2,345 research outputs found
Coadjoint Poisson actions of Poisson-Lie groups
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie
algebra induces on it a non-trivial class of quadratic Poisson structures
extending the linear Poisson bracket on the coadjoint orbits
A note on sub-Riemannian structures associated with complex Hopf fibrations
Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf
fibration naturally appear in quantum mechanics. We study the curvature maps
for such a sub-Riemannian structure and express them using the Riemannian
curvature tensor of the Fubini-Study metric of the complex projective space and
the curvature form of the Hopf fibration. We also estimate the number of
conjugate points of a sub-Riemannian extremal in terms of the bounds of the
sectional curvature and the curvature form. It presents a typical example for
the study of curvature maps and comparison theorms for a general corank 1
sub-Riemannian structure with symmetries done by C.Li and I.Zelenko.Comment: 6 pages. arXiv admin note: substantial text overlap with
arXiv:0908.439
Deciding universality of quantum gates
We say that collection of -qudit gates is universal if there exists
such that for every every -qudit unitary operation
can be approximated with arbitrary precision by a circuit built from gates of
the collection. Our main result is an upper bound on the smallest with
the above property. The bound is roughly , where is the number of
levels of the base system (the '' in the term quit.) The proof is based
on a recent result on invariants of (finite) linear groups.Comment: 8 pages, minor correction
Optimal Control of Motorway Tidal Flow
When inbound and outbound traffic on a bi-directional motorway is unbalanced throughout the day a lane management strategy called tidal (reversible) flow lane control is usually applied. In this control case, the direction of one or more contraflow buffer lanes is reversed according to the needs of each direction. This paper introduces a basic dynamical model for tidal traffic flow and considers the minimum traveltime, minimum-time, and maximum throughput optimal control problems for efficient motorway tidal flow lane control. Lane management is effectuated by a control variable, indicating the number of lanes opened or closed in each direction of traffic. To derive the analytical form of optimal control, the Pontryagin's maximum principle is employed. The obtained optimal control is intuitively natural of bang-bang type, as also shown in a previous work by the authors [1]. It takes only the values ±1 and switches between these values at most once. In other words, the optimal control strategy consists of switching between opening and closing in each direction of traffic one contraflow buffer lane. Of course it is an open-loop control, and thus the switch time (if applicable) depends on the initial conditions. In the case of the maximum throughput optimal control problem, semi-state feedback control is obtained and singular arcs might exist. Finally, cumulative arrival rate and output curves for both directions of traffic are used to provide a graphical interpretation of the minimum travel-time optimal control problem and obtained bang-bang control
Almost maximally almost-periodic group topologies determined by T-sequences
A sequence in a group is a {\em -sequence} if there is a
Hausdorff group topology on such that
. In this paper, we provide several
sufficient conditions for a sequence in an abelian group to be a -sequence,
and investigate special sequences in the Pr\"ufer groups
. We show that for , there is a Hausdorff group
topology on that is determined by a -sequence,
which is close to being maximally almost-periodic--in other words, the von
Neumann radical is a non-trivial finite
subgroup. In particular, . We also prove that the
direct sum of any infinite family of finite abelian groups admits a group
topology determined by a -sequence with non-trivial finite von Neumann
radical.Comment: v2 - accepted (discussion on non-abelian case is removed, replaced by
new results on direct sums of finite abelian groups
Markov Process of Muscle Motors
We study a Markov random process describing a muscle molecular motor
behavior. Every motor is either bound up with a thin filament or unbound. In
the bound state the motor creates a force proportional to its displacement from
the neutral position. In both states the motor spend an exponential time
depending on the state. The thin filament moves at its velocity proportional to
average of all displacements of all motors. We assume that the time which a
motor stays at the bound state does not depend on its displacement. Then one
can find an exact solution of a non-linear equation appearing in the limit of
infinite number of the motors.Comment: 10 page
Qualitative Criterion for Interception in a Pursuit/Evasion Game
A qualitative account is given of a differential pursuit/evasion game. A
criterion for the existence of an intercept solution is obtained using future
cones that contain all attainable trajectories of target or interceptor
originating from an initial position. A sufficient and necessary conditon that
an opportunity to intercept always exist is that, after some initial time, the
future cone of the target be contained within the future cone of the
interceptor. The sufficient condition may be regarded as a kind of Nash
equillibrium.Comment: 8 pages; revsions and corrigend
Topological surface states in three-dimensional magnetic insulators
An electron moving in a magnetically ordered background feels an effective
magnetic field that can be both stronger and more rapidly varying than typical
externally applied fields. One consequence is that insulating magnetic
materials in three dimensions can have topologically nontrivial properties of
the effective band structure. For the simplest case of two bands, these "Hopf
insulators" are characterized by a topological invariant as in quantum Hall
states and Z_2 topological insulators, but instead of a Chern number or parity,
the underlying invariant is the Hopf invariant that classifies maps from the
3-sphere to the 2-sphere. This paper gives an efficient algorithm to compute
whether a given magnetic band structure has nontrivial Hopf invariant, a
double-exchange-like tight-binding model that realizes the nontrivial case, and
a numerical study of the surface states of this model.Comment: 4 pages, 2 figures; published versio
General solution of equations of motion for a classical particle in 9-dimensional Finslerian space
A Lagrangian description of a classical particle in a 9-dimensional flat
Finslerian space with a cubic metric function is constructed. The general
solution of equations of motion for such a particle is obtained. The Galilean
law of inertia for the Finslerian space is confirmed.Comment: 10 pages, LaTeX-2e, no figures; added 2 reference
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