Potential composed of two multivariate Gaussian functions. More...

#include <gaussian_potential.hpp>

Inheritance diagram for BubbleProfiler::Gaussian_potential:

Collaboration diagram for BubbleProfiler::Gaussian_potential:

Public Member Functions
	Gaussian_potential (double gamma_, double lambda_, std::size_t n_fields_)
	instantiate a new Gaussian potential More...

virtual	~Gaussian_potential ()=default

Gaussian_potential *	clone () const
	return a copy of this potential More...

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

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

virtual double	partial (const Eigen::VectorXd &coords, int i, int j) 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 &) override
	Shift the location of the origin by a specified vector. More...

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

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

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

Private Member Functions
double	gaussian (const Eigen::VectorXd &, const Eigen::VectorXd &) const

double	gaussian_deriv (const Eigen::VectorXd &, const Eigen::VectorXd &, int i) const

double	gaussian_deriv2 (const Eigen::VectorXd &, const Eigen::VectorXd &, int i, int j) const

Private Attributes
double	gamma {2.}

double	lambda {1.}

std::size_t	n_fields {0}

double	constant_term {0.}

Eigen::VectorXd	origin {}

Eigen::VectorXd	origin_translation {}

Eigen::VectorXd	mu {}

Eigen::MatrixXd	basis_transform {}

Detailed Description

Potential composed of two multivariate Gaussian functions.

This class implements a potential made of two (multivariate) Gaussian functions. The functional form of the potential is

\[ V(\phi) = -(N(\phi, 0) + \gamma N(\phi, \mu)), \]

where \(N(\phi,\mu) = \frac{1}{(2\pi)^{n/2}} \exp(-\frac{1}{2} | \phi - \mu|^2)\) is a unit Gaussian, \(\gamma\) controls the relative depth of the two minima, and \(\mu = \frac{1}{\sqrt{n_f}} (\lambda, \ldots, \lambda)\), where \(n_f\) is the number of fields and the parameter \(\lambda\) controls the geometric distance between the minima.

Note that we enforce \(\gamma > 1\), so that the Gaussian at the origin is a false vacuum.

Definition at line 53 of file gaussian_potential.hpp.

Constructor & Destructor Documentation

BubbleProfiler::Gaussian_potential::Gaussian_potential	(	double	gamma_,
		double	lambda_,
		std::size_t	n_fields_
	)

instantiate a new Gaussian potential

Parameters

gamma_	relative depth of the two minima
lambda_	geometric distance between minima ( \(\mu = \frac{1}{\sqrt{n_fields}}(\lambda, ..., \lambda)\))
n_fields_	number of fields

Definition at line 31 of file gaussian_potential.cpp.

References basis_transform, gamma, lambda, mu, n_fields, origin, and origin_translation.

Referenced by clone().

virtual BubbleProfiler::Gaussian_potential::~Gaussian_potential ( )

virtualdefault