651 research outputs found
Optimal Dynamical Decoherence Control of a Qubit
A theory of dynamical control by modulation for optimal decoherence reduction
is developed. It is based on the non-Markovian Euler-Lagrange equation for the
energy-constrained field that minimizes the average dephasing rate of a qubit
for any given dephasing spectrum.Comment: 6 pages, including 2 figures and an appendi
Observability inequalities for transport equations through Carleman estimates
We consider the transport equation \ppp_t u(x,t) + H(t)\cdot \nabla u(x,t) =
0 in \OOO\times(0,T), where and \OOO\subset \R^d is a bounded
domain with smooth boundary \ppp\OOO. First, we prove a Carleman estimate for
solutions of finite energy with piecewise continuous weight functions. Then,
under a further condition which guarantees that the orbits of intersect
\ppp\OOO, we prove an energy estimate which in turn yields an observability
inequality. Our results are motivated by applications to inverse problems.Comment: 18 pages, 3 figure
Rediscovering Manning’S Equation Using Genetic Programming
Open-channel hydraulics’ (OCH) research traditionally links empirical formulas to observational data. One of the most common equations in OCH is Manning’s formula for open channel flow (Q) driven by gravity (also known as the Gauckler-Manning-Strickler formula). The formula relates the cross-sectional average velocity (V=Q/A), the hydraulic radius (R), and the slope of the water surface (S) with a friction coefficient n, characteristic of the channel’s surface. Here we show a practical example where Genetic Programming (GP), a technique derived from Bioinformatics, can be used to derive an empirical relationship based on different synthetic datasets of the aforementioned parameters. Specifically, we evaluated if Manning’s formula could be retrieved from datasets with 300 pentads of A, n, R, S, and Q (from Manning’s equation) using GP. The cross-validated results show success retrieving the functional form from the synthetic data and encourage the application of GP on problems where traditional empirical relationships show high biases, like sediment transport. The results also show alternative flow equations that can be used in the absence of one of the predictors and approximate Manning’s equation
Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction
We construct a minimal robust controlled-NOT gate with an Ising-type
interaction by which elementary two-qubit gates are implemented. It is robust
against inaccuracy of the coupling strength and the obtained quantum circuits
are constructed with the minimal number (N=3) of elementary two-qubit gates and
several one-qubit gates. It is noteworthy that all the robust circuits can be
mapped to one-qubit circuits robust against a pulse length error. We also prove
that a minimal robust SWAP gate cannot be constructed with N=3, but requires
N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure
Microscopic Analysis of the Non-Dissipative Force on a Line Vortex in a Superconductor: Berry's Phase, Momentum Flows and the Magnus Force
A microscopic analysis of the non-dissipative force acting on
a line vortex in a type-II superconductor at is given. We first examine
the Berry phase induced in the true superconducting ground state by movement of
the vortex and show how this induces a Wess-Zumino term in the hydrodynamic
action of the superconducting condensate. Appropriate variation of
gives and variation of the Wess-Zumino term is seen to
contribute the Magnus (lift) force of classical hydrodynamics to . This first calculation confirms and strengthens earlier work by Ao and
Thouless which was based on an ansatz for the many-body ground state. We also
determine through a microscopic derivation of the continuity
equation for the condensate linear momentum. This equation yields the
acceleration equation for the superflow and shows that the vortex acts as a
sink for the condensate linear momentum. The rate at which momentum is lost to
the vortex determines and the result obtained agrees with the
Berry phase calculation. The Magnus force contribution to is
seen to be a consequence of the vortex topology. Preliminary remarks are made
regarding finite temperature extensions, with emphasis on its relevance to the
sign anomaly occurring in Hall effect experiments done in the flux flow regime.Comment: 40 pages, RevTex, UBCTP-94-00
The Sound of Sonoluminescence
We consider an air bubble in water under conditions of single bubble
sonoluminescence (SBSL) and evaluate the emitted sound field nonperturbatively
for subsonic gas-liquid interface motion. Sound emission being the dominant
damping mechanism, we also implement the nonperturbative sound damping in the
Rayleigh-Plesset equation for the interface motion. We evaluate numerically the
sound pulse emitted during bubble collapse and compare the nonperturbative and
perturbative results, showing that the usual perturbative description leads to
an overestimate of the maximal surface velocity and maximal sound pressure. The
radius vs. time relation for a full SBSL cycle remains deceptively unaffected.Comment: 25 pages; LaTex and 6 attached ps figure files. Accepted for
publication in Physical Review
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