A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. ...

The Cl(3, 0) Clifford algebra is represented with the commutative ring of hyperbolic numbers H . The canonical form of the Poincaré mass operator defined in this vector space corresponds to a sixteen-dimensional structure. This conflicts with the natural perception of a four-dimensional space-time. The assumption that the generalized mass operator is an hermitian observable forms the basis of a...

In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral t and on-site repulsion U on a square lat...

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P 5aN points that are uniformly distributed in all the directions but one on the N-dimensional space. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two Gaussians of variable separation and width. The typical optimal performance is measured ...

In this work spontaneous (non-dynamical) breaking (effective hiding) of the unitary quantum mechanical dynamical symmetry (superposition) is considered. It represents an especial but very interesting case of the general formalism of the spontaneous symmetry breaking (effective hiding). Conceptual analogies with spontaneous breaking of the gauge symmetry in Weinberg-Sallam’s electro-weak interac...

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. ...

We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasione-dimensional quantum wires perturbed by weak quenched disorder. Past works using this approach have considered a single chain. Here, we extend the formalism to treat a quasi-one-dimensiona...

We report theoretical investigations of the quantized spin-Hall conductance fluctuation of graphene in the presence of disorder. Two graphene models that exhibit the quantized spin-Hall effect (QSHE) are analyzed. Model I is with unitary symmetry under an external magnetic field B not = 0 but with a zero spin-orbit interaction, t(SO)=0. Model II is with symplectic symmetry where B=0 but t(SO) n...

We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a class two-step non-unitary quantum walks. The model possesses joint parity time-reversal symmetry or PT-symmetry supports topological phases when this is unbroken by its eigenstates. An asymptotic analysis at long times reveals that walk can indefinitely sustain phase even gain loss mechanisms are prese...

We develop a method to build new 5D N=1 gauge models based on Sasaki-Einstein manifolds Yp,q. These extend the standard ones having unitary SU(p)q symmetry Particular focus is put building of family with symplectic SP(2r,R) symmetry. super QFTs are embedded in M-theory compactified folded toric Calabi-Yau threefolds Xˆ(Y2r,0) constructed from conical Y2r,0. By using outer-automorphism symmetrie...