相关论文: Critical dimension of Spectral Triples
The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.
We consider infinite matrices obtained by restricting Hardy integral kernels to natural numbers. For a suitable class of Hardy kernels we describe the absolutely continuous spectrum, the essential spectrum and the asymptotic spectral…
We discuss deep inelastic scattering at low $x$ as a critical phenomenon in 2+1 space-time dimensions. QCD (SU2) near the light cone becomes a critical theory in the limit of $\lim x \to 0$ with a correlation mass $m(x) \propto x^{\nu/2}$.…
A new upper bound is given for the dimension of the space of holomorphic cusp forms of weight one and prime level $q$: $$ \hbox{dim}\, S_1(q) << q^{11/12} \log^4{q} $$ with an absolute implied constant.
The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
In solar neutrino oscillations, if $\nu_e$ has a significant third massive component, the allowed parameter space in $\Delta m^2$ and $\sin^2 2 \theta$ for the first two components is shown to be greatly increased. This third component may…
We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical…
Among the 25 planetary systems detected up to now by gravitational microlensing, there are two cases of a star with two planets, and two cases of a binary star with a planet. Other, yet undetected types of triple lenses include triple stars…
We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte…
We give a formula for the essential dimension of a cohomology class $\alpha$ in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselian field. This formula is particularly explicit in the case, where $\alpha$ is a Brauer…
We determine the pseudo-critical line in the temperature - chemical potential plane of 2-color QCD by direct Monte Carlo simulations and by analytic continuation from imaginary chemical potential.
Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put…
It is known that contrary to expectations, the order parameter of chiral symmetry breaking, the Dirac spectral density at zero virtuality does not vanish above the critical temperature of QCD. Instead, the spectral density develops a…
Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation of Quantum Gravity assuming the existence of a global time foliation. In our earlier study we analyzed the effect of including $d$ copies of a massless scalar…
We study the decision version of tensor spectral norm from the viewpoint of real algebraic complexity. For a rationally specified tensor, the tensor spectral threshold problem asks whether its spectral norm exceeds a prescribed rational…
For each $\alpha > 2$ there is a binary word with critical exponent $\alpha$.
We compute the d-dimensional critical exponents corresponding to the wave function and mass renormalization of the quark in QCD in the Landau gauge at a new order, O(1/N_f^2), in the large N_f expansion. The computations are simplified by…
A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field…
The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a…