Related papers: Gap-labelling conjecture with nonzero magnetic fie…

It is well known that, given a $2d$ purely magnetic Landau Hamiltonian with a constant magnetic field $b$ which generates a magnetic flux $\varphi$ per unit area, then any spectral island $\sigma_b$ consisting of $M$ infinitely degenerate…

Let $\Gamma$ be a countable discrete group, $H$ a lcsc totally disconnected group and $\rho : \Gamma \rightarrow H$ a homomorphism with dense image. We develop a general and explicit technique which provides, for every compact open subgroup…

In a Euclidean path integral formulation of gauge theory and quantum mechanics, the theta-term induces a sign problem, and relatedly, a complex phase for the fugacity of topological defects; whereas in Minkowskian formulation, it induces a…

We investigate the topological classification of the subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. The wave functions for these bands are…

Let $S_n$ denote the symmetric group on $n$ elements, and $\Sigma\subseteq S_{n}$ a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Richthammer [arXiv:0906.1238], states that if $\Sigma$ is a…

Keeping in mind our conjecture of modelling cuprates and related systems by quantum groups and our claim that the existence of stripes is intimately related to quantum groups and more strongly is a consequence of the underlying quantum…

To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which…

Optical conductivity of the weakly doped two-dimensional repulsive Hubbard model on the square lattice with nearest and next nearest hoppings is calculated within the generalized dynamical-mean field (DMFT+\Sigma_p) approach which includes…

We present the first systematic study of the filling constraints to realize a `trivial' insulator symmetric under magnetic space group $\mathcal{M}$. The filling $\nu$ must be an integer multiple of $m^{\mathcal{M}}$ to avoid spontaneous…

We conjecture that the pseudogap is an inhomogeneous condensate above the homogeneous state whose existence is granted by topological stability. We consider the simplest possible order parameter theory that provides this interpretation of…

We give a proof of the Gap Labeling Conjecture formulated by J. Bellissard. This gives information about the spectrum of a Schrodinger operator associated to a quasicrystal. The proof makes use of a version of Connes' Index Theorem for…

The distribution of the current density and the profile of the trapped magnetic field of a superconducting disk magnetized by uniform field are calculated from first principles. The effect of the superconducting parameters is taken into…

We present a Bayesian maximum likelihood analysis of Faraday rotation measure (RM) maps of extended radio sources to determine magnetic field power spectra in clusters of galaxies. Using this approach, it is possible to determine the…

In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…

Let $ (\Theta,T,\mu) $ be an ergodic topological dynamical system. The fibered rotation number for cocycles in $ \Theta\times \mathrm{SL}(2,\mathbb{R}) $, acting on $ \Theta\times \mathbb{R}\mathbb{P}^1 $ is well-defined and has wide…

The assumption that the Weinberg rotation between the gauge fields associated with the third component of the ``weak isospin" ($T_3$) and the hypercharge ($Y$) proceeds in a natural way from a global homomorphism of the $SU(2)\otimes U(1)$…

Despite decades of intense researches, the enigmatic pseudo-gap (PG) phase of superconducting cuprates remains an unsolved mystery. In the last 15 years, various symmetry breakings in the PG state have been discovered, spanning an…

Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…

We define a class of groups equipped with an invariant probability measure, which includes all compact groups and is closed under taking ultraproducts with the induced Loeb measure; in fact, this class also contains the ultraproducts all…