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Jun 30, 2018
06/18

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Anna M. Barry; F. Hajir; P. G. Kevrekidis

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In this work, we construct suitable generating functions for vortices of alternating signs in the realm of Bose-Einstein condensates. In addition to the vortex-vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we...

Topics: Nonlinear Sciences, Quantum Gases, Mathematics, Pattern Formation and Solitons, Mathematical...

Source: http://arxiv.org/abs/1407.7965

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Jun 30, 2018
06/18

by
Farhad A. Goodarzi; Daewon Lee; Taeyoung Lee

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We derived a coordinate-free form of equations of motion for a complete model of a quadrotor UAV with a payload which is connected via a flexible cable according to Lagrangian mechanics on a manifold. The flexible cable is modeled as a system of serially-connected links and has been considered in the full dynamic model. A geometric nonlinear control system is presented to exponentially stabilize the position of the quadrotor while aligning the links to the vertical direction below the...

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1407.8164

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Jun 30, 2018
06/18

by
Fernando Cordero; Lavinia Perez-Ostafe

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We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim to determine the size of the transaction costs needed to eliminate the arbitrage from these models. To gain more insight, we first consider only 1-step trading strategies and we...

Topics: Probability, Mathematics, Quantitative Finance, Pricing of Securities

Source: http://arxiv.org/abs/1407.8068

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5.0

Jun 30, 2018
06/18

by
Franziska Jahnke; Jochen Koenigsmann

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Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply...

Topics: Mathematics, Logic, Commutative Algebra

Source: http://arxiv.org/abs/1407.8156

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3.0

Jun 30, 2018
06/18

by
Frederic Legoll; William Minvielle

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We consider a variance reduction approach for the stochastic homogenization of divergence form linear elliptic problems. Although the exact homogenized coefficients are deterministic, their practical approximations are random. We introduce a control variate technique to reduce the variance of the computed approximations of the homogenized coefficients. Our approach is based on a surrogate model inspired by a defect-type theory, where a perfect periodic material is perturbed by rare defects....

Topics: Mathematics, Numerical Analysis, Probability

Source: http://arxiv.org/abs/1407.8029

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Jun 30, 2018
06/18

by
Friedrich Knop; Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

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We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure $L^p$-integrability of matrix coefficients on Z.

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.8006

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4.0

Jun 30, 2018
06/18

by
Issam Ibnouhsein; Fabio Costa; Alexei Grinbaum

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Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behaviour is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We...

Topics: Quantum Physics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1407.8050

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3.0

Jun 30, 2018
06/18

by
Jing Zhang; Yu-xi Liu; Re-Bing Wu; Kurt Jacobs; Sahin Kaya Ozdemir; Lan Yang; Tzyh-Jong Tarn; Franco Nori

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Quantum input-output theory plays a very important role for analyzing the dynamics of quantum systems, especially large-scale quantum networks. As an extension of the input-output formalism of Gardiner and Collet, we develop a new approach based on the quantum version of the Volterra series which can be used to analyze nonlinear quantum input-output dynamics. By this approach, we can ignore the internal dynamics of the quantum input-output system and represent the system dynamics by a series of...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1407.8108

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3.0

Jun 30, 2018
06/18

by
John M. Myers; F. Hadi Madjid

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Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply...

Topics: Quantum Physics, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1407.8020

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7.0

Jun 30, 2018
06/18

by
Leandro Cagliero; Fernando Szechtman

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Let ${\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\mathfrak r}$ and nilpotent radical ${\mathfrak n}=[{\mathfrak g},{\mathfrak r}]$. Given a finite dimensional ${\mathfrak g}$-module $U$, its nilpotency series $ 0\subset U({\mathfrak n}^1)\subset\cdots\subset U({\mathfrak n}^m)=U$ is defined so that $U({\mathfrak n}^1)$ is the 0-weight space of ${\mathfrak n}$ in $U$, $U({\mathfrak n}^2)/U({\mathfrak n}^1)$ is the 0-weight space of...

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.8125

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4.0

Jun 30, 2018
06/18

by
M. Zuppardo; J. P. Santos; G. De Chiara; M. Paternostro; F. L. Semiao; G. M. Palma

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We describe an apparatus designed to make non-demolition measurements on a Bose-Einstein condensate (BEC) trapped in a double-well optical cavity. This apparatus contains, as well as the bosonic gas and the trap, an optical cavity. We show how the interaction between the light and the atoms, under appropriate conditions, can allow for a weakly disturbing yet highly precise measurement of the population imbalance between the two wells and its variance. We show that the setting is well suited for...

Topics: Quantum Physics, Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1407.8077

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Jun 30, 2018
06/18

by
Yuchen Peng; Frank Gaitan

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Successful implementation of a fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold $P_{a}$ exists for any quantum gate that is to be used in such a computation. Specifically, the error probability $P_{e}$ for such a gate must fall below the accuracy threshold: $P_{e} < P_{a}$. Estimates of $P_{a}$ vary widely, though $P_{a}\sim 10^{-4}$ has emerged as a challenging target...

Topics: Quantum Physics, Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1407.8074