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Solving phase-noise Fokker-Planck equations using the motion-group Fourier transform

2006
*
IEEE Transactions on Communications
*

*The*

*Fokker*-

*Planck*(FP) approach has been recognized as a rigorous way to describe these statistical properties. ... A quantity of importance in coherent optical communications is

*the*probability density of a filtered signal in

*the*presence of

*phase*

*noise*(PN). ...

*Solving*

*Phase*-

*Noise*

*Fokker*-

*Planck*

*Equations*

*Using*

*the*

*Motion*-

*Group*

*Fourier*

*Transform*I. ...

##
###
Brownian motion of molecules: the classical theory
[article]

2011
*
arXiv
*
pre-print

A new method is proposed for derivation of

arXiv:1005.1490v3
fatcat:yonbicqtszgnjhzswu7bcizaam
*the**Fokker*-*Planck**equations*, describing*the*probability density evolution, from stochastic differential*equations*. ... A short review of*the*classical theory of Brownian*motion*is presented. ...*the*inverse*Fourier**transformation*to this*equation*and*using*definition (12) one derives*the*evolution*equation*for*the*probability density ( , , ) t r v in*the**phase*space / [ ( ) / ] t U m b P mb ...##
###
Flocking from a quantum analogy: spin–orbit coupling in an active fluid

2018
*
New Journal of Physics
*

*The*connection between self-propelled particles and quantum spins may help realize exotic

*phases*of matter

*using*active fluids via analogies with systems composed of strongly correlated electrons. ... Furthermore, by coarse-graining this microscopic model, we establish expressions for

*the*coefficients of

*the*Toner-Tu

*equations*---

*the*hydrodynamic

*equations*that describe an active fluid composed of these ... and

*the*Syracuse Soft & Living Matter Program. ...

##
###
Collective Dynamics of Interacting Particles in Unsteady Flows

2014
*
SIAM Journal on Applied Dynamical Systems
*

We

doi:10.1137/130911536
fatcat:cy4iqrepn5avjnt7si6cts2xfi
*use**the**Fokker*-*Planck**equation*and its moment*equations*to study*the*collective behavior of interacting particles in unsteady one-dimensional flows. ...*The*results of linear perturbation analysis are confirmed through*the*numerical solution of*the*fully nonlinear*Fokker*-*Planck**equation*. ... ACKNOWLEDGMENTS We thank anonymous referees for their*useful*comments, which helped*us*to substantially improve*the*presentation of*the*paper. ...##
###
Theory of Brownian motion of a massive particle in spaces with curvature and torsion

1998
*
Journal of Physics A: Mathematical and General
*

We thereby calculate

doi:10.1088/0305-4470/31/34/003
fatcat:lx5wn7oar5dw7egsipgm3m5hkq
*the*single-particle spectral function of*the*Cooper pair and obtain*the*dispersion relation for its translational*motion*. ... An exact-diagonalization technique on small clusters is*used*to study low-lying excitations and superconductivity in*the*two-dimensional negative-U Hubbard model. ... Acknowledgments SS thanks all members of*the*research*group*(http://www.physik.fu-berlin.de/˜kleinert/ kleiner.html) for their kind hospitality. ...##
###
Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

2006
*
Journal of Physics A: Mathematical and General
*

Quantitative results are obtained by

doi:10.1088/0305-4470/39/37/006
fatcat:o7q7fx3harfbnfiaden7fdrgce
*solving**the**Fokker*-*Planck**equation*with a numerical scheme based on splitting: back propagation and biquadratic interpolation for*the*integrable part, implicit finite ...*The**noise*reduces*the*echo amplitude by e −c 2 τ 3 , where c depends on*the**Fourier*components of*the*initial angular distribution, and of*the*disturbance applied at time τ . ... Bassi wishes to thank DESY for a doctoral fellowship and*the**US*department of Energy for a partial support by Contract DE-FG03-99ER41104. ...##
###
Introductory statistical mechanics

1997
*
ChoiceReviews
*

I hope that

doi:10.5860/choice.35-0964
fatcat:nvbeib2bwnasrkicmrxdwicf7a
*the*list of references will serve as*the*extension of this list to those from whom I have learned through their writings. ... This especially applies to Ewan Paterson and my colleagues in*the*Accelerator Department for*the*hospitality, shared wisdom and friendship which made my visit so enjoyable and instructive. ...*Fokker*-*Planck**equations*reduce to diffusion*equations*in cases like this where*the*coherent forces K(X, t) vanish. 2.6*SOLVING**FOKKER*-*PLANCK**EQUATIONS*We speak of*solving**Fokker*-*Planck**equations*...##
###
Dynamics of spontaneous symmetry breaking in a space-time crystal
[article]

2021
*
arXiv
*
pre-print

For both cases,

arXiv:2107.14505v1
fatcat:cfahm2i2qrgfhm6se7p7p4ozou
*the*Langevin*equation*and*Fokker*-*Planck**equation*are derived, and*the*resulting equilibrium distribution is studied. ...*The*non-equilibrium physics related to such a driven-dissipative system is discussed in both*the*Langevin as well as*the**Fokker*-*Planck*formulation. ... Numerical solution We have numerically*solved**the**Fokker*-*Planck**equation*in Eq. (29) by*using*an implicit finite-difference method, see App. B for details. ...##
###
Stationary States in Infinite Networks of Spiking Oscillators with Noise

2013
*
SIAM Journal on Applied Dynamical Systems
*

We model networks of identical, all-to-all, pulse-coupled

doi:10.1137/120880264
fatcat:utuscy3hfbbp7im6woo4wnt7ba
*phase*oscillators with white*noise*, in*the*limit of infinite network size and Dirac pulses,*using*a*Fokker*-*Planck**equation*for*the**phase*probability ...*The**noise*-free version of (1.2) has been extensively*used*as a thermodynamic limit (i.e., * ... This work was conducted with*the*support of*the*Max*Planck*Institute for Mathematics in*the*Sciences, Leipzig, Germany. We thank our two reviewers for their valuable comments and suggestions. ...##
###
Rate of Entropy Production in Stochastic Mechanical Systems

2021
*
Entropy
*

In all cases, it is shown that

doi:10.3390/e24010019
pmid:35052045
pmcid:PMC8774488
fatcat:brudrifv5ve3fmez7cwh4udaqi
*the*rate of entropy production is closely related to*the*appropriate concept of Fisher information matrix of*the*probability density defined by*the**Fokker*–*Planck**equation*... Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie*groups*, as well as systems evolving on*phase*space for which*the*fluctuation-dissipation theorem applies, i.e., return-to-equilibrium ...*The**Fokker*-*Planck**equations*describing*phase**noise*have been developed and*solved**using*various methods [71] [72] [73] . ...##
###
Canonical phase-space approach to the noisy Burgers equation: Probability distributions

1999
*
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
*

Mapping

doi:10.1103/physreve.59.5065
pmid:11969463
fatcat:ff5kk7dmwjabfcawlb2pnosllm
*the*associated*Fokker*-*Planck**equation*to a Hamilton-Jacobi*equation*in*the*nonperturbative weak*noise*limit we invoke a principle of least action for*the*determination of*the*probability distributions ... We present a canonical*phase*space approach to stochastic systems described by Langevin*equations*driven by white*noise*. ...*The*issue of*solving**the*stochastic Langevin*equation*or*the*associated*Fokker*-*Planck**equation*is thus replaced by*solving*coupled Hamilton*equations*of*motion*determining*the*orbits in*phase*space. ...##
###
Multistate quantum Fokker–Planck approach to nonadiabatic wave packet dynamics in pump–probe spectroscopy

1994
*
Journal of Chemical Physics
*

*The*quantum

*Fokker*-

*Planck*

*equation*of Caldeira and Leggett is generalized to a multistate system with anharmonic potentials and a coordinate dependent nonadiabatic coupling. ... A rigorous procedure for calculating

*the*dynamics of nonadiabatic transitions in condensed phasesapd t+$ mon$oring _ by femtosecond pump-probe spectroscopy is developed

*using*this

*equation*. ...

*equation*of,

*motion*for

*phase*space distribution functions is known as

*the*quantum

*Fokker*-

*Planck*

*equation*.28-30 In this paper, we extend

*the*quantum

*Fokker*-

*Planck*

*equation*to a multistate system with anharmonic ...

##
###
Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture

2017
*
Journal of statistical physics
*

In this work, we investigate

doi:10.1007/s10955-017-1718-x
fatcat:m763ebcfxjbmpnpo3vpuze4jcu
*the*effects of*noise*in*the*continuous-time version of*the*model as described by its mean-field*Fokker*-*Planck**equation*. ... In*the*presence of a finite number of agents,*the*system exhibits a*phase*transition from order to disorder as*the**noise*increases. ... Acknowledgements We wish to thank*the*anonymous referees for many*useful*comments and suggestions. ...##
###
Gaussian phase-space representation of fermion dynamics: Beyond the time-dependent Hartree-Fock approximation

2009
*
Physical Review B
*

In this approach

doi:10.1103/physrevb.79.165103
fatcat:ttfcnfl5qrbsfmggrss4y3gili
*the*reduced single electron density matrix elements serve as stochastic variables which satisfy an exact*Fokker*-*Planck**equation*. ... An approximate closed set of*equations*of*motion*for*the*one and two-particle reduced density matrices, provides a direct generalization of*the*TDHF. ... ACKNOWLEDGMENT We gratefully acknowledge*the*support of*the*National Science Foundation through Grant No. CHE-0745892. APPENDIX A: GAUGE FREEDOM IN*THE**FOKKER*-*PLANCK**EQUATION*...##
###
Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets

1997
*
Physical Review B (Condensed Matter)
*

a "Landau-Lifshitz-Bloch" (LLB)

doi:10.1103/physrevb.55.3050
fatcat:pj3kkzu4z5axzif53alv2sdqaq
*equation*can be derived exactly from*the**Fokker*-*Planck**equation*, if*the*external conditions change slowly enough. ... A macroscopic*equation*of*motion*for*the*magnetization of a ferromagnet at elevated temperatures should contain both transverse and longitudinal relaxation terms and interpolate between Landau-Lifshitz ... APPENDIX: DERIVATION OF*THE**FOKKER*-*PLANCK**EQUATION*Here*the*derivation of*the**Fokker*-*Planck**equation*(2. 3) is presented, which is more direct and simple than*the*original one by Brown 23 and which ...
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