Journal ArticleDOI
RPA for the linewidth of the van der Pol Oscillator
K. Ziegler,Heinz Horner +1 more
TLDR
In this paper, the linewidth of the van der Pol Oxcillator was calculated in random phase approximation for weak and strong pumping and also in the largen limit for all pumping.Abstract:
The linewidth of then component van der Pol Oxcillator is calculated in random phase approximation. Forn=2 this model describes a single mode laser. This approximation is asymptotically correct for weak and strong pumping and also in the largen limit for all pumping. The result is in good agreement with numerical results forn=2 in the whole range including the threshold. The corresponding vertex renormalized approximation on the other hand yields poor agreement and the wrong asymptotic value in the limit of strong pumping. The reason for this failure is discussed.read more
Citations
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Journal ArticleDOI
Solutions and applications of tridiagonal vector recurrence relations
Hannes Risken,H. D. Vollmer +1 more
TL;DR: A general method is presented by which the initial value problem can be solved by iteration and the applicability of the method is demonstrated by calculating the eigenvalues of the laser Fokker-Planck operator.
Journal ArticleDOI
A polynomial expansion method for solving the laser Fokker-Planck equation
Hannes Risken,H. D. Vollmer +1 more
TL;DR: In this article, a system of ordinary differential equations for the coefficients of the expansion is derived and is shown to have the form of a recurrence relation with length four, and applied to the transient solution, the averaged amplitude and the first four cumulants of the intensity distribution are obtained.
Journal ArticleDOI
Parametric self pulsing in a quantum opto‐mechanical system
C. A. Holmes,Gerard J. Milburn +1 more
TL;DR: In this paper, the authors describe an opto-mechanical system in which the coupling between optical and mechanical degrees of freedom takes the form of a fully quantised third-order parametric interaction.
Book ChapterDOI
Statistical Properties of Laser Light
TL;DR: In this article, the Fokker-Planck equation has been used for treating noise in a simple laser model (one mode, adiabatic elimination of all variables with the exception of the laser field, threshold region).
Posted Content
Parametric self pulsing in a quantum opto-mechanical system
C. A. Holmes,Gerard J. Milburn +1 more
TL;DR: In this article, the authors describe an opto-mechanical system in which the coupling between optical and mechanical degrees of freedom takes the form of a fully quantised third-order parametric interaction.
References
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Journal ArticleDOI
On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties
TL;DR: In this paper, a Lagrangean for nonlinear stochastic processes is derived from the path probability density for classical field dynamics, which provides a convenient approach to the mode coupling equations and the renormalization group theory of critical dynamics.
Journal ArticleDOI
Generalized Onsager-Machlup function and classes of path integral solutions of the Fokker-Planck equation and the master equation
TL;DR: In this article, the path integral solution of a stochastic process described by a generalized Langevin equation with coordinate-dependent fluctuating forces and white spectrum was determined, and the exponent of the exponential function occurring in that solution was interpreted as generalization of the Onsager-Machlup function.
Journal ArticleDOI
Goldstone mode singularities and equation of state of an isotropic magnet
Lothar Schäfer,Heinz Horner +1 more
TL;DR: In this article, a resummation of renormalized perturbation theory without use of recursion relations is proposed, which is based on Ward identities and exhibits the form of the Goldstone mode singularities at the magnetization curve.
Journal ArticleDOI
Memory effects in the linewidth and line shape near the laser threshold
TL;DR: In this paper, a mode-coupling approximation and a continued fraction representation are used to calculate the memory kernels of the dynamical field and photon-number correlation functions near a single-mode laser's threshold.