Related papers: Mayet-Godowski Hilbert Lattice Equations
We illustrate the current status of heavy quark physics on the lattice. Special emphasis is paid to the question of systematic uncertainties and to the connection of lattice computations to continuum physics. Latest results are presented…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
We introduce an efficient method to solve the Mott-Hubbard model. The Schr\"{o}dinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body…
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
I review a selection of recent finite temperature lattice results of the past years. First I discuss the extension of the equation of state towards high temperatures and fi- nite densities, then I show recent results on the QCD topological…
The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
We study formulations of bound state (Bethe-Salpeter) equations on arbitrary Riemannian manifolds. We obtain a hierarchy of equations for multipartice wave functions. These equations, at each number of particles, depend on certain choices…
We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.
The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism…
We focused on the Ablowitz--Ladik equation on a zero background, specifically considering the scenario of $N$ pairs of multiple poles. Our first goal was to establish a mapping between the initial data and the scattering data. This allowed…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured…
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient…
Lattice calculations of heavy quark systems provide very good measures of the lattice spacing, a key element in recent determinations of the strong coupling constant using lattice methods. They also provide excellent testing grounds for…
In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
Some results obtained by a new method for solving the Bethe-Salpeter equation are presented. The method is valid for any kernel given by irreducible Feynman graphs. The Bethe-Salpeter amplitude, both in Minkowski and in Euclidean spaces,…
This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem…