相关论文: Geometry of backflow transformation ansatz for qua…
An efficient and expressive wavefunction ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wavefunction ans\"{a}tze,…
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…
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…
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…
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…
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
In this work, dissipative quantum backflow is studied for a superposition of two stretched Gaussian wave packets and two identical spinless particles within the Caldirola-Kanai framework. Backflow is mainly an interference process and…
Some notable systems, such as room-temperature superconductors and materials for controlled nuclear fusion, require an accurate description of finite-temperature quantum matter. Stochastic path integral methods are finite-temperature and…
A way is presented to design quantum wave functions that exhibit backflow, namely negative probability current despite having a strictly positive spectrum of momentum. These wave functions are derived from rational complex functions which…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
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…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
The construction of fully (anti-)symmetric states with many particles, when the single particle state carries multiple quantum numbers, is a problem that seems to have not been systematically addressed in the literature. A quintessential…
Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum -- a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively…
Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant…
The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear…
We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated…