Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states

Dykman, M. I.; Krivoglaz, M. A.

doi:10.1016/0378-4371(80)90010-2

Cited by 93 publications

(121 citation statements)

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“…Close to the bifurcation frequency where the high-amplitude state disappears, the activation energy is predicted by variational calculations and asymptotic scaling theory to display system-independent scaling. [14][15][16][17] Our measurement of activation energy as a function of frequency detuning yields critical exponents of 1.38± 0.15 and 1.40± 0.15, respectively, for two samples with different parameters, in good agreement with the theoretical predictions for escape in nonequilibrium systems near a spinodal point.In our experiment, measurements were performed on two micromechanical oscillators ͑samples A and B͒. Each oscillator consists of a movable polysilicon plate ͑500 m by 500 m by 3.5 m͒ that is supported by two torsional rods ͑40 m by 4 m by 2 m͒.…”

supporting

confidence: 75%

“…Despite the different resonant frequencies and a factor of 4 difference in damping, the critical exponents obtained for both samples are in good agreement with theoretical predictions. [14][15][16][17] Such scaling behavior near a spinodal point is expected to be universal in all systems far from thermal equilibrium. Apart from periodically driven micromechanical oscillators, 8 a critical exponent of 3 / 2 was recently observed in rf-driven Josephson junctions.…”

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confidence: 99%

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Noise-activated switching in a driven nonlinear micromechanical oscillator

2006

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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. Fluctuation-induced escape from a metastable state is an important problem that is relevant to many phenomena, such as protein folding and nucleation in phase transitions. For systems in thermal equilibrium, the escape rate can be deduced from the height of the free-energy barrier.1 The barrier decreases as the control parameter approaches a critical ͑bifurcational͒ value c where the metastable state disappears. It has been established theoretically and experimentally 2,3 that, in the simplest and arguably most common case of the saddle-node ͑spinodal͒ bifurcation, 4 the barrier height scales as ͑ − c ͒ 3/2 . Much less is known about escape in systems far from thermal equilibrium.5-7 Such systems are not characterized by free energy, and the scaling behavior of the escape rate near a saddle-node bifurcation has not been studied experimentally until recently. 8,9 In particular, the problem of escape far from equilibrium has attracted significant experimental attention in the context of systems where multistability itself arises as a result of strong periodic modulation. Escape was studied in parametrically driven electrons in a Penning trap, 10 doubly clamped nanomechanical oscillators, 11,12 and radio frequency driven Josephson junctions. 13 We report here our investigation of noise-activated switching in systems far from equilibrium. By using a wellcharacterized system, an underdamped micromechanical torsional oscillator periodically driven into nonlinear oscillations, we study the dependence of the escape rate on the control parameter as it approaches the critical value and reveal the scaling of the activation energy of escape in a system far from thermal equilibrium. The strongly driven micromechanical oscillator has two stable dynamical states with different oscillation amplitude within a certain range of driving frequencies. We induce the oscillator to escape from one state into the other by injecting noise in the driving force. By measuring the rate of random transitions as a function of noise intensity, we demonstrate the activated behavior for switching and deduce the activation energy as a function of frequency detuning. Close to the bifurcation frequency where the high-amplitude state disappears, the activation energy is predicted by variati...

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confidence: 75%

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confidence: 99%

Noise-activated switching in a driven nonlinear micromechanical oscillator

2006

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“…The dynamics of this system are well described by the Du¢ ng equation, in which the sinusoidal current phase relationship of the junction is truncated after the …rst nonlinear term [62],…”

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confidence: 99%

SQUID magnetometry from nanometer to centimeter length scales

Hatridge

2010

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Information stored in magnetic …elds plays an important role in everyday life. This information exists over a remarkably wide range of sizes, so that magnetometry at a variety of length scales can extract useful information. Examples at centimeter to millimeter length scales include measurement of spatial and temporal character of …elds generated in the human brain and heart, and active manipulation of spins in the human body for non-invasive magnetic resonance imaging (MRI). At micron length scales, magnetometry can be used to measure magnetic objects such as ‡ux qubits; at nanometer length scales it can be used to study individual magnetic domains, and even individual spins. The development of Superconducting QUantum Interference Device (SQUID) based magnetometer for two such applications, in vivo prepolarized, ultra-low …eld MRI of humans and dispersive readout of SQUIDs for micro-and nanoscale magnetometry, are the focus of this thesis.Conventional MRI has developed into a powerful clinical tool for imaging the human body. This technique is based on nuclear magnetic resonance of protons with the addition application of three-dimensional magnetic …eld gradients to encode spatial information. Most clinical MRI systems involve magnetic …elds generated by superconducting magnets, and the current trend is to higher magnetic …elds than the widely used 1.5-T systems. Nonetheless, there is ongoing interest in the development of less expensive imagers operating at lower …elds. The prepolarized, SQUID detected ultra-low …eld MRI (ULF MRI) developed by the Clarke group allows imaging in very weak …elds (typically 132 T, corresponding to a resonant frequency of 5.6 kHz). At these low …eld strengths, there is enhanced contrast in the longitudinal relaxation time of various tissue types, enabling imaging of objects which are not visible to conventional MRI, for instance prostate cancer. We are currently investigating the contrast between normal and cancerous prostate tissue in ex vivo prostate specimens in collaboration with the UCSF Genitourinary Oncology/Prostate SPORE Tissue Core. In characterizing pairs of nominally normal and cancerous tissue, we measure a marked di¤erence in the longitudinal relaxation times, with an average value of cancerous tissue 0.66 times shorter than normal prostate tissue. However, in vivo imaging is required to de…nitively demonstrate the feasibility of ULF MR imaging of prostate cancer. To that end, we have worked to improve the performance of the system to facilitate human imaging. This is accomplished by increasing the prepolarizing …eld amplitude, and minimizing magnetic noise in the SQUID detector. We have achieved polarizing …elds as high 2 as 150 mT and SQUID e¤ective …eld noise below 1 fT Hz 1=2 , enabling us to demonstrate proof-of-principle in vivo images of the human forearm with 2 x 2 x 10 mm 3 resolution in 6 minutes.On a much smaller spatial scale, there is currently fundamental and technological interest in measuring and manipulating nanoscale magnets, particularly in the qua...

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“…While these studies focussed on the light at the output of the resonator, as mentioned above here we are focussing on the light inside the resonator. Moreover, our work adds to an already quite extensive literature concerning nonlinear resonators -see for example Refs [3,4,23,[31][32][33][34][35][36]. Here however the usual assumptions, such as very small nonlinearities, small qubitresonator dispersive coupling, or strictly two-level qubits cannot be made when comparing to the experimental results of Ref.…”

Section: Introductionmentioning

confidence: 96%