Example thin wall potential as given by Coleman. More...

#include <thin_wall_potential.hpp>

Inheritance diagram for BubbleProfiler::Thin_wall_potential:

Collaboration diagram for BubbleProfiler::Thin_wall_potential:

Public Member Functions
	Thin_wall_potential ()=default

	Thin_wall_potential (double, double, double)

virtual	~Thin_wall_potential ()=default

	Thin_wall_potential (const Thin_wall_potential &)=default

	Thin_wall_potential (Thin_wall_potential &&)=default

Thin_wall_potential &	operator= (const Thin_wall_potential &)=default

Thin_wall_potential &	operator= (Thin_wall_potential &&)=default

virtual Thin_wall_potential *	clone () const override
	Subclasses must implement a clone method. More...

virtual double	operator() (const Eigen::VectorXd &) const override
	Evaluate potential at point. More...

virtual double	partial (const Eigen::VectorXd &, int) const override
	Partial derivative WRT coordinate i at a point. More...

virtual double	partial (const Eigen::VectorXd &, int, int) const override
	Partial derivative WRT coordinates i, j at a a point. More...

virtual std::size_t	get_number_of_fields () const override

virtual void	translate_origin (const Eigen::VectorXd &translation) override
	Shift the location of the origin by a specified vector. More...

virtual void	apply_basis_change (const Eigen::MatrixXd &cob_matrix) override
	Apply a change of basis matrix. More...

virtual void	add_constant_term (double _offset) override
	Add a constant offset to the potential. More...

double	operator() (double) const
	evaluates the potential for the given field value More...

double	first_deriv (double) const
	evaluates the first derivative of the potential More...

double	second_deriv (double) const
	evaluates the second derivative of the potential More...

double	get_local_minimum_location () const
	returns the location of the local minimum More...

double	get_local_maximum_location () const
	returns the location of the local maximum More...

double	get_global_minimum_location () const
	returns the location of the global minimum More...

double	get_thin_wall_action () const
	returns the approximate action in the thin-wall approximation More...

Public Member Functions inherited from BubbleProfiler::Potential
virtual	~Potential ()=default

Private Attributes
double	lambda {1.}

double	a {1.}

double	epsilon {0.01}

double	origin {0.}

double	scale {1.}

double	offset {0.}

Detailed Description

Example thin wall potential as given by Coleman.

This class implements the example potential

\[ V(\phi) = \frac{\lambda}{8} (\phi^2 - a^2)^2 + \frac{\epsilon}{2 a} (\phi - a) . \]

and provides analytic expressions for the tunnelling action in the thin-wall approximation.

Examples:: thin_wall.cpp.

Definition at line 40 of file thin_wall_potential.hpp.

Constructor & Destructor Documentation

BubbleProfiler::Thin_wall_potential::Thin_wall_potential ( )

default

Referenced by clone().

BubbleProfiler::Thin_wall_potential::Thin_wall_potential	(	double	lambda_,
		double	a_,
		double	epsilon_
	)

Definition at line 24 of file thin_wall_potential.cpp.

References a, BubbleProfiler::Abs(), epsilon, lambda, and BubbleProfiler::Sqrt().

virtual BubbleProfiler::Thin_wall_potential::~Thin_wall_potential ( )

virtualdefault

BubbleProfiler::Thin_wall_potential::Thin_wall_potential ( const Thin_wall_potential & )

default

BubbleProfiler::Thin_wall_potential::Thin_wall_potential ( Thin_wall_potential && )

default

Member Function Documentation

virtual void BubbleProfiler::Thin_wall_potential::add_constant_term ( double offset )

inlineoverridevirtual

Add a constant offset to the potential.

Parameters

offset constant term to add to potential

Implements BubbleProfiler::Potential.

Definition at line 70 of file thin_wall_potential.hpp.

References first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), get_thin_wall_action(), offset, operator()(), and second_deriv().

virtual void BubbleProfiler::Thin_wall_potential::apply_basis_change ( const Eigen::MatrixXd & cob_matrix )

inlineoverridevirtual

Apply a change of basis matrix.

Parameters

cob_matrix

Implements BubbleProfiler::Potential.

Definition at line 66 of file thin_wall_potential.hpp.

References scale.

virtual Thin_wall_potential* BubbleProfiler::Thin_wall_potential::clone ( ) const

inlineoverridevirtual

Subclasses must implement a clone method.

Implements BubbleProfiler::Potential.

Definition at line 52 of file thin_wall_potential.hpp.

References operator()(), partial(), and Thin_wall_potential().

double BubbleProfiler::Thin_wall_potential::first_deriv ( double coords ) const

evaluates the first derivative of the potential

Parameters

coords the value of the field to evaluate the derivative at

Returns: the value of \(\partial V / \partial \phi\)

Definition at line 101 of file thin_wall_potential.cpp.

References a, epsilon, lambda, origin, and scale.

Referenced by add_constant_term(), and partial().

double BubbleProfiler::Thin_wall_potential::get_global_minimum_location ( ) const

returns the location of the global minimum

Returns: the location of the global minimum

The location of the global minimum is computed exactly using the solution to the cubic equation that results from imposing \( \partial V / \partial \phi = 0\). For \(\epsilon / (\lambda a^2) \ll 1\), one finds that the global minimum is located approximately at \(\phi_t \approx -a\).

Definition at line 166 of file thin_wall_potential.cpp.

References a, BubbleProfiler::Abs(), BubbleProfiler::ArcSin(), epsilon, lambda, origin, scale, BubbleProfiler::Sin(), and BubbleProfiler::Sqrt().

Referenced by add_constant_term(), BubbleProfiler::solve_perturbative(), and BubbleProfiler::solve_shooting().

double BubbleProfiler::Thin_wall_potential::get_local_maximum_location ( ) const

returns the location of the local maximum

Returns: the location of the local maximum

The location of the local maximum (i.e., the potential barrier) is computed exactly using the solution to the cubic equation that results from imposing \( \partial V / \partial \phi = 0\). For \(\epsilon / (\lambda a^2) \ll 1\), one finds that the barrier is approximately located at \(\phi_b \approx \epsilon / (\lambda a^3)\).

Definition at line 148 of file thin_wall_potential.cpp.

References a, BubbleProfiler::Abs(), BubbleProfiler::ArcSin(), epsilon, lambda, origin, scale, BubbleProfiler::Sin(), and BubbleProfiler::Sqrt().

Referenced by add_constant_term(), and BubbleProfiler::solve_shooting().

double BubbleProfiler::Thin_wall_potential::get_local_minimum_location ( ) const

returns the location of the local minimum

Returns: the location of the local minimum

The location of the local minimum is computed exactly using the solution to the cubic equation that results from imposing \( \partial V / \partial \phi = 0\). For \(\epsilon / (\lambda a^2) \ll 1\), one finds that the local minimum is located approximately at \(\phi_f \approx a\).

Definition at line 124 of file thin_wall_potential.cpp.

References a, BubbleProfiler::Abs(), BubbleProfiler::ArcSin(), epsilon, lambda, origin, scale, BubbleProfiler::Sin(), and BubbleProfiler::Sqrt().

Referenced by add_constant_term(), BubbleProfiler::solve_perturbative(), and BubbleProfiler::solve_shooting().

virtual std::size_t BubbleProfiler::Thin_wall_potential::get_number_of_fields ( ) const

inlineoverridevirtual

Implements BubbleProfiler::Potential.

Definition at line 60 of file thin_wall_potential.hpp.

double BubbleProfiler::Thin_wall_potential::get_thin_wall_action ( ) const

returns the approximate action in the thin-wall approximation

Returns: value of the Euclidean action in the thin-wall approximation

An approximate value for the Euclidean action is calculated using the analytic expression for the action derived in the thin-wall approximation,

\[ S \approx \frac{8 \pi^2 \lambda^2 a^{12}}{3 \epsilon^3} . \]

Examples:: thin_wall.cpp.

Definition at line 190 of file thin_wall_potential.cpp.

References a, epsilon, and lambda.

Referenced by add_constant_term(), and main().

double BubbleProfiler::Thin_wall_potential::operator() ( const Eigen::VectorXd & coords ) const

overridevirtual

Evaluate potential at point.

Parameters

coords Coordinates at which to evaluate

Returns: Value of potential at coordinates

Implements BubbleProfiler::Potential.

Definition at line 42 of file thin_wall_potential.cpp.

Referenced by add_constant_term(), and clone().

double BubbleProfiler::Thin_wall_potential::operator() ( double coords ) const

evaluates the potential for the given field value

Parameters

coords the value of the field to evaluate the potential at

Returns: the value of the potential

Definition at line 93 of file thin_wall_potential.cpp.

References a, epsilon, lambda, origin, and scale.

Thin_wall_potential& BubbleProfiler::Thin_wall_potential::operator= ( const Thin_wall_potential & )

default

Thin_wall_potential& BubbleProfiler::Thin_wall_potential::operator= ( Thin_wall_potential && )

default

double BubbleProfiler::Thin_wall_potential::partial	(	const Eigen::VectorXd &	coords,
		int	i
	)		const

overridevirtual

Partial derivative WRT coordinate i at a point.

Parameters

coords	Coordinates at which to evaluate
i	Index of coordinate to be differentiated

Returns: Value of specified partial at point

Implements BubbleProfiler::Potential.

Definition at line 53 of file thin_wall_potential.cpp.

References first_deriv().

Referenced by clone().

double BubbleProfiler::Thin_wall_potential::partial	(	const Eigen::VectorXd &	coords,
		int	i,
		int	j
	)		const

overridevirtual

Partial derivative WRT coordinates i, j at a a point.

Parameters

coords	Coordinates at which to evaluate
i	Index of first coordinate to be differentiated
j	Index of second coordinate to be differentiated

Returns: Value of specified partial at point

Implements BubbleProfiler::Potential.

Definition at line 70 of file thin_wall_potential.cpp.

References second_deriv().

double BubbleProfiler::Thin_wall_potential::second_deriv ( double coords ) const

evaluates the second derivative of the potential

Parameters

coords the value of the field to evaluate the derivative at

Returns: the value of \(\partial^ V / \partial \phi^2\)

Definition at line 109 of file thin_wall_potential.cpp.

References a, lambda, origin, and scale.

Referenced by add_constant_term(), and partial().

virtual void BubbleProfiler::Thin_wall_potential::translate_origin ( const Eigen::VectorXd & translation )

inlineoverridevirtual

Shift the location of the origin by a specified vector.

Parameters

translation shift of origin

Implements BubbleProfiler::Potential.

Definition at line 62 of file thin_wall_potential.hpp.

References origin.

Member Data Documentation

double BubbleProfiler::Thin_wall_potential::a {1.}

private

Definition at line 121 of file thin_wall_potential.hpp.

Referenced by first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), get_thin_wall_action(), operator()(), second_deriv(), and Thin_wall_potential().

double BubbleProfiler::Thin_wall_potential::epsilon {0.01}

private

Definition at line 122 of file thin_wall_potential.hpp.

Referenced by first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), get_thin_wall_action(), operator()(), and Thin_wall_potential().

double BubbleProfiler::Thin_wall_potential::lambda {1.}

private

Definition at line 120 of file thin_wall_potential.hpp.

Referenced by first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), get_thin_wall_action(), operator()(), second_deriv(), and Thin_wall_potential().

double BubbleProfiler::Thin_wall_potential::offset {0.}

private

Definition at line 125 of file thin_wall_potential.hpp.

Referenced by add_constant_term().

double BubbleProfiler::Thin_wall_potential::origin {0.}

private

Definition at line 123 of file thin_wall_potential.hpp.

Referenced by first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), operator()(), second_deriv(), and translate_origin().

double BubbleProfiler::Thin_wall_potential::scale {1.}

private

Definition at line 124 of file thin_wall_potential.hpp.

Referenced by apply_basis_change(), first_deriv(), get_global_minimum_location(), get_local_maximum_location(), get_local_minimum_location(), operator()(), and second_deriv().

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

/home/michael/bubbleprofiler_release/examples/thin-wall/thin_wall_potential.hpp
/home/michael/bubbleprofiler_release/examples/thin-wall/thin_wall_potential.cpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation