to be put in a separate file More...

#include <diamagneticpotentialfactor.h>

Collaboration diagram for madness::Diamagnetic_potential_factor:

[legend]

Public Member Functions
	Diamagnetic_potential_factor (World &world, const Nemo_complex_Parameters &param, const std::vector< coord_3d > &coords)
	constructor takes a world and the parameters for the calculation

std::vector< complex_function_3d >	apply_potential (const std::vector< complex_function_3d > &rhs) const
	apply the diamagnetic potential on rhs

real_function_3d	bare_diamagnetic_potential () const
	compute the bare potential without confinement or factors

complex_function_3d	compute_lz_commutator () const
	compute the commutator of the orbital-zeeman term with the diamagnetic factor

std::vector< real_function_3d >	compute_nabla_R_div_R () const
	returns $R^{-1} \vec\nabla R$

real_function_3d	compute_R_times_T_commutator_scalar_term_numerically () const

real_function_3d	compute_U2 () const

real_function_3d	custom_factor (const coord_3d &B, const std::vector< coord_3d > &vv, const double extra_exponent=1.0) const
	return a custom factor for a given magnetic field

double	estimate_wavefunction_radius (const double eps=1.e-8) const

real_function_3d	factor () const
	return the diamagnetic factor

real_function_3d	factor_square () const
	return the square of the diamagnetic factor

complex_function_3d	factor_with_phase (const coord_3d &B, const std::vector< coord_3d > &vv) const
	return a custom factor for a given magnetic field

std::vector< coord_3d >	get_coords () const

coord_3d	get_explicit_B () const

coord_3d	get_physical_B () const

double	get_potential_radius () const
	compute the radius for the diamagnetic potential

std::vector< coord_3d >	get_v () const

std::vector< complex_function_3d >	make_fake_orbitals (const int n, const coord_3d &offset={0.0, 0.0, 0.0}) const
	make a set orbitals for testing (not orthonormalized!)

void	print_info () const

void	recompute_factors_and_potentials ()
	recompute the factor and the potentials for given physical and explicit magnetic fields

void	reset_explicit_B_and_v (const coord_3d &eB)

bool	test_me (const int level) const
	run the tests

Static Public Member Functions
static bool	B_along_z (const coord_3d &B)
	make sure the magnetic field is oriented along the z axis

static std::vector< coord_3d >	compute_v_vector (const coord_3d &B, const std::vector< coord_3d > &coords, bool use_v_vector)

Private Member Functions
bool	test_factor () const
	compute a factor for comparison in coordinate space

bool	test_harmonic_potential () const
	test the harmonic potential

bool	test_lz_commutator () const

bool	test_scalar_potentials () const
	test analytical vs numerical computation of the potentials

bool	test_vector_potentials () const
	test analytical vs numerical computation of the potentials

Private Attributes
std::vector< coord_3d >	coords
	the position of the nuclei in the coordinate space:

real_function_3d	diamagnetic_factor_
	the diamagnetic factor to cancel the diamagnetic potential

real_function_3d	diamagnetic_factor_square

std::vector< real_function_3d >	diamagnetic_U1

real_function_3d	diamagnetic_U2
	the boxed diamagnetic potential (for a given B)

coord_3d	explicit_B ={0,0,0}
	the magnetic field strength encoded in the diamagnetic factor

coord_3d	physical_B ={0,0,0}
	the actual magnetic field strength

double	potential_radius
	radius where the diamagnetic potential flattens out

bool	use_v_vector =true

std::vector< coord_3d >	v
	the position of the nuclei in the "A" space: v = 1/2 B cross R

World &	world
	the world

Detailed Description

to be put in a separate file

Constructor & Destructor Documentation

◆ Diamagnetic_potential_factor()

madness::Diamagnetic_potential_factor::Diamagnetic_potential_factor	(	World &	world,
		const Nemo_complex_Parameters &	param,
		const std::vector< coord_3d > &	coords
	)

inline

constructor takes a world and the parameters for the calculation

References compute_v_vector(), coords, diamagnetic_factor_, diamagnetic_factor_square, diamagnetic_U1, diamagnetic_U2, explicit_B, madness::Vector< T, N >::normf(), param, physical_B, potential_radius, print_info(), recompute_factors_and_potentials(), use_v_vector, v, and world.

Member Function Documentation

◆ apply_potential()

std::vector< complex_function_3d > madness::Diamagnetic_potential_factor::apply_potential ( const std::vector< complex_function_3d > & rhs ) const

apply the diamagnetic potential on rhs

compute the diamagnetic local potential (B is in z direction -> dia = x^2 + y^2

References madness::apply(), diamagnetic_U1, diamagnetic_U2, explicit_B, madness::Vector< T, N >::normf(), physical_B, madness::World::size(), madness::truncate(), and world.

◆ B_along_z()

static bool madness::Diamagnetic_potential_factor::B_along_z ( const coord_3d & B )

inlinestatic

make sure the magnetic field is oriented along the z axis

Referenced by bare_diamagnetic_potential(), compute_nabla_R_div_R(), compute_R_times_T_commutator_scalar_term_numerically(), and compute_U2().

◆ bare_diamagnetic_potential()

real_function_3d madness::Diamagnetic_potential_factor::bare_diamagnetic_potential ( ) const

inline

compute the bare potential without confinement or factors

References B_along_z(), madness::inner(), MADNESS_ASSERT, physical_B, and world.

◆ compute_lz_commutator()

complex_function_3d madness::Diamagnetic_potential_factor::compute_lz_commutator ( ) const

compute the commutator of the orbital-zeeman term with the diamagnetic factor

Returns: a local potential: iB \sum_i \vec r \cdot \vec v_i

References diamagnetic_U1, madness::dot(), explicit_B, madness::scale(), and world.

Referenced by test_lz_commutator().

◆ compute_nabla_R_div_R()

std::vector< real_function_3d > madness::Diamagnetic_potential_factor::compute_nabla_R_div_R ( ) const

returns $R^{-1} \vec\nabla R$

References B_along_z(), madness::cross(), explicit_B, madness::FunctionDefaults< NDIM >::get_cell(), madness::inner(), MADNESS_ASSERT, madness::Tensor< T >::normf(), madness::Vector< T, N >::normf(), physical_B, madness::truncate(), v, and world.

Referenced by recompute_factors_and_potentials(), and test_vector_potentials().

◆ compute_R_times_T_commutator_scalar_term_numerically()

real_function_3d madness::Diamagnetic_potential_factor::compute_R_times_T_commutator_scalar_term_numerically ( ) const

References B_along_z(), madness::div(), factor(), get_potential_radius(), madness::grad_bspline_one(), MADNESS_ASSERT, madness::Vector< T, N >::normf(), physical_B, madness::Function< T, NDIM >::scale(), madness::Function< T, NDIM >::truncate(), and world.

Referenced by test_scalar_potentials().

◆ compute_U2()

real_function_3d madness::Diamagnetic_potential_factor::compute_U2 ( ) const

References B_along_z(), madness::cross(), explicit_B, get_potential_radius(), madness::inner(), MADNESS_ASSERT, madness::Vector< T, N >::normf(), physical_B, madness::Function< T, NDIM >::truncate(), v, and world.

Referenced by recompute_factors_and_potentials(), and test_scalar_potentials().

◆ compute_v_vector()

static std::vector< coord_3d > madness::Diamagnetic_potential_factor::compute_v_vector	(	const coord_3d &	B,
		const std::vector< coord_3d > &	coords,
		bool	use_v_vector
	)

inlinestatic

References c, coords, madness::cross(), use_v_vector, and v.

Referenced by Diamagnetic_potential_factor(), and reset_explicit_B_and_v().

◆ custom_factor()

real_function_3d madness::Diamagnetic_potential_factor::custom_factor	(	const coord_3d &	B,
		const std::vector< coord_3d > &	vv,
		const double	extra_exponent = `1.0`
	)		const

inline

return a custom factor for a given magnetic field

References madness::arg(), madness::cross(), madness::inner(), v, and world.

Referenced by recompute_factors_and_potentials(), and test_factor().

◆ estimate_wavefunction_radius()

double madness::Diamagnetic_potential_factor::estimate_wavefunction_radius ( const double eps = 1.e-8 ) const

inline

given the explicit and the physical B, estimate the radius of the wave function

References get_explicit_B(), and get_physical_B().

◆ factor()

real_function_3d madness::Diamagnetic_potential_factor::factor ( ) const

inline

return the diamagnetic factor

References diamagnetic_factor_.

Referenced by compute_R_times_T_commutator_scalar_term_numerically(), test_factor(), test_lz_commutator(), test_scalar_potentials(), and test_vector_potentials().

◆ factor_square()

real_function_3d madness::Diamagnetic_potential_factor::factor_square ( ) const

inline

return the square of the diamagnetic factor

References diamagnetic_factor_square.

Referenced by test_factor(), and test_scalar_potentials().

◆ factor_with_phase()

complex_function_3d madness::Diamagnetic_potential_factor::factor_with_phase	(	const coord_3d &	B,
		const std::vector< coord_3d > &	vv
	)		const

inline

return a custom factor for a given magnetic field

References madness::arg(), madness::cross(), madness::inner(), madness::Vector< T, N >::normf(), madness::phase(), v, and world.

◆ get_coords()

std::vector< coord_3d > madness::Diamagnetic_potential_factor::get_coords ( ) const

inline

References coords.

◆ get_explicit_B()

coord_3d madness::Diamagnetic_potential_factor::get_explicit_B ( ) const

inline

References explicit_B.

Referenced by estimate_wavefunction_radius().

◆ get_physical_B()

coord_3d madness::Diamagnetic_potential_factor::get_physical_B ( ) const

inline

References physical_B.

Referenced by estimate_wavefunction_radius().

◆ get_potential_radius()

double madness::Diamagnetic_potential_factor::get_potential_radius ( ) const

inline

compute the radius for the diamagnetic potential

References potential_radius.

Referenced by compute_R_times_T_commutator_scalar_term_numerically(), and compute_U2().

◆ get_v()

std::vector< coord_3d > madness::Diamagnetic_potential_factor::get_v ( ) const

inline

References v.

◆ make_fake_orbitals()

std::vector< complex_function_3d > madness::Diamagnetic_potential_factor::make_fake_orbitals	(	const int	n,
		const coord_3d &	offset = `{0.0,0.0,0.0}`
	)		const