One-Dimensional Diffusion in a Semiinfinite Poisson Random Force
Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of...
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| Autor*in: |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Umfang: |
27 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Journal of statistical physics - 1969, 97(1999) vom: Jan./Feb., Seite 323-349 |
| Übergeordnetes Werk: |
volume:97 ; year:1999 ; month:01/02 ; pages:323-349 ; extent:27 |
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NLEJ197948812 |
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| 520 | |a Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. | ||
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(DE-627)NLEJ197948812 DE-627 ger DE-627 rakwb eng One-Dimensional Diffusion in a Semiinfinite Poisson Random Force 1999 27 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. Springer Online Journal Archives 1860-2002 Chvosta, Petr oth Pottier, Noëlle oth in Journal of statistical physics 1969 97(1999) vom: Jan./Feb., Seite 323-349 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:97 year:1999 month:01/02 pages:323-349 extent:27 http://dx.doi.org/10.1023/A:1004627404379 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 97 1999 1/2 323-349 27 |
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(DE-627)NLEJ197948812 DE-627 ger DE-627 rakwb eng One-Dimensional Diffusion in a Semiinfinite Poisson Random Force 1999 27 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. Springer Online Journal Archives 1860-2002 Chvosta, Petr oth Pottier, Noëlle oth in Journal of statistical physics 1969 97(1999) vom: Jan./Feb., Seite 323-349 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:97 year:1999 month:01/02 pages:323-349 extent:27 http://dx.doi.org/10.1023/A:1004627404379 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 97 1999 1/2 323-349 27 |
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(DE-627)NLEJ197948812 DE-627 ger DE-627 rakwb eng One-Dimensional Diffusion in a Semiinfinite Poisson Random Force 1999 27 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. Springer Online Journal Archives 1860-2002 Chvosta, Petr oth Pottier, Noëlle oth in Journal of statistical physics 1969 97(1999) vom: Jan./Feb., Seite 323-349 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:97 year:1999 month:01/02 pages:323-349 extent:27 http://dx.doi.org/10.1023/A:1004627404379 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 97 1999 1/2 323-349 27 |
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(DE-627)NLEJ197948812 DE-627 ger DE-627 rakwb eng One-Dimensional Diffusion in a Semiinfinite Poisson Random Force 1999 27 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. Springer Online Journal Archives 1860-2002 Chvosta, Petr oth Pottier, Noëlle oth in Journal of statistical physics 1969 97(1999) vom: Jan./Feb., Seite 323-349 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:97 year:1999 month:01/02 pages:323-349 extent:27 http://dx.doi.org/10.1023/A:1004627404379 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 97 1999 1/2 323-349 27 |
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(DE-627)NLEJ197948812 DE-627 ger DE-627 rakwb eng One-Dimensional Diffusion in a Semiinfinite Poisson Random Force 1999 27 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. Springer Online Journal Archives 1860-2002 Chvosta, Petr oth Pottier, Noëlle oth in Journal of statistical physics 1969 97(1999) vom: Jan./Feb., Seite 323-349 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:97 year:1999 month:01/02 pages:323-349 extent:27 http://dx.doi.org/10.1023/A:1004627404379 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 97 1999 1/2 323-349 27 |
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One-Dimensional Diffusion in a Semiinfinite Poisson Random Force |
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Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. |
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Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. |
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Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ197948812</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210705230530.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">070527s1999 xx |||||o 00| ||eng c</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ197948812</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">One-Dimensional Diffusion in a Semiinfinite Poisson Random Force</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">27</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider the one-dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker–Planck equation, valid for any deterministic construction of the potential profile. The force is then taken to be an asymmetric dichotomic process. Solving the corresponding energy-dependent stochastic Riccati equation in the space-asymptotic regime, we give an exact probabilistic description of returns to the origin. This method allows for a time-asymptotic characterization of the underlying dynamical phases. When the two values taken by the dichotomic force are of different signs, there occur trapping potential wells with a broad distribution of trapping times, and dynamical phases may appear, depending on the man force. If both values are negative, the time-asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force. If they are both positive, traps no longer exist and the dynamics is always normal. Problems with a shot-noise force and with a Gaussian white-noise force are solved as appropriate limiting cases.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Springer Online Journal Archives 1860-2002</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chvosta, Petr</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pottier, Noëlle</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">in</subfield><subfield code="t">Journal of statistical physics</subfield><subfield code="d">1969</subfield><subfield code="g">97(1999) vom: Jan./Feb., Seite 323-349</subfield><subfield code="w">(DE-627)NLEJ188991786</subfield><subfield code="w">(DE-600)2017302-7</subfield><subfield code="x">1572-9613</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:97</subfield><subfield code="g">year:1999</subfield><subfield code="g">month:01/02</subfield><subfield code="g">pages:323-349</subfield><subfield code="g">extent:27</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://dx.doi.org/10.1023/A:1004627404379</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-SOJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">97</subfield><subfield code="j">1999</subfield><subfield code="c">1/2</subfield><subfield code="h">323-349</subfield><subfield code="g">27</subfield></datafield></record></collection>
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7.401326 |