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Math Tags > Tag based links for Amplitude

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Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy: Appl. Opt., Vol. 24 (May 1985), pp. 1270-1282.Accu rate correlation techniques are used to analyze the performance characteristic s of a tunable, femtosecond pulse dye laser which is passively mode locked and uses either one or two intracavity prisms to control frequency and its modulation. The main advantages of the interferometri c second-order autocorrelatio ns used are the provision of phase information and a high sensitivity to pulse shape. A numerical method is used to analyze the more complex pulse shapes and chirps generated by the laser. Comparisons of autocorrelatio ns and cross correlations calculated for the dispersed pulses with actual measurements demonstrate the accuracy of the fitting procedure used.

Source: Appl. Opt., Vol. 24 (May 1985), pp. 1270-1282.
Multimodal Interfaces for Cell Phones and Mobile Technology: International Journal of Speech Technology, Vol. 8, No. 2. (June 2005), pp. 127-132.

Source: International Journal of Speech Technology, Vol. 8, No. 2. (June 2005), pp. 127-132.
Quantum computers can search rapidly by using almost any transformation: (3 Dec 1997)A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.

Source: (3 Dec 1997)
Quantum Amplitude Amplification and Estimation: (15 May 2000)Consider a Boolean function $?: X \to {0,1}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $?(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A \ket0 = ?_x? X ?_x \ketx$ is a quantum superposition of the elements of $X$, and let $a$ denote the probability that a good element is produced if $A \ket0$ is measured. If we repeat the process of running $A$, measuring the output, and using $?$ to check the validity of the result, we shall expect to repeat $1/a$ times on the average before a solution is found. *Amplitude amplification* is a process that allows to find a good $x$ after an expected number of applications of $A$ and its inverse which is proportional to $1/\sqrta$, assuming algorithm $A$ makes no measurements. This is a generalization of Grover's searching algorithm in which $A$ was restricted to producing an equal superposition of all members of $X$ and we had a promise that a single $x$ existed such that $?(x)=1$. Our algorithm works whether or not the value of $a$ is known ahead of time. In case the value of $a$ is known, we can find a good $x$ after a number of applications of $A$ and its inverse which is proportional to $1/\sqrta$ even in the worst case. We show that this quadratic speedup can also be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform amplitude estimation, a process that allows to estimate the value of $a$. We apply amplitude estimation to the problem of *approximate counting*, in which we wish to estimate the number of $x? X$ such that $?(x)=1$. We obtain optimal quantum algorithms in a variety of settings.

Source: (15 May 2000)
Vlasov simulations of very-large-amp litude-wave generation in the plasma wake-field accelerator: Physical Review A, Vol. 44, No. 10. (15 November 1991), 6854.Simulatio ns of the plasma wake-field accelerator are carried out by following the time evolution of the plasma distribution function in one dimension via the Vlasov-Maxwell equations. Simulation results are compared to numerical solutions of the nonlinear relativistic cold plasma equations and to previous theoretical estimations of trapping and thermal effects on plasma waves. It is found that highly nonlinear wakes are obtainable in the vicinity of the driving beam; where the thermal velocity spread of the plasma is reduced. In this region; wake amplitudes can significantly exceed the expectations of relativistic warm plasma models and agree closely with cold fluid theory. In all cases; however; particle trapping and thermalization due to particle scattering from the large-amplitud e plasma wave reduce the wake to below the nonrelativisti c wave-breaking limit after the initial accelerating peak.

Source: Physical Review A, Vol. 44, No. 10. (15 November 1991), 6854.
Generating Tree Amplitudes in N=4 SYM and N=8 SG: (22 May 2008)We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. The recursion relations remain valid for a subset of N=8 supergravity amplitudes which do not vanish asymptotically for all |X]. The MHV-vertex expansion of the n-graviton NMHV amplitude for n=5,6,...,11 is independent of |X] and exhibits the asymptotic behavior z^n-12. This presages difficulties for n > 12. Generating functions show how the symmetries of supergravity can be implemented in the quadratic map between supergravity and gauge theory embodied in the KLT and other similar relations between amplitudes in the two theories.

Source: (22 May 2008)
Twistor-inspir ed construction of massive quark amplitudes: (30 Oct 2008)The analog of the Cachazo-Svrvce k-Witten rules for scattering amplitudes with massive quarks is derived following an approach previously employed for amplitudes with massive scalars. A prescription for the external wave-functions is given that leads to a one-to one relation between fields in the action and spin-states of massive quarks. Several examples for the application of the rules are given and the structure of some all-multiplici ty amplitudes with a pair of massive quarks is discussed. The rules make supersymmetric relations to amplitudes with massive scalars manifest at the level of the action. The formalism is extended to several quark flavors with different masses.

Source: (30 Oct 2008)
Supersymmetry Relations and MHV Amplitudes in Superstring Theory: (5 Oct 2007)We discuss supersymmetric Ward identities relating various scattering amplitudes in type I open superstring theory. We show that at the disk level, the form of such relations remains exactly the same, to all orders in alpha', as in the low-energy effective field theory describing the alpha'-> 0 limit. This result holds in D=4 for all compactificati ons, even for those that break supersymmetry. We apply SUSY relations to the computations of N-gluon MHV superstring amplitudes, simplifying the existing results for N

Source: (5 Oct 2007)
Multi-Gluon Scattering in Open Superstring Theory: (6 Oct 2006)We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world-sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (alpha' -> 0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4,5 and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals - generalized Euler integrals - which for N>= 6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their alpha'-expansi ons lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O(alpha'^2), originate from the well-known alpha'^2 Tr F^4 effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in alpha'. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multi-jet production at the Large Hadron Collider (LHC).

Source: (6 Oct 2006)
Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD: (27 Oct 2008)We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in $\cal N$=4 SYM to large-N (or quenched) QCD. We show that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Venezian o behavior of scattering amplitudes at high energies and fixed momentum transfer, when quark mass is small and/or the number of particles is large. We elaborate on this duality for string theory in a flat space, identifying the asymptotes of the disk amplitude and the Wilson loop of large-N QCD.

Source: (27 Oct 2008)

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