43,305 research outputs found
Functional Equations and Fourier Analysis
By exploring the relations among functional equations, harmonic analysis and
representation theory, we give a unified and very accessible approach to solve
three important functional equations -- the d'Alembert equation, the Wilson
equation, and the d'Alembert long equation, on compact groups.Comment: 8 pages, to appear in CM
General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion
In this paper, we give the general expressions for a special series of tree
amplitudes of the Yang-Mills theory. This series of amplitudes have two
adjacent massless spin-1 particles with extra-dimensional momenta and any
number of positive helicity gluons. With special helicity choices, we use the
spinor helicity formalism to express these n-point amplitudes in compact forms,
and find a clever way to use the BCFW recursion relations to prove the results.
Then these amplitudes are used to form the complete 1-loop all-plus integrand
with any number of gluons, expressed in the Q-cut representation.Comment: Published version with 20 pages, 8 figure, and 1 new referenc
Quantum trajectory analysis of a thresholdlike transition in the microlaser
In a recent microlaser experiment [K. An et al., Phys. Rev. Lett. 73, 3375 (1994)], a thresholdlike transition of intracavity mean photon number as a function of intracavity mean atom number has been observed. In this paper the behavior is explored with quantum trajectory simulations. It is shown that the transition is caused by enhanced atom-cavity Rabi interaction due to the increase of the intracavity photon number as the intracavity atom number is increased. The transition is further accentuated by the position-dependent variation of the coupling constant in the Fabry-Pérot cavity. In addition, it is demonstrated that multiatom collective effects are negligible in the microlaser under consideration, in which atoms are injected into the cavity at random times and the product of the coupling constant and atom-cavity interaction time is much less than π. In this case the analytic theory of the one-atom micromaser [P. Filipowicz et al., Phys. Rev. A 34, 3077 (1986)] can be extrapolated into the multiatom region, assuming uniform atom-cavity coupling throughout the cavity and monovelocity atomic injection. Finally, simulations are performed which account for spatial variation of coupling constant, velocity distribution of injected atoms, and spontaneous atomic decay in the actual experiment. The results are in good agreement with experiment
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