相关论文: Minimal Soft Lattice Theta Functions
An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is…
We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale…
The objective of this paper is to present some geometric aspects of surfaces associated with theta function solutions of the periodic 2D-Toda lattice. For this purpose we identify the $(N^2-1)$-dimensional Euclidean space with the ${\frak…
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in…
We study the zeros of theta functions $\Theta_{\Gamma_{4k}}$ associated with the lattices $\Gamma_{4k}$, a family of self-dual lattices generalizing the $\mathsf{E}_{8}$ lattice. Our results show two different behaviors of the zeros…
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…
Embedding the lattice gauge theory into a continuum theory allows to use the continuum action as trial action in the variational calculation. Only originally divergent graphs contribute. This leads to a very simple scheme which makes it…
The present neutrino oscillation data allow $m^{}_1 = 0$ (or $m^{}_3 = 0$) for the neutrino mass spectrum and support $\theta^{}_{23} \simeq \pi/4$ and $\delta \simeq -\pi/2$ as two good approximations for the PMNS lepton flavor mixing…
In this paper, a new lattice concept called the locally symmetric lattice is proposed for storage ring light sources. In this new lattice, beta functions are made locally symmetric about two mirror planes of the lattice cell, and the phase…
Let M be a compact spin manifold with a smooth action of the n-torus. Connes and Landi constructed theta-deformations M_{theta} of M, parameterized by n by n real skew-symmetric matrices theta. The M_{theta}'s together with the canonical…
We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
The breaking of rotational symmetry on the lattice for bound eigenstates of the two lightest alpha conjugate nuclei is explored. Moreover, a macroscopic alpha-cluster model is used for investigating the general problems associated with the…
As one of the asymptotic formulas for the zeta-function, Hardy and Littlewood gave asymptotic formulas called the approximate functional equation. In 2003, R. Garunk\v{s}tis, A. Laurin\v{c}ikas, and J. Steuding (in [1]) proved the…
We derive lattice invariants from the heat flux of a lattice. Using systems of harmonic polynomials, we obtain sums of products of spherical theta functions which give new invariants of integer lattices which are modular forms. In…
Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We update the present-day sensitivities of precision data using the new experimental…
We study the low temperature properties of the two-dimensional weakly interacting Hubbard model on $\ZZZ^2$ with renormalized chemical potential $\mu=2-\mu_0$, $\mu_0=10^{-10}$ fixed, in which case the Fermi surface is close to a perfect…
Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1 \leq m_2 \leq ... \leq m_k$ of natural numbers we construct a modular form $\Theta_{m_1,m_2,...,m_k,\Lambda}$ of level $N=N(\Lambda)$. The weight of this modular…
In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ in lattice QCD. Such correlation functions involve…
In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $| \zeta(z) |$ was conjectured by R. Spira. The $\zeta$-monotonicity property can be written as follows: $$ | \zeta (x_2 + y i ) | < | \zeta \left (…