The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simu...

We construct a model of spin-Hall effect on a noncommutative four sphere S4 θ with isospin degrees of freedom, coming from a noncommutative instanton, and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on highe...

We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is λ ≪ l, where λ is the wavelength of a typical particle and l is the mean free path between collisions. For fermions with Fermi wavelength λF ≪ l, this implies that all energy eigenstates, including the gro...

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than 2. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence ...

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure θ on the CR sphere S ⊂ C, achieves its maximum when θ is the standard contact form.

We use the automorphism group Aut(H), of holes in the lattice L8 = A2 ⊕ A2 ⊕ D4, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, L4 = A2 ⊕ A2, enters the construction because a subgroup of Aut(L4) is isomorphic to Aut(H). The lattices L8 and L4, when glued together through this relationship, provide an alternative construction of the lamin...

Let p be an odd prime. We construct a non-abelian extension Γ of S1 by Z/p × Z/p, and prove that any finite subgroup of Γ acts freely and smoothly on S2p−1 × S2p−1. In particular, for each odd prime p we obtain free smooth actions of infinitely many non-metacyclic rank two p-groups on S2p−1 × S2p−1. These results arise from a general approach to the existence problem for finite group actions on...

In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In thi...

Superhydrophobic particulate films were fabricated via deposition of raspberry-like fluorescent PS/CdTe/silica microspheres on clean glass substrates and surface modification. Particularly, the fluorescent microspheres were prepared by a kind of modified strategy, namely introducing poly (acrylic acid)-functionalized polystyrene microspheres and thiol-stabilized CdTe quantum dots into a hydroly...