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

Yunfeng Wang, Yu Zhou, D.K. Maslen, G.S. Chirikjian
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.  ... 
doi:10.1109/tcomm.2006.873988 fatcat:xenbog4r2vgv7kki6tbvp6rcqq

Brownian motion of molecules: the classical theory [article]

Roumen Tsekov
2011 arXiv   pre-print
A new method is proposed for derivation of 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  ... 
arXiv:1005.1490v3 fatcat:yonbicqtszgnjhzswu7bcizaam

Flocking from a quantum analogy: spin–orbit coupling in an active fluid

Benjamin Loewe, Anton Souslov, Paul M Goldbart
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.  ... 
doi:10.1088/1367-2630/aa9cdc fatcat:3ugib6w2zrdu3l5r3hdmpje5au

Collective Dynamics of Interacting Particles in Unsteady Flows

Maryam Abedi, Mir Abbas Jalali
2014 SIAM Journal on Applied Dynamical Systems  
We 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.  ... 
doi:10.1137/130911536 fatcat:cy4iqrepn5avjnt7si6cts2xfi

Theory of Brownian motion of a massive particle in spaces with curvature and torsion

H Kleinert, S V Shabanov
1998 Journal of Physics A: Mathematical and General  
We thereby calculate 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.  ... 
doi:10.1088/0305-4470/31/34/003 fatcat:lx5wn7oar5dw7egsipgm3m5hkq

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

Giorgio Turchetti, Gabriele Bassi, Armando Bazzani, Bruno Giorgini, Helmut Mais
2006 Journal of Physics A: Mathematical and General  
Quantitative results are obtained by 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.  ... 
doi:10.1088/0305-4470/39/37/006 fatcat:o7q7fx3harfbnfiaden7fdrgce

Introductory statistical mechanics

1997 ChoiceReviews  
I hope that 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  ... 
doi:10.5860/choice.35-0964 fatcat:nvbeib2bwnasrkicmrxdwicf7a

Dynamics of spontaneous symmetry breaking in a space-time crystal [article]

J.N. Stehouwer, J. Smits, P. van der Straten, H.T.C. Stoof
2021 arXiv   pre-print
For both cases, 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.  ... 
arXiv:2107.14505v1 fatcat:cfahm2i2qrgfhm6se7p7p4ozou

Stationary States in Infinite Networks of Spiking Oscillators with Noise

Stilianos Louca, Fatihcan M. Atay
2013 SIAM Journal on Applied Dynamical Systems  
We model networks of identical, all-to-all, pulse-coupled 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.  ... 
doi:10.1137/120880264 fatcat:utuscy3hfbbp7im6woo4wnt7ba

Rate of Entropy Production in Stochastic Mechanical Systems

Gregory S. Chirikjian
2021 Entropy  
In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the FokkerPlanck 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] .  ... 
doi:10.3390/e24010019 pmid:35052045 pmcid:PMC8774488 fatcat:brudrifv5ve3fmez7cwh4udaqi

Canonical phase-space approach to the noisy Burgers equation: Probability distributions

Hans C. Fogedby
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Mapping 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.  ... 
doi:10.1103/physreve.59.5065 pmid:11969463 fatcat:ff5kk7dmwjabfcawlb2pnosllm

Multistate quantum Fokker–Planck approach to nonadiabatic wave packet dynamics in pump–probe spectroscopy

Yoshitaka Tanimura, Shaul Mukamel
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  ... 
doi:10.1063/1.467618 fatcat:gznpnziaara7vdhl726xn5bq34

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

Chu Wang, Qianxiao Li, Weinan E, Bernard Chazelle
2017 Journal of statistical physics  
In this work, we investigate 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.  ... 
doi:10.1007/s10955-017-1718-x fatcat:m763ebcfxjbmpnpo3vpuze4jcu

Gaussian phase-space representation of fermion dynamics: Beyond the time-dependent Hartree-Fock approximation

Saar Rahav, Shaul Mukamel
2009 Physical Review B  
In this approach 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  ... 
doi:10.1103/physrevb.79.165103 fatcat:ttfcnfl5qrbsfmggrss4y3gili

Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets

D. A. Garanin
1997 Physical Review B (Condensed Matter)  
a "Landau-Lifshitz-Bloch" (LLB) 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  ... 
doi:10.1103/physrevb.55.3050 fatcat:pj3kkzu4z5axzif53alv2sdqaq
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