solid::RK4< T1, T2, T3 > Class Template Reference

Runge–Kutta forth order method (RK4) for solving differentional equations. More...

#include <RungeKutta4.hpp>

Inheritance diagram for solid::RK4< T1, T2, T3 >:

Collaboration diagram for solid::RK4< T1, T2, T3 >:

Public Member Functions
std::string	getLabel () override
	Get the Label object (IQuantumDynamicSolver override) More...
void	Propagate (double time, double dtime, QuantumDynamics< T1, T2, T3 > &qDynamics)
	Propagate the state \(|\psi\rangle\) (IQuantumDynamicSolver override) More...
Public Member Functions inherited from solid::IQuantumDynamicSolver< T1, T2, T3 >
virtual	~IQuantumDynamicSolver ()

Static Public Attributes
static constexpr auto	label = "rk4"
	label, default = "rk4" More...

Detailed Description

template<template< typename > class T1, typename T2, typename T3>
class solid::RK4< T1, T2, T3 >

Runge–Kutta forth order method (RK4) for solving differentional equations.

Propagation of the state is obtained in the following way:

\[ |\psi(t+\Delta t)\rangle = |\psi(t)\rangle + \frac16(|k_1\rangle+2|k_2\rangle+2|k_3\rangle+|k_4\rangle), \]

where corresponding states \(|k_1\rangle,\,|k_2\rangle,\,|k_3\rangle,\,|k_4\rangle\) are given by:

• \(|k_1\rangle =-i\Delta t \hat H(t) |\psi(t)\rangle \)
• \(|k_2\rangle =-i\Delta t \hat H(t+\Delta t/2) (|\psi(t)\rangle +\frac12|k_1\rangle)\)
• \(|k_3\rangle =-i\Delta t \hat H(t+\Delta t/2) (|\psi(t)\rangle +\frac12|k_2\rangle)\)
• \(|k_4\rangle =-i\Delta t \hat H(t+\Delta t) (|\psi(t)\rangle +|k_3\rangle)\)

Member Function Documentation

template<template< typename > class T1, typename T2, typename T3>

std::string solid::RK4< T1, T2, T3 >::getLabel ( )

inlineoverridevirtual

Get the Label object (IQuantumDynamicSolver override)

Returns

std::string label

Implements solid::IQuantumDynamicSolver< T1, T2, T3 >.

template<template< typename > class T1, typename T2, typename T3>

void solid::RK4< T1, T2, T3 >::Propagate ( double  time, double  dtime, QuantumDynamics< T1, T2, T3 > &  qDynamics  )

inlinevirtual

Propagate the state \(|\psi\rangle\) (IQuantumDynamicSolver override)

Parameters

time	current time
dtime	time step
qDynamics	QuantumDynamics<T1,T2,T3> object

Implements solid::IQuantumDynamicSolver< T1, T2, T3 >.

Member Data Documentation

template<template< typename > class T1, typename T2, typename T3>

constexpr auto solid::RK4< T1, T2, T3 >::label = "rk4"

inlinestatic

label, default = "rk4"

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The documentation for this class was generated from the following file:

• Modules/SOLIDstate_bits/QuantumDynamics/Solvers/RungeKutta4.hpp