80,361 research outputs found
An algorithmically random family of MultiAspect Graphs and its topological properties
This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical graphs to plain and prefix algorithmically random MultiAspect Graphs (MAGs). First, we show that there is an infinite recursively labeled infinite family of nested MAGs (or, as a particular case, of nested classical graphs) that behaves like (and is determined by) an algorithmically random real number. Then, we study some of their important topological properties, in particular, vertex degree, connectivity, diameter, and rigidity
SUSY Relics in One-Flavor QCD from a New 1/N Expansion
We suggest a new large-N_c limit for multi flavor QCD. Since fundamental and
two-index antisymmetric representations are equivalent in SU(3), we have the
option to define SU(N_c) QCD keeping quarks in the latter. We can then define a
new 1/N_c expansion (at fixed number of flavors N_f) that shares appealing
properties with the topological (fixed N_f/N_c) expansion while being more
suitable for theoretical analysis. In particular, for N_f=1, our large-N_c
limit gives a theory that we recently proved to be equivalent, in the bosonic
sector, to N=1 supersymmetric gluodynamics. Using known properties of the
latter, we derive several qualitative and semi-quantitative predictions for
N_f=1 massless QCD which can be easily tested in lattice simulations. Finally,
we comment on possible applications for pure SU(3) Yang-Mills theory and real
QCD.Comment: 4 pages, RevTex. v2: note added at the end of the paper, ref. added.
To appear in Phys.Rev.Let
Topological properties of medium voltage electricity distribution networks
With a large penetration of low carbon technologies (LCTs) at medium voltage and low voltage levels, electricity distribution networks are undergoing rapid changes. Much research has been carried out to analyse the impact of employing LCTs in distribution networks based on either real or synthetic network samples. Results of such studies are usually case specific and of limited applicability to other networks. Topological properties of a distribution networks describe how different network components are located and connected, which are critical for the investigation of network performance. However, the number of network modelling and simulation platforms are limited in the open literature which can provide random realistic representations of electricity distribution networks. Thus, it is difficult to arrive to generalized and robust conclusions on impact studies of LCTs. As the initial step to bridge this gap, this paper studies the topological properties of real-world electricity distribution networks at the medium voltage level by employing the techniques from complex networks analysis and graph theory. The networks have been modelled as graphs with nodes representing electrical components of the network and links standing for the connections between the nodes through distribution lines. The key topological properties that characterize different types (urban and sub-urban) of distribution networks have been identified and quantified. A novel approach to obtain depth-dependent topological properties has also been developed. Results show that the node degree and edge length related graph properties are a key to characterize different types of electricity distribution networks and depth dependent network properties are able to better characterize the topological properties of urban and sub-urban networks
Optimising Qubit Designs for Topological Quantum Computation
The goal of this thesis is to examine some of the ways in which we might
optimise the design of topological qubits. The topological operations which
are imposed on qubits, in order to perform logic gates for topological quantum
computations, are governed by the exchange group of the constituent particles.
We examine representations of these exchange groups and investigate what restrictions
their structure places on the effciency, reliability and universality of
qubits (and multi-qubit systems) as a function of the number of particles composing
them. Specific results are given for the limits placed on d-dimensional
qudits where logic gates are imposed by braiding anyons in 2+1 dimensions.
We also study qudits designed from ring-shaped, anyon-like excitations in
3+1 dimensions, where logic gates are implemented by elements of the loop
braid group. We introduce the concept of local representations, where the generators
of the loop braid group are defined to act non-trivially only on the local
vector spaces associated with the rings which undergo the motion. We present
a method for obtaining local representations of qudits and show how any such
representation can be decomposed into representations which come from the
quantum doubles of groups. Due to the dimension of the local representation
being related to the number of generators, any non-Abelian properties of the
representation are not compromised with an addition of extra operations, we
conclude that universal representations may be easier to find than in previously
discussed cases (though not for topological operations alone).
We model a ring of Ising anyons in a fractional quantum Hall
uid to study
how interactions in a real environment may impact any qubits we have created.
Fractional quantum Hall liquids are currently one of the most promising possibilities
for the physical realisation of TQC and so present a natural choice of
system in which to study these effects. We show how interactions between the
anyons compromise the practicality of qubits defined by the fusion channels
of anyon pairs and explore the use of the fermion number parity sectors as
qubit states. Interactions between the anyon ring and the edge of the liquid
are modelled to study the effect they will have on the state of the qubit. We
perform numerical simulations, for a small system, to give some indication of
how the edge interaction will in
uence the reliability of the qubit
Optimising Qubit Designs for Topological Quantum Computation
The goal of this thesis is to examine some of the ways in which we might
optimise the design of topological qubits. The topological operations which
are imposed on qubits, in order to perform logic gates for topological quantum
computations, are governed by the exchange group of the constituent particles.
We examine representations of these exchange groups and investigate what restrictions
their structure places on the effciency, reliability and universality of
qubits (and multi-qubit systems) as a function of the number of particles composing
them. Specific results are given for the limits placed on d-dimensional
qudits where logic gates are imposed by braiding anyons in 2+1 dimensions.
We also study qudits designed from ring-shaped, anyon-like excitations in
3+1 dimensions, where logic gates are implemented by elements of the loop
braid group. We introduce the concept of local representations, where the generators
of the loop braid group are defined to act non-trivially only on the local
vector spaces associated with the rings which undergo the motion. We present
a method for obtaining local representations of qudits and show how any such
representation can be decomposed into representations which come from the
quantum doubles of groups. Due to the dimension of the local representation
being related to the number of generators, any non-Abelian properties of the
representation are not compromised with an addition of extra operations, we
conclude that universal representations may be easier to find than in previously
discussed cases (though not for topological operations alone).
We model a ring of Ising anyons in a fractional quantum Hall
uid to study
how interactions in a real environment may impact any qubits we have created.
Fractional quantum Hall liquids are currently one of the most promising possibilities
for the physical realisation of TQC and so present a natural choice of
system in which to study these effects. We show how interactions between the
anyons compromise the practicality of qubits defined by the fusion channels
of anyon pairs and explore the use of the fermion number parity sectors as
qubit states. Interactions between the anyon ring and the edge of the liquid
are modelled to study the effect they will have on the state of the qubit. We
perform numerical simulations, for a small system, to give some indication of
how the edge interaction will in
uence the reliability of the qubit
More on one class of fractals
This article is devoted to Cantor-like sets. We describe topological, metric
and fractal properties of certain sets whose elements have restrictions on
using digits or combinations of digits in own representations. Also, such
properties are considered for the cases of special type of sets, i.e., sets
whose elements represented in terms of certain series related with classical
representations of real numbers.Comment: 14 page
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