scholarly journals Efficient numerical integrator based on Fer expansion: Application to solid-state NMR experiments and to solve quantum Liouville equation and quantum Fokker-Planck equation

2017 ◽  
pp. 4799-4803
Author(s):  
Eugene Stephane Mananga
Keyword(s):  
Solid State ◽  
Liouville Equation ◽  
Solid State Nmr ◽  
Spin Dynamics ◽  
Planck Equation ◽  
Research Areas ◽  
Numerical Integrator ◽  
Fokker Planck Equation ◽  
Quantum Phenomena ◽  
Fokker Planck

There are two important related research areas that I propose to investigate. First, we plan to develop an efficient numerical integrator based on Fer expansion for solid-state NMR simulation of experiments. Second, we intend to extend the method to solve quantum Liouville equation and quantum Fokker-Planck equation in order to improve the understanding of the dynamics of quantum systems subject to dissipation due to its relation to macroscopic quantum phenomena. The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular. The Fer integrator will provide to experts in quantum mechanics, NMR spectroscopy, and spin dynamics researchers, additional means for controlling spin dynamics in SSNMR. The efficient diagram will be used to compare the different orders of the Fer integrators obtained.

scholarly journals Grid-free powder averages: On the applications of the Fokker–Planck equation to solid state NMR

2013 ◽  
Vol 235 ◽  
pp. 121-129 ◽  
Author(s):  
Luke J. Edwards ◽  
D.V. Savostyanov ◽  
A.A. Nevzorov ◽  
M. Concistrè ◽  
G. Pileio ◽  
...  
Keyword(s):  
Solid State ◽  
Solid State Nmr ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Efficient simulation of ultrafast magnetic resonance experiments

2017 ◽  
Vol 19 (27) ◽  
pp. 17577-17586 ◽  
Author(s):  
Ludmilla Guduff ◽  
Ahmed J. Allami ◽  
Carine van Heijenoort ◽  
Jean-Nicolas Dumez ◽  
Ilya Kuprov
Keyword(s):  
Nmr Spectroscopy ◽  
Magnetic Resonance ◽  
Spin Dynamics ◽  
Spatial Dynamics ◽  
Planck Equation ◽  
Quantum Mechanical ◽  
Efficient Simulation ◽  
Fokker Planck Equation ◽  
Fokker Planck

We present a convenient and powerful simulation formalism for ultrafast NMR spectroscopy. The formalism is based on the Fokker–Planck equation that supports systems with complicated combinations of classical spatial dynamics and quantum mechanical spin dynamics.

Numerical Computation of Time-Fractional Fokker–Planck Equation Arising in Solid State Physics and Circuit Theory Numerical Computation of Time-Fractional Fokker–Planck Equation Arising in Solid State Physics and Circuit Theory

2013 ◽  
Vol 68 (12) ◽  
pp. 777-784 ◽  
Author(s):  
Sunil Kumar
Keyword(s):  
State Physics ◽  
Solid State ◽  
Numerical Computation ◽  
Theoretical Biology ◽  
Planck Equation ◽  
Simple Algorithm ◽  
Circuit Theory ◽  
Solid State Physics ◽  
Fokker Planck Equation ◽  
Fokker Planck

The main aim of the present work is to propose a new and simple algorithm to obtain a quick and accurate analytical solution of the time fractional Fokker-Plank equation which arises in various fields in natural science, including solid-state physics, quantum optics, chemical physics, theoretical biology, and circuit theory. This new and simple algorithm is an innovative adjustment in Laplace transform algorithm which makes the calculations much simpler and applicable to several practical problems in science and engineering. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore reduces the numerical computations to a great extent. Furthermore, several numerical examples are presented to illustrate the accuracy and the stability of the method.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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