Related papers: Towards Antisymmetric Neural Ansatz Separation

In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot…

What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…

We consider an operator function (F(\lambda)) for (\lambda\in(\sigma,\tau)\subseteq\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal…

For sequences of random backward nested subspaces as occur, say, in dimension reduction for manifold or stratified space valued data, asymptotic results are derived. In fact, we formulate our results more generally for backward nested…

The basic question is addressed, how the space dimension $d$ is encoded in the Hilbert space of $N$ identical fermions. There appears a finite number $N!^{d-1}$ of many-body wave functions, called shapes, which cannot be generated by…

We consider asymptotics of power series coefficients of rational functions of the form $1/Q$ where $Q$ is a symmetric multilinear polynomial. We review a number of such cases from the literature, chiefly concerned either with positivity of…

We study the optimal Slater-determinant approximation of an $N$-fermion wave function analytically. That is, we seek the Slater-determinant (constructed out of $N$ orthonormal single-particle orbitals) wave function having largest overlap…

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks…

Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to…

In a coupled-channel model, we explore the effects of coupling between configurations on the radial behavior of the wave function and, in particular, on the spectroscopic factor (SF) and the asymptotic normalization coefficient (ANC). We…

For various arithmetic functions $f:\mathbb{N} \to \mathbb{R}$, the behavior of $f(n!)$ and that of $\sum_{n\le N} f(n!)$ can be intriguing. For instance, for some functions $f$, we have ${f(n!)=\sum_{k\le n}f(k)}$, for others, we have…

Let $p$ and $q$ be anisotropic quadratic forms of dimension $\geq 2$ over a field $F$. In a recent article, we formulated a conjecture describing the general constraints which the dimensions of $p$ and $q$ impose on the isotropy index of…

The effect of inertial spin dynamics is compared between ferromagnetic, antiferromagnetic and ferrimagnetic systems. The linear response to an oscillating external magnetic field is calculated within the framework of the inertial…

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents…

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…

We formulate N-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix 2-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems,…

We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = \Lambda$ and $f = \tau$,…

A method to create instructive, nonuniform aperture functions using spatial frequency filtering is described. The diffraction from a single slit in the Fresnel limit and the interference from a double slit in the Fraunhofer limit are…

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…

We perform lattice studies of meson mass spectra and decay constants of the $Sp(4)$ gauge theory in the quenched approximation. We consider two species of (Dirac) fermions as matter field content, transforming in the 2-index antisymmetric…