24,372 research outputs found
Supersymmetric partners of the trigonometric Poschl-Teller potentials
The first and second-order supersymmetry transformations are used to generate
Hamiltonians with known spectra departing from the trigonometric Poschl-Teller
potentials. The several possibilities of manipulating the initial spectrum are
fully explored, and it is shown how to modify one or two levels, or even to
leave the spectrum unaffected. The behavior of the new potentials at the
boundaries of the domain is studied.Comment: 20 pages, 4 figure
On Packet Scheduling with Adversarial Jamming and Speedup
In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes
arrive over time to be transmitted over a channel in which instantaneous
jamming errors occur at times chosen by the adversary and not known to the
algorithm. The transmission taking place at the time of jamming is corrupt, and
the algorithm learns this fact immediately. An online algorithm maximizes the
total size of packets it successfully transmits and the goal is to develop an
algorithm with the lowest possible asymptotic competitive ratio, where the
additive constant may depend on packet sizes.
Our main contribution is a universal algorithm that works for any speedup and
packet sizes and, unlike previous algorithms for the problem, it does not need
to know these properties in advance. We show that this algorithm guarantees
1-competitiveness with speedup 4, making it the first known algorithm to
maintain 1-competitiveness with a moderate speedup in the general setting of
arbitrary packet sizes. We also prove a lower bound of on
the speedup of any 1-competitive deterministic algorithm, showing that our
algorithm is close to the optimum.
Additionally, we formulate a general framework for analyzing our algorithm
locally and use it to show upper bounds on its competitive ratio for speedups
in and for several special cases, recovering some previously known
results, each of which had a dedicated proof. In particular, our algorithm is
3-competitive without speedup, matching both the (worst-case) performance of
the algorithm by Jurdzinski et al. and the lower bound by Anta et al.Comment: Appeared in Proc. of the 15th Workshop on Approximation and Online
Algorithms (WAOA 2017
Optimal quantum state reconstruction for cold trapped ions
We study the physical implementation of an optimal tomographic reconstruction
scheme for the case of determining the state of a multi-qubit system, where
trapped ions are used for defining qubits. The protocol is based on the use of
mutually unbiased measurements and on the physical information described in H.
H\"{a}ffner \emph{et. al} [Nature \textbf{438}, 643-646 (2005)]. We introduce
the concept of physical complexity for different types of unbiased measurements
and analyze their generation in terms of one and two qubit gates for trapped
ions.Comment: Accepted for publication in Phys. Rev. A as Rap. Com
Structure of the Vacuum in Deformed Supersymmetric Chiral Models
We analyze the vacuum structure of N=1/2 chiral supersymmetric theories in
deformed superspace. In particular we study O'Raifeartaigh models with
C-deformed superpotentials and canonical and non-canonical deformed Kahler
potentials. We find conditions under which the vacuum configurations are
affected by the deformations.Comment: 15 pages, minor corrections. Version to appear in JHE
Separation and fractionation of order and disorder in highly polydisperse systems
Microcanonical Monte Carlo simulations of a polydisperse soft-spheres model
for liquids and colloids have been performed for very large polydispersity, in
the region where a phase-separation is known to occur when the system (or part
of it) solidifies. By studying samples of different sizes, from N=256 to N=864,
we focus on the nature of the two distinct coexisting phases. Measurements of
crystalline order in particles of different size reveal that the solid phase
segregates between a crystalline solid with cubic symmetry and a disordered
phase. This phenomenon is termed fractionation.Comment: 8 pages, 5 figure
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