Nielsen's theorem and the super-Teichmüller space
Noise effects in the quantum search algorithm from the viewpoint of computational complexity
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on the computational complexity of the quantum search algorithm. We show that it is only for small amounts of noise that the quantum search algorithm is still more efficient than any classical algorithm.
Nonatomic states
Noncommutative 3-sphere as an example of noncommutative contact algebras
The notion of deformation quantization was introduced by F.Bayen, M.Flato et al. in [1]. The basic idea is to formally deform the pointwise commutative multiplication in the space of smooth functions on a symplectic manifold to a noncommutative associative multiplication, whose first order commutator is proportional to the Poisson bracket. It is of interest to compute this quantization for naturally occuring cases. In this paper, we discuss deformations of contact algebras and give a definition...
Noncommutative extensions of the Fourier transform and its logarithm
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗ ν̂ ∘ Δ when...
Noncommutative geometry: fuzzy spaces, the Groenewold-Moyal plane.
Non-commutative Markov processes in free groups factors, related to Berezin's quantization and automorphic forms.
Non-commutative matrix integrals and representation varieties of surface groups in a finite group
A new formula is established for the asymptotic expansion of a matrix integral with values in a finite-dimensional von Neumann algebra in terms of graphs on surfaces which are orientable or non-orientable.
Non-commutative mechanics in mathematical and in condensed matter physics.
Non-commutative probability limit theorems
Non-Hermitian quantum mechanics with minimal length uncertainty.
Non-Hermitian quantum systems and time-optimal quantum evolution.
Nonlinear Dirac equations.
Nonlinear Schrödinger equation on four-dimensional compact manifolds
We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness for small energy...
Nonlinear Schrödinger equation on real hyperbolic spaces
Nonlinear Small Data Scattering for the Wave and Klein-Gordon Equation.
Non-local finite-size effects in the dimer model.
Non-minimal Yang-Mills fields and dynamics.
Non-topological condensates in self-dual Chern-Simons gauge theory
This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.
Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials.