Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics

Abstract

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) Effects of finite sampling-rate and -time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile micro-organisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensionalization.

12 pages, 8 figures

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• Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells
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• Power Spectrum Analysis for Optical Tweezers, II: Laser Wavelength Dependence of Parasitic Filtering, and how to Achieve High Band-Width
• Elementary simulation of tethered Brownian motion
• Parameter exploration of optically trapped liquid aerosols

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