79,935 research outputs found
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Localization of Relative-Position of Two Atoms Induced by Spontaneous Emission
We revisit the back-action of emitted photons on the motion of the relative
position of two cold atoms. We show that photon recoil resulting from the
spontaneous emission can induce the localization of the relative position of
the two atoms through the entanglement between the spatial motion of individual
atoms and their emitted photons. The result provides a more realistic model for
the analysis of the environment-induced localization of a macroscopic object.Comment: 8 pages and 4 figure
Spectral Representation Theory for Dielectric Behavior of Nonspherical Cell Suspensions
Recent experiments revealed that the dielectric dispersion spectrum of
fission yeast cells in a suspension was mainly composed of two sub-dispersions.
The low-frequency sub-dispersion depended on the cell length, while the
high-frequency one was independent of it. The cell shape effect was simulated
by an ellipsoidal cell model but the comparison between theory and experiment
was far from being satisfactory. Prompted by the discrepancy, we proposed the
use of spectral representation to analyze more realistic cell models. We
adopted a shell-spheroidal model to analyze the effects of the cell membrane.
It is found that the dielectric property of the cell membrane has only a minor
effect on the dispersion magnitude ratio and the characteristic frequency
ratio. We further included the effect of rotation of dipole induced by an
external electric field, and solved the dipole-rotation spheroidal model in the
spectral representation. Good agreement between theory and experiment has been
obtained.Comment: 19 pages, 5 eps figure
Decay of Loschmidt Echo Enhanced by Quantum Criticality
We study the transition of a quantum system from a pure state to a mixed
one, which is induced by the quantum criticality of the surrounding system
coupled to it. To characterize this transition quantitatively, we carefully
examine the behavior of the Loschmidt echo (LE) of modelled as an Ising
model in a transverse field, which behaves as a measuring apparatus in quantum
measurement. It is found that the quantum critical behavior of strongly
affects its capability of enhancing the decay of LE: near the critical value of
the transverse field entailing the happening of quantum phase transition, the
off-diagonal elements of the reduced density matrix describing vanish
sharply.Comment: 4 pages, 3 figure
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