Stochastic resonance

Last updated

Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. The frequencies in the white noise corresponding to the original signal's frequencies will resonate with each other, amplifying the original signal while not amplifying the rest of the white noise – thereby increasing the signal-to-noise ratio, which makes the original signal more prominent. Further, the added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal.

Contents

This phenomenon of boosting undetectable signals by resonating with added white noise extends to many other systems – whether electromagnetic, physical or biological – and is an active area of research. [1]

Stochastic resonance was first proposed by the Italian physicists Roberto Benzi, Alfonso Sutera and Angelo Vulpiani in 1981, [2] and the first application they proposed (together with Giorgio Parisi) was in the context of climate dynamics. [3] [4]

Technical description

Stochastic resonance (SR) is observed when noise added to a system changes the system's behaviour in some fashion. More technically, SR occurs if the signal-to-noise ratio of a nonlinear system or device increases for moderate values of noise intensity. It often occurs in bistable systems or in systems with a sensory threshold and when the input signal to the system is "sub-threshold." For lower noise intensities, the signal does not cause the device to cross threshold, so little signal is passed through it. For large noise intensities, the output is dominated by the noise, also leading to a low signal-to-noise ratio. For moderate intensities, the noise allows the signal to reach threshold, but the noise intensity is not so large as to swamp it. Thus, a plot of signal-to-noise ratio as a function of noise intensity contains a peak.

Strictly speaking, stochastic resonance occurs in bistable systems, when a small periodic (sinusoidal) force is applied together with a large wide band stochastic force (noise). The system response is driven by the combination of the two forces that compete/cooperate to make the system switch between the two stable states. The degree of order is related to the amount of periodic function that it shows in the system response. When the periodic force is chosen small enough in order to not make the system response switch, the presence of a non-negligible noise is required for it to happen. When the noise is small, very few switches occur, mainly at random with no significant periodicity in the system response. When the noise is very strong, a large number of switches occur for each period of the sinusoid, and the system response does not show remarkable periodicity. Between these two conditions, there exists an optimal value of the noise that cooperatively concurs with the periodic forcing in order to make almost exactly one switch per period (a maximum in the signal-to-noise ratio).

Such a favorable condition is quantitatively determined by the matching of two timescales: the period of the sinusoid (the deterministic time scale) and the Kramers rate [5] (i.e., the average switch rate induced by the sole noise: the inverse of the stochastic time scale [6] [7] ).

Stochastic resonance was discovered and proposed for the first time in 1981 to explain the periodic recurrence of ice ages. [8] Since then, the same principle has been applied in a wide variety of systems. Nowadays stochastic resonance is commonly invoked when noise and nonlinearity concur to determine an increase of order in the system response.

Suprathreshold

Suprathreshold stochastic resonance is a particular form of stochastic resonance, in which random fluctuations, or noise, provide a signal processing benefit in a nonlinear system. Unlike most of the nonlinear systems in which stochastic resonance occurs, suprathreshold stochastic resonance occurs when the strength of the fluctuations is small relative to that of an input signal, or even small for random noise. It is not restricted to a subthreshold signal, hence the qualifier.

Neuroscience, psychology and biology

Stochastic resonance has been observed in the neural tissue of the sensory systems of several organisms. [9] Computationally, neurons exhibit SR because of non-linearities in their processing. SR has yet to be fully explained in biological systems, but neural synchrony in the brain (specifically in the gamma wave frequency [10] ) has been suggested as a possible neural mechanism for SR by researchers who have investigated the perception of "subconscious" visual sensation. [11] Single neurons in vitro including cerebellar Purkinje cells [12] and squid giant axon [13] could also demonstrate the inverse stochastic resonance, when spiking is inhibited by synaptic noise of a particular variance.

Medicine

SR-based techniques have been used to create a novel class of medical devices for enhancing sensory and motor functions such as vibrating insoles especially for the elderly, or patients with diabetic neuropathy or stroke. [14]

See the Review of Modern Physics [15] article for a comprehensive overview of stochastic resonance.

Stochastic Resonance has found noteworthy application in the field of image processing.

Signal analysis

A related phenomenon is dithering applied to analog signals before analog-to-digital conversion. [16] Stochastic resonance can be used to measure transmittance amplitudes below an instrument's detection limit. If Gaussian noise is added to a subthreshold (i.e., immeasurable) signal, then it can be brought into a detectable region. After detection, the noise is removed. A fourfold improvement in the detection limit can be obtained. [17]

See also

Related Research Articles

<span class="mw-page-title-main">Brownian ratchet</span> Perpetual motion device

In the philosophy of thermal and statistical physics, the Brownian ratchet or Feynman–Smoluchowski ratchet is an apparent perpetual motion machine of the second kind, first analysed in 1912 as a thought experiment by Polish physicist Marian Smoluchowski. It was popularised by American Nobel laureate physicist Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962, during his Messenger Lectures series The Character of Physical Law in Cornell University in 1964 and in his text The Feynman Lectures on Physics as an illustration of the laws of thermodynamics. The simple machine, consisting of a tiny paddle wheel and a ratchet, appears to be an example of a Maxwell's demon, able to extract mechanical work from random fluctuations (heat) in a system at thermal equilibrium, in violation of the second law of thermodynamics. Detailed analysis by Feynman and others showed why it cannot actually do this.

<span class="mw-page-title-main">Brownian motor</span> Nanoscale machine

Brownian motors are nanoscale or molecular machines that use chemical reactions to generate directed motion in space. The theory behind Brownian motors relies on the phenomenon of Brownian motion, random motion of particles suspended in a fluid resulting from their collision with the fast-moving molecules in the fluid.

Bart Andrew Kosko is a writer and professor of electrical engineering and law at the University of Southern California (USC). He is a researcher and popularizer of fuzzy logic, neural networks, and noise, and the author of several trade books and textbooks on these and related subjects of machine intelligence. He was awarded the 2022 Donald O. Hebb Award for neural learning by the International Neural Network Society.

<span class="mw-page-title-main">Optical parametric oscillator</span>

An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies. It converts an input laser wave with frequency into two output waves of lower frequency by means of second-order nonlinear optical interaction. The sum of the output waves' frequencies is equal to the input wave frequency: . For historical reasons, the two output waves are called "signal" and "idler", where the output wave with higher frequency is the "signal". A special case is the degenerate OPO, when the output frequency is one-half the pump frequency, , which can result in half-harmonic generation when signal and idler have the same polarization.

<span class="mw-page-title-main">Neuronal noise</span> Random electric fluctuations in neurons

Neuronal noise or neural noise refers to the random intrinsic electrical fluctuations within neuronal networks. These fluctuations are not associated with encoding a response to internal or external stimuli and can be from one to two orders of magnitude. Most noise commonly occurs below a voltage-threshold that is needed for an action potential to occur, but sometimes it can be present in the form of an action potential; for example, stochastic oscillations in pacemaker neurons in suprachiasmatic nucleus are partially responsible for the organization of circadian rhythms.

The gravitational wave background is a random background of gravitational waves permeating the Universe, which is detectable by gravitational-wave experiments, like pulsar timing arrays. The signal may be intrinsically random, like from stochastic processes in the early Universe, or may be produced by an incoherent superposition of a large number of weak independent unresolved gravitational-wave sources, like supermassive black-hole binaries. Detecting the gravitational wave background can provide information that is inaccessible by any other means about astrophysical source population, like hypothetical ancient supermassive black-hole binaries, and early Universe processes, like hypothetical primordial inflation and cosmic strings.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in D spacetime dimensions can be redefined in a lower number of dimensions d, by taking all the fields to be independent of the location in the extra D − d dimensions.

Spin pumping is the dynamical generation of pure spin current by the coherent precession of magnetic moments, which can efficiently inject spin from a magnetic material into an adjacent non-magnetic material. The non-magnetic material usually hosts the spin Hall effect that can convert the injected spin current into a charge voltage easy to detect. A spin pumping experiment typically requires electromagnetic irradiation to induce magnetic resonance, which converts energy and angular momenta from electromagnetic waves to magnetic dynamics and then to electrons, enabling the electronic detection of electromagnetic waves. The device operation of spin pumping can be regarded as the spintronic analog of a battery.

Kurt Wiesenfeld is an American physicist working primarily on non-linear dynamics. His works primarily concern stochastic resonance, spontaneous synchronization of coupled oscillators, and non-linear laser dynamics. Since 1987, he has been professor of physics at the Georgia Institute of Technology.

<span class="mw-page-title-main">Landau–Zener formula</span> Formula for the probability that a system will change between two energy states.

The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a diabatic transition between the two energy states, was published separately by Lev Landau, Clarence Zener, Ernst Stueckelberg, and Ettore Majorana, in 1932.

Within quantum technology, a quantum sensor utilizes properties of quantum mechanics, such as quantum entanglement, quantum interference, and quantum state squeezing, which have optimized precision and beat current limits in sensor technology. The field of quantum sensing deals with the design and engineering of quantum sources and quantum measurements that are able to beat the performance of any classical strategy in a number of technological applications. This can be done with photonic systems or solid state systems.

<span class="mw-page-title-main">Primordial black hole</span> Hypothetical black hole formed soon after the Big Bang

In cosmology, primordial black holes (PBHs) are hypothetical black holes that formed soon after the Big Bang. In the inflationary era and early radiation-dominated universe, extremely dense pockets of subatomic matter may have been tightly packed to the point of gravitational collapse, creating primordial black holes without the supernova compression typically needed to make black holes today. Because the creation of primordial black holes would pre-date the first stars, they are not limited to the narrow mass range of stellar black holes.

Peter Hänggi is a theoretical physicist from Switzerland, Professor of Theoretical Physics at the University of Augsburg. He is best known for his original works on Brownian motion and the Brownian motor concept, stochastic resonance and dissipative systems. Other topics include, driven quantum tunneling, such as the discovery of coherent destruction of tunneling (CDT), phononics, relativistic statistical mechanics and the foundations of classical and quantum thermodynamics.

Stochastic resonance is a phenomenon that occurs in a threshold measurement system when an appropriate measure of information transfer is maximized in the presence of a non-zero level of stochastic input noise thereby lowering the response threshold; the system resonates at a particular noise level.

Luca Gammaitoni is a scientist in the area of noise and nonlinear dynamics. He is currently the Director of the Noise in Physical System Laboratory at the Physics Department of the Università di Perugia, in Italy.

Double ionization is a process of formation of doubly charged ions when laser radiation is exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

Dynamical decoupling (DD) is an open-loop quantum control technique employed in quantum computing to suppress decoherence by taking advantage of rapid, time-dependent control modulation. In its simplest form, DD is implemented by periodic sequences of instantaneous control pulses, whose net effect is to approximately average the unwanted system-environment coupling to zero. Different schemes exist for designing DD protocols that use realistic bounded-strength control pulses, as well as for achieving high-order error suppression, and for making DD compatible with quantum gates. In spin systems in particular, commonly used protocols for dynamical decoupling include the Carr-Purcell and the Carr-Purcell-Meiboom-Gill schemes. They are based on the Hahn spin echo technique of applying periodic pulses to enable refocusing and hence extend the coherence times of qubits.

<span class="mw-page-title-main">Crispin Gardiner</span> New Zealand physicist (born 1942)

Crispin William Gardiner is a New Zealand physicist, who has worked in the fields of quantum optics, ultracold atoms and stochastic processes. He has written about 120 journal articles and several books in the fields of quantum optics, stochastic processes and ultracold atoms.

<span class="mw-page-title-main">Sergej Flach</span>

Sergej Flach is a theoretical physicist whose research has spanned a number of scientific fields in his career. With about 240 publications to his name, his research has been cited over 16,000 times giving him an h-index of 58 and i10-index of 174. He is a member of the American Physical Society, German Physical Society, Korean Physical Society, and New Zealand Institute of Physics. He is an editorial board member of Chaos (2016-) and was an editorial board member of Physical Review E (2009-2011).

References

  1. Moss F, Ward LM, Sannita WG (February 2004). "Stochastic resonance and sensory information processing: a tutorial and review of application". Clinical Neurophysiology. 115 (2): 267–81. doi:10.1016/j.clinph.2003.09.014. PMID   14744566. S2CID   4141064.
  2. Benzi, R; Sutera, A; Vulpiani, A (1 November 1981). "The mechanism of stochastic resonance". Journal of Physics A: Mathematical and General. 14 (11): L453–L457. Bibcode:1981JPhA...14L.453B. doi: 10.1088/0305-4470/14/11/006 . ISSN   0305-4470. S2CID   123005407.
  3. BENZI, ROBERTO; PARISI, GIORGIO; SUTERA, ALFONSO; VULPIANI, ANGELO (February 1982). "Stochastic resonance in climatic change". Tellus. 34 (1): 10–16. doi:10.1111/j.2153-3490.1982.tb01787.x. ISSN   0040-2826.
  4. Benzi, Roberto; Parisi, Giorgio; Sutera, Alfonso; Vulpiani, Angelo (June 1983). "A Theory of Stochastic Resonance in Climatic Change". SIAM Journal on Applied Mathematics. 43 (3): 565–578. doi:10.1137/0143037. ISSN   0036-1399.
  5. Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica (Utrecht) 7, 284–304 (1940)}
  6. Peter Hänggi; Peter Talkner; Michal Borkovec (1990). "Reaction-rate theory: fifty years after Kramers". Reviews of Modern Physics. 62 (2): 251–341. Bibcode:1990RvMP...62..251H. doi:10.1103/RevModPhys.62.251. S2CID   122573991.
  7. Hannes Risken (1989). The Fokker-Planck Equation', 2nd edition. Springer.
  8. Benzi R, Parisi G, Sutera A, Vulpiani A (1982). "Stochastic resonance in climatic change". Tellus. 34 (1): 10–6. Bibcode:1982Tell...34...10B. doi:10.1111/j.2153-3490.1982.tb01787.x.
  9. Kosko, Bart (2006). Noise . New York, N.Y: Viking. ISBN   978-0-670-03495-6.
  10. Ward LM, Doesburg SM, Kitajo K, MacLean SE, Roggeveen AB (December 2006). "Neural synchrony in stochastic resonance, attention, and consciousness". Can J Exp Psychol. 60 (4): 319–26. doi:10.1037/cjep2006029. PMID   17285879.
  11. Melloni L, Molina C, Pena M, Torres D, Singer W, Rodriguez E (March 2007). "Synchronization of neural activity across cortical areas correlates with conscious perception". J. Neurosci. 27 (11): 2858–65. doi:10.1523/JNEUROSCI.4623-06.2007. PMC   6672558 . PMID   17360907. Final proof of role of neural coherence in consciousness?
  12. Buchin, Anatoly; Rieubland, Sarah; Häusser, Michael; Gutkin, Boris S.; Roth, Arnd (19 August 2016). "Inverse Stochastic Resonance in Cerebellar Purkinje Cells". PLOS Computational Biology. 12 (8): e1005000. Bibcode:2016PLSCB..12E5000B. doi: 10.1371/journal.pcbi.1005000 . PMC   4991839 . PMID   27541958.
  13. Paydarfar, D.; Forger, D. B.; Clay, J. R. (9 August 2006). "Noisy Inputs and the Induction of On-Off Switching Behavior in a Neuronal Pacemaker". Journal of Neurophysiology. 96 (6): 3338–3348. doi:10.1152/jn.00486.2006. PMID   16956993. S2CID   10035457.
  14. E. Sejdić, L. A. Lipsitz, "Necessity of noise in physiology and medicine," Computer Methods and Programs in Biomedicine, vol. 111, no. 2, pp. 459–470, Aug. 2013.
  15. Gammaitoni L, Hänggi P, Jung P, Marchesoni F (1998). "Stochastic resonance" (PDF). Reviews of Modern Physics. 70 (1): 223–87. Bibcode:1998RvMP...70..223G. doi:10.1103/RevModPhys.70.223.
  16. Gammaitoni L (1995). "Stochastic resonance and the dithering effect in threshold physical systems" (PDF). Phys. Rev. E. 52 (5): 4691–8. Bibcode:1995PhRvE..52.4691G. doi:10.1103/PhysRevE.52.4691. PMID   9963964.
  17. Palonpon A, Amistoso J, Holdsworth J, Garcia W, Saloma C (1998). "Measurement of weak transmittances by stochastic resonance". Optics Letters. 23 (18): 1480–2. Bibcode:1998OptL...23.1480P. doi:10.1364/OL.23.001480. PMID   18091823.

Bibliography

Bibliography for suprathreshold stochastic resonance