Publications
| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Chan, H. B., Dykman, M. I. & Stambaugh, C. | Paths of Fluctuation Induced Switching | 2008 | Phys. Rev. Lett. | article | DOIURL |
| Abstract: We demonstrate that the paths followed by a system in fluctuation-activated switching form a narrow tube in phase space. A theory of the path distribution is developed and its direct measurement is performed in a micromechanical oscillator. The experimental and theoretical results are in excellent agreement, with no adjustable parameters. We also demonstrate the lack of time-reversal symmetry in switching of systems far from thermal equilibrium. | |||||
BibTeX:
@article{Chan2008,
author = {H. B. Chan and M. I. Dykman and C. Stambaugh},
title = {Paths of Fluctuation Induced Switching},
journal = {Phys. Rev. Lett.},
publisher = {APS},
year = {2008},
volume = {100},
number = {13},
pages = {130602},
url = {http://link.aps.org/abstract/PRL/v100/e130602},
doi = {10.1103/PhysRevLett.100.130602}
}
|
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| Chan, H. B. & Stambaugh, C. | Activation Barrier Scaling and Crossover for Noise-Induced Switching in Micromechanical Parametric Oscillators | 2007 | Phys. Rev. Lett. | article | DOIURL |
| Abstract: We explore fluctuation-induced switching in parametrically driven micromechanical torsional oscillators. The oscillators possess one, two, or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific. | |||||
BibTeX:
@article{Chan2007a,
author = {H. B. Chan and C. Stambaugh},
title = {Activation Barrier Scaling and Crossover for Noise-Induced Switching in Micromechanical Parametric Oscillators},
journal = {Phys. Rev. Lett.},
publisher = {APS},
year = {2007},
volume = {99},
number = {6},
pages = {060601},
url = {http://link.aps.org/abstract/PRL/v99/e060601},
doi = {http://dx.doi.org/10.1103/PhysRevLett.99.060601}
}
|
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| Chan, H. B. & Stambaugh, C. | Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator | 2006 | Phys. Rev. B | article | DOI |
| Abstract: We study noise-enhanced frequency mixing in an underdamped micromechanical torsional oscillator. The oscillator is electrostatically driven into bistability by a strong, periodic voltage at frequency $d$. A second, weak ac voltage is applied at a frequency $ close to $d$. Due to nonlinearity in the system, vibrations occur at both $ and $2d-. White noise is injected into the excitation, allowing the system to occasionally overcome the activation barrier and switch between the two states. At the primary drive frequency where the occupations of the two states are approximately equal, we observe noise-induced enhancement of the oscillation amplitudes at both $ and the down-converted frequency $2d-, in agreement with theoretical predictions. Such enhancement occurs as a result of the noise-induced interstate transitions becoming synchronous with the beating between the two driving frequencies. | |||||
BibTeX:
@article{Chan2006,
author = {H. B. Chan and C. Stambaugh},
title = {Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator},
journal = {Phys. Rev. B},
year = {2006},
volume = {73,},
pages = {224301},
doi = {http://dx.doi.org/10.1103/PhysRevB.73.224301}
}
|
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| Stambaugh, C. & Chan, H. B. | Supernarrow spectral peaks near a kinetic phase transition in a driven, nonlinear micromechanical oscillator | 2006 | Phys. Rev. Lett. | article | DOI |
| Abstract: We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving frequency. White noise is injected into the excitation, allowing the system to overcome the activation barrier and switch between the two states. While the oscillator Phys. Rev. Edominately resides in one of the two states for most excitation frequencies, a narrow range of frequencies exist where the occupations of the two states are approximately equal. At these frequencies, the oscillator undergoes a kinetic phase transition that resembles the phase transition of thermal equilibrium systems. We observe a supernarrow peak in the power spectral densities of fluctuations of the oscillator. This peak is centered at the excitation frequency and arises as a result of noise-induced transitions between the two dynamical states. | |||||
BibTeX:
@article{Stambaugh2006,
author = {C. Stambaugh and H. B. Chan},
title = {Supernarrow spectral peaks near a kinetic phase transition in a driven, nonlinear micromechanical oscillator},
journal = {Phys. Rev. Lett.},
year = {2006},
volume = {97,},
pages = {110602},
doi = {http://dx.doi.org/10.1103/PhysRevLett.97.110602}
}
|
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| Stambaugh, C. & Chan, H. B. | Noise activated switching in a driven, nonlinear micromechanical oscillator | 2006 | Phys. Rev. B | article | DOIURL |
| Abstract: We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two stable dynamical states with different oscillation amplitudes. We induce the oscillator to escape from one dynamical state into the other by introducing noise in the excitation. By measuring the rate of random transitions as a function of noise intensity, we deduce the activation energy as a function of frequency detuning. Close to the critical point, the activation energy is expected to display system-independent scaling. The measured critical exponent is in good agreement with variational calculations and asymptotic scaling theory. | |||||
BibTeX:
@article{Stambaugh2006a,
author = {C. Stambaugh and H. B. Chan},
title = {Noise activated switching in a driven, nonlinear micromechanical oscillator},
journal = {Phys. Rev. B},
year = {2006},
volume = {73,},
pages = {172302},
url = {http://link.aps.org/abstract/PRB/v73/e172302},
doi = {http://dx.doi.org/10.1103/PhysRevB.73.172302}
}
|
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Talks
| Author | Title | Year | Conference | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Stambaugh, C. & Chan, H. B. | Activation barrier scaling and crossover for noise-induced
switching in a micromechanical parametric oscillator [Abstract] |
2006 | APS March Meeting, Baltimore, MD | Talk | URL |
| Abstract: We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical torsional oscillator. By applying a sufficiently large periodic driving force, two stable dynamical states occur within a particular range of drive frequency. White noise is injected into the driving force allowing the system to overcome the activation barrier and to switch between the two states. While the system predominately resides in one of the two states for most excitation frequencies, a narrow range of frequencies exist where the population levels are approximately equal and the system is at a `kinetic phase transition' that bears resemblance to the phase transition of thermal equilibrium systems. By examining the power spectral densities of the measured oscillation amplitude, the fluctuation characteristics of the system can be studied. At the `kinetic phase transition' a supernarrow peak, centered at the excitation frequency, arises as a result of noise-induced transitions between the two dynamic states. Smaller, secondary peaks associated with fluctuations about the two attractors are also examined. Its dependence on noise and excitation frequency is shown to be distinct from that of the supernarrow peak. | |||||
BibTeX:
@article{Stambaugh2005t,
}
|
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| Stambaugh, C. & Chan, H. B. | Activation barrier scaling and crossover for noise-induced switching in a micromechanical parametric oscillator [Abstract] |
2007 | APS March Meeting, Denver, CO | Talk | URL |
| Abstract: We explore fluctuation-induced switching in a parametrically-driven micromechanical torsional oscillator, a system far from thermal equilibrium. Under sufficiently strong parametric modulation of the spring constant, the oscillator possesses one, two or three stable attractors depending on the modulation frequency. Near the bifurcation points where the number of attractors changes, the activation barrier for switching out of a stable state is predicted to display universal, system-independent scaling relationships. We induce the oscillator to switch between the coexisting states by injecting noise in the excitation. By measuring the rate of random transitions as a function of noise intensity, we deduce the activation barrier as a function of frequency. Near both bifurcation points, the activation barriers are found to depend on frequency detuning with critical exponent of 2, consistent with the predicted universal scaling in parametrically driven systems. Away from the immediate vicinity of the bifurcation point, universal scaling relationships for the activation barrier no longer hold. At large detuning, we observe a crossover to a different power law dependence with an exponent that is specific to our device. | |||||
BibTeX:
@article{Stambaugh2007t,
}
|
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| Stambaugh, C. & Chan, H. B. | Fluctuation relations in a micromechanical oscillator driven far from thermal equilibrium [Abstract] |
2008 | APS March Meeting, New Orleans, NO | Talk | URL |
| Abstract: We explore fluctuation relations in a micromechanical torsional oscillator. In the linear regime when the modulation is weak, we verify that the ratio of the work variance to the mean work is independent of the driving frequency, consistent with standard fluctuation relations for a steady state system near thermal equilibrium. We then apply a strong drive to force the system into nonlinearity. Here the system displays bistability and the relationship between the work and variance is expected to deviate from the linear regime. For a bistable system the total variance has two distinct contributing components. The first results from small fluctuations about a stable state. The work variance is expected to diverge as the system approaches the bifurcation point where the state disappears. The other part of the variance results from the system switching between coexisting states. This part of the variance is expected to show a sharp peak near the kinetic phase transition when the populations of the two states are comparable. We compare our experimental results to theoretical predictions that distinguish nonlinear oscillators from equilibrium systems. | |||||
BibTeX:
@article{Stambaugh2008t,
}
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Created by JabRef on 06/01/2008.