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Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle
Cyclic structure and dynamics are of great interest in both the fields of
stochastic processes and nonequilibrium statistical physics. In this paper, we
find a new symmetry of the Brownian motion named as the quasi-time-reversal
invariance. It turns out that such an invariance of the Brownian motion is the
key to prove the cycle symmetry for diffusion processes on the circle, which
says that the distributions of the forming times of the forward and backward
cycles, given that the corresponding cycle is formed earlier than the other,
are exactly the same. With the aid of the cycle symmetry, we prove the strong
law of large numbers, functional central limit theorem, and large deviation
principle for the sample circulations and net circulations of diffusion
processes on the circle. The cycle symmetry is further applied to obtain
various types of fluctuation theorems for the sample circulations, net
circulation, and entropy production rate.Comment: 28 page
Steady-State Ab Initio Laser Theory for N-level Lasers
We show that Steady-state Ab initio Laser Theory (SALT) can be applied to
find the stationary multimode lasing properties of an N-level laser. This is
achieved by mapping the N-level rate equations to an effective two-level model
of the type solved by the SALT algorithm. This mapping yields excellent
agreement with more computationally demanding N-level time domain solutions for
the steady state
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