Related papers: Hydrogen Atom in a Fuzzy Spherical Cavity
The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…
Modern quantum theory introduces quantum structures (decompositions into subsystems) as a new discourse that is not fully comparable with the classical-physics counterpart. To this end, so-called Entanglement Relativity appears as a…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most…
The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the…
In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at…
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing…
Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials.…
We present a numerical study of a two dimensional model of the Wess-Zumino type. We formulate this model on a sphere, where the fields are expanded in spherical harmonics. The sphere becomes fuzzy by a truncation in the angular momenta.…
The matrix model with mass term has a nontrivially classical solution which is known to represent a noncommutative fuzzy sphere. The fuzzy sphere has a lower energy then that of the trivial solution. In this letter we investigate the…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves…
The heat kernel expansion can be used as a tool to obtain the effective geometric quantities in fuzzy spaces. Generalizing the efficient method presented in the previous work on the global quantities, it is applied to the effective local…
The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are…
We study the eigenvalue equation for the 'Cartesian coordinates' observables $x_i$ on the fully $O(2)$-covariant fuzzy circle $\{S^1_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2$) and on the fully $O(3)$-covariant fuzzy 2-sphere…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
The rank-three tensor models, which have a rank-three tensor as their only dynamical variable, may be interpreted as models of dynamical fuzzy spaces. In this interpretation, the generalized Hermiticity condition on the rank-three tensor…