33,428 research outputs found
Separation probabilities for products of permutations
We study the mixing properties of permutations obtained as a product of two
uniformly random permutations of fixed cycle types. For instance, we give an
exact formula for the probability that elements are in distinct
cycles of the random permutation of obtained as product of two
uniformly random -cycles
Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
We express modular and weak values of observables of three- and higher-level
quantum systems in their polar form. The Majorana representation of N-level
systems in terms of symmetric states of N-1 qubits provides us with a
description on the Bloch sphere. With this geometric approach, we find that
modular and weak values of observables of N-level quantum systems can be
factored in N-1 contributions. Their modulus is determined by the product of
N-1 ratios involving projection probabilities between qubits, while their
argument is deduced from a sum of N-1 solid angles on the Bloch sphere. These
theoretical results allow us to study the geometric origin of the quantum phase
discontinuity around singularities of weak values in three-level systems. We
also analyze the three-box paradox [1] from the point of view of a bipartite
quantum system. In the Majorana representation of this paradox, an observer
comes to opposite conclusions about the entanglement state of the particles
that were successfully pre- and postselected
Group Theory of Non-Abelian Vortices
We investigate the structure of the moduli space of multiple BPS non-Abelian
vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our
attention on the action of the exact global (color-flavor diagonal) SU(N)
symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is
spanned by a vector in the fundamental representation of the global SU(N)
symmetry. The moduli space of winding-number k vortices is instead spanned by
vectors in the direct-product representation: they decompose into the sum of
irreducible representations each of which is associated with a Young tableau
made of k boxes, in a way somewhat similar to the standard group composition
rule of SU(N) multiplets. The K\"ahler potential is exactly determined in each
moduli subspace, corresponding to an irreducible SU(N) orbit of the
highest-weight configuration.Comment: LaTeX 46 pages, 4 figure
Rotated multifractal network generator
The recently introduced multifractal network generator (MFNG), has been shown
to provide a simple and flexible tool for creating random graphs with very
diverse features. The MFNG is based on multifractal measures embedded in 2d,
leading also to isolated nodes, whose number is relatively low for realistic
cases, but may become dominant in the limiting case of infinitely large network
sizes. Here we discuss the relation between this effect and the information
dimension for the 1d projection of the link probability measure (LPM), and
argue that the node isolation can be avoided by a simple transformation of the
LPM based on rotation.Comment: Accepted for publication in JSTA
Probing Brownstein-Moffat Gravity via Numerical Simulations
In the standard scenario of the Newtonian gravity, a late-type galaxy (i.e.,
a spiral galaxy) is well described by a disk and a bulge embedded in a halo
mainly composed by dark matter. In Brownstein-Moffat gravity, there is a claim
that late-type galaxy systems would not need to have halos, avoiding as a
result the dark matter problem, i.e., a modified gravity (non-Newtonian) would
account for the galactic structure with no need of dark matter. In the present
paper, we probe this claim via numerical simulations. Instead of using a
"static galaxy," where the centrifugal equilibrium is usually adopted, we probe
the Brownstein-Moffat gravity dynamically via numerical -body simulations.Comment: 33 pages and 14 figures - To appear in The Astrophysical Journa
- …