Escape driven by -stable white noises

2007
journal article
article
90
dc.abstract.enWe explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Levy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Levy white noise parameters. Depending on the value of the skewness beta of the Levy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of Levy noise, exhibiting a marked discontinuity at alpha=1. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorDybiec, Bartłomiej - 102110 pl
dc.contributor.authorGudowska-Nowak, Ewa - 128235 pl
dc.contributor.authorHanggi, P.pl
dc.date.accessioned2018-04-12T12:24:38Z
dc.date.available2018-04-12T12:24:38Z
dc.date.issued2007pl
dc.description.number2pl
dc.description.volume75pl
dc.identifier.articleid021109pl
dc.identifier.doi10.1103/PhysRevE.75.021109pl
dc.identifier.eissn1550-2376pl
dc.identifier.issn1539-3755pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/53327
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subtypeArticlepl
dc.titleEscape driven by $\alpha$-stable white noisespl
dc.title.journalPhysical Review. E, Statistical, Nonlinear, and Soft Matter Physicspl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Levy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Levy white noise parameters. Depending on the value of the skewness beta of the Levy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of Levy noise, exhibiting a marked discontinuity at alpha=1. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Dybiec, Bartłomiej - 102110
dc.contributor.authorpl
Gudowska-Nowak, Ewa - 128235
dc.contributor.authorpl
Hanggi, P.
dc.date.accessioned
2018-04-12T12:24:38Z
dc.date.available
2018-04-12T12:24:38Z
dc.date.issuedpl
2007
dc.description.numberpl
2
dc.description.volumepl
75
dc.identifier.articleidpl
021109
dc.identifier.doipl
10.1103/PhysRevE.75.021109
dc.identifier.eissnpl
1550-2376
dc.identifier.issnpl
1539-3755
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/53327
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subtypepl
Article
dc.titlepl
Escape driven by $\alpha$-stable white noises
dc.title.journalpl
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
dc.typepl
JournalArticle
dspace.entity.type
Publication

* The migration of download and view statistics prior to the date of April 8, 2024 is in progress.

Views
1
Views per month
Views per city
Shanghai
1

No access

No Thumbnail Available