185 research outputs found
Finite Bruck loops
Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X, showing that X is essentially the direct product of a Bruck loop of odd order with a 2-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2-element Bruck loops are 2-loops, leaving open the question of whether such obstructions actually exist
A microscopic model for Josephson currents
A microscopic model of a Josephson junction between two superconducting
plates is proposed and analysed. For this model, the nonequilibrium steady
state of the total system is explicitly constructed and its properties are
analysed. In particular, the Josephson current is rigorously computed as a
function of the phase difference of the two plates and the typical properties
of the Josephson current are recovered
An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
Extraspecial groups form a remarkable subclass of p-groups. They are also
present in quantum information theory, in particular in quantum error
correction. We give here a polynomial time quantum algorithm for finding hidden
subgroups in extraspecial groups. Our approach is quite different from the
recent algorithms presented in [17] and [2] for the Heisenberg group, the
extraspecial p-group of size p3 and exponent p. Exploiting certain nice
automorphisms of the extraspecial groups we define specific group actions which
are used to reduce the problem to hidden subgroup instances in abelian groups
that can be dealt with directly.Comment: 10 page
On right conjugacy closed loops of twice prime order
The right conjugacy closed loops of order 2p, where p is an odd prime, are
classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl
Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition
We generalize the method of third quantization to a unified exact treatment
of Redfield and Lindblad master equations for open quadratic systems of n
fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal
driving in terms of the Redfield equation is analyzed in detail. We explain how
to compute all physically relevant quantities, such as non-equilibrium
expectation values of local observables, various entropies or information
measures, or time evolution and properties of relaxation. We also discuss how
to exactly treat explicitly time dependent problems. The general formalism is
then applied to study a thermally driven open XY spin 1/2 chain. We find that
recently proposed non-equilibrium quantum phase transition in the open XY chain
survives the thermal driving within the Redfield model. In particular, the
phase of long-range magnetic correlations can be characterized by
hypersensitivity of the non-equilibrium-steady state to external (bath or bulk)
parameters. Studying the heat transport we find negative thermal conductance
for sufficiently strong thermal driving, as well as non-monotonic dependence of
the heat current on the strength of the bath coupling.Comment: 24 pages, 12 figures, submitted to New Journal of Physics, Focus
issue "Quantum Information and Many-Body Theory
Policy for Robust Space-based Earth Science, Technology and Applications
Satellite remote sensing technology has contributed to the transformation of multiple earth science domains, putting space observations at the forefront of innovation in earth science. With new satellite missions being launched every year, new types of earth science data are being incorporated into science models and decision-making systems in a broad array of organizations. Policy guidance can influence the degree to which user needs influence mission design and when, and ensure that satellite missions serve both the scientific and user communities without becoming unfocused and overly expensive. By considering the needs of the user community early on in the mission-design process, agencies can ensure that satellites meet the needs of multiple constituencies. This paper describes the mission development process in NASA and ESA and compares and contrasts the successes and challenges faced by these agencies as they try to balance science and applications within their missions
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over
groups such that the underlying rack is braided and the homogeneous component
of degree three of the Nichols algebra satisfies a given inequality. This
assumption turns out to be equivalent to a factorization assumption on the
Hilbert series. Besides the known Nichols algebras we obtain a new example. Our
method is based on a combinatorial invariant of the Hurwitz orbits with respect
to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure
Hjelmslev Geometry of Mutually Unbiased Bases
The basic combinatorial properties of a complete set of mutually unbiased
bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a
prime and r a positive integer, are shown to be qualitatively mimicked by the
configuration of points lying on a proper conic in a projective Hjelmslev plane
defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a
basis of H\_q correspond to the q points of a (so-called) neighbour class and
the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour
classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more
illustrative and in colour; v3 - one more figure and section added, paper
made easier to follow, references update
Conversion of a general quantum stabilizer code to an entanglement distillation protocol
We show how to convert a quantum stabilizer code to a one-way or two-way
entanglement distillation protocol. The proposed conversion method is a
generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence
protocol and the quantum privacy amplification protocol are equivalent to the
protocols converted from [[2,1]] stabilizer codes. We also give an example of a
two-way protocol converted from a stabilizer better than the recurrence
protocol and the quantum privacy amplification protocol. The distillable
entanglement by the class of one-way protocols converted from stabilizer codes
for a certain class of states is equal to or greater than the achievable rate
of stabilizer codes over the channel corresponding to the distilled state, and
they can distill asymptotically more entanglement from a very noisy Werner
state than the hashing protocol.Comment: LaTeX2e, 18 pages, 1 figure. Version 4 added an example of two-way
protocols better than the recurrence protocol and the quantum privacy
amplification protocol. Version 2 added the quantum privacy amplification
protocol as an example converted from a stabilizer code, and corrected many
errors. Results unchanged from V
- …