Numerical Integration of Multiplicative-Noise Stochastic Differential Equations

Klauder, John R.; Petersen, Wesley P.

doi:10.1137/0722069

Cited by 96 publications

(54 citation statements)

References 11 publications

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“…(6) is integrated by the fast Fourier transform method plus the split-operator [14], as in a closed quantum system. The terms involving L m are integrated using a second order scheme [15]. The dynamics resulting from the Stochastic Schrödinger equation (6), when averaged over many realizations of the Wiener process, provides the solution to Eq.…”

Section: Decoherence: Formulation and Computationmentioning

confidence: 99%

Decoherence effects in reactive scattering

Han

Brumer

2005

The Journal of Chemical Physics

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Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H + H 2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.

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Section: Decoherence: Formulation and Computationmentioning

confidence: 99%

Decoherence effects in reactive scattering

Han

Brumer

2005

The Journal of Chemical Physics

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“…The stochastic differential equation (38) can be treated numerically using first-order Euler integration. For small ∆t, the deterministic integral is…”

Section: Appendixmentioning

confidence: 99%

Langevin simulation of thermally activated magnetization reversal in nanoscale pillars

2001

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Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars of dimension 9 nm × 9 nm × 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 ± 14 Oe using linear field sweeps at T = 0 K. Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an external magnetic field less than the coercive value. The distribution of switching times is compared to a simple analytic theory that describes reversal with nucleation at the ends of the nanomagnets. Results are also presented for arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a separation of 300 nm, where the field from neighboring pillars is only ∼ 1 Oe, the interactions have a significant effect on the switching of the magnets.

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“…The first order and the second order systems are numerically simulated by the modified Heun algorithm of the order 2 [5]. To solve Langevin equations with third order systems which involve chaos, treated in section 4, one needs to adopt a higher order algorithm.…”

Section: Methodsmentioning

confidence: 99%

Superstatistics and System Identification for a Class of Generalized Cauchy Processes

Konno

Uchiyama

Pázsit

2014

Stochastic Systems Theory and its Applications (SSS)

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A generalized Cauchy process has been extensively studied since it gives one of the three universal distributions in Beck-Cohen superstatistics. There are many stochastic processes which give Cauchy type distributions in non-equilibrium open systems. However, their different features of intermittency and associated nonlinear structures are not elucidated completely. This paper exhibits a class of generalized Cauchy processes with their temporal features in the first, second and third order systems. A theoretical method for discriminating their various stochastic models is also discussed.

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Numerical Integration of Multiplicative-Noise Stochastic Differential Equations

Cited by 96 publications

References 11 publications

Decoherence effects in reactive scattering

Decoherence effects in reactive scattering

Langevin simulation of thermally activated magnetization reversal in nanoscale pillars

Superstatistics and System Identification for a Class of Generalized Cauchy Processes

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