We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal…

When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…

A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…