HardSpherePotential Class Reference

Computes the effective potential from the exact two-body density matrix for hard spheres in 3D. More...

#include <potential.h>

Inheritance diagram for HardSpherePotential:

Collaboration diagram for HardSpherePotential:

Public Member Functions
	HardSpherePotential (double)
	Constructor. More...
	~HardSpherePotential ()
	Destructor.
virtual double	V (const dVec &r)
	The classical potential.
double	V (const dVec &, const dVec &)
	The effective potential. More...
double	dVdlambda (const dVec &, const dVec &)
	The derivative of the effective potential with respect to lambda. More...
double	dVdtau (const dVec &, const dVec &)
	The derivative of the effective potential with respect to tau. More...
Public Member Functions inherited from PotentialBase
	PotentialBase ()
	Constructor.
virtual	~PotentialBase ()
	Destructor.
virtual dVec	gradV (const dVec &)
	The gradient of the potential.
virtual double	grad2V (const dVec &)
	Grad^2 of the potential.
virtual Array< dVec, 1 >	initialConfig (const Container *, MTRand &, const int)
	Default Initial configuration of particles. More...
void	output (const double)
	A debug method that output's the potential to a supplied separation. More...
virtual Array< double, 1 >	getExcLen ()
	Array to hold data elements. More...

Additional Inherited Members
Data Fields inherited from PotentialBase
double	tailV
	Tail correction factor.
Protected Member Functions inherited from PotentialBase
double	deltaSeparation (double sep1, double sep2) const
	Return the minimum image difference for 1D separations.

Detailed Description

Computes the effective potential from the exact two-body density matrix for hard spheres in 3D.

See also

: S. Pilati, K. Sakkos, J. Boronat, J. Casulleras, and S. Giorgini, Phys Rev A 74, 043621 (2006).

Definition at line 1032 of file potential.h.

Constructor & Destructor Documentation

HardSpherePotential()

HardSpherePotential::HardSpherePotential

(

double

_a

)

Constructor.

Parameters

_a	The radius of the hard sphere (also the scattering length)

Definition at line 2053 of file potential.cpp.

                                                  : 
    PotentialBase(),
    a(_a) {
 
}

Member Function Documentation

dVdlambda()

double HardSpherePotential::dVdlambda ( const dVec &  sep1, const dVec &  sep2  )

virtual

The derivative of the effective potential with respect to lambda.

Computes the non-local two-body effective pair potential.

Tested and working with Mathematica on 2013-06-12.

Parameters

sep1	the first separation
sep2	the second separation

Returns

the derivative of the effective potential with respect to lambda

Reimplemented from PotentialBase.

Definition at line 2108 of file potential.cpp.

{
 
    double r1 = sqrt(dot(sep1,sep1));
    double r2 = sqrt(dot(sep2,sep2));
 
    double cosTheta = dot(sep1,sep2)/(r1*r2);
 
    double t1 = -(r1*r2 + a*a - a*(r1 + r2)) * (1.0 + cosTheta);
    t1 /= (4.0*constants()->lambda()*constants()->tau());
 
    double t2 = (a*(r1+r2) - a*a)/(r1*r2);
    double t3 = 1.0 - t2*exp(t1);
 
    double t4 = (1.0/t3)*(t2*exp(t1))*(t1/constants()->lambda());
 
    return -t4;
}

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dVdtau()

double HardSpherePotential::dVdtau ( const dVec &  sep1, const dVec &  sep2  )

virtual

The derivative of the effective potential with respect to tau.

Computes the non-local two-body effective pair potential.

Tested and working with Mathematica on 2013-06-12.

Parameters

sep1	the first separation
sep2	the second separation
lambda	\lambda = \hbar^2/2m
tau	the imaginary timestep tau

Returns

the derivative of the effective potential with respect to tau

Reimplemented from PotentialBase.

Definition at line 2140 of file potential.cpp.

{
 
    double r1 = sqrt(dot(sep1,sep1));
    double r2 = sqrt(dot(sep2,sep2));
 
    double cosTheta = dot(sep1,sep2)/(r1*r2);
 
    double t1 = -(r1*r2 + a*a - a*(r1 + r2)) * (1.0 + cosTheta);
    t1 /= (4.0*constants()->lambda()*constants()->tau());
 
    double t2 = (a*(r1+r2) - a*a)/(r1*r2);
    double t3 = 1.0 - t2*exp(t1);
 
    double t4 = (1.0/t3)*(t2*exp(t1))*(t1/constants()->tau());
 
    return -t4;
}

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V()

double HardSpherePotential::V ( const dVec &  sep1, const dVec &  sep2  )

virtual

The effective potential.

Computes the non-local two-body effective pair potential.

Tested and working with Mathematica on 2013-06-12.

Parameters

sep1	The first separation
sep2	The second separation

Returns

the two-body effective pair potential

Reimplemented from PotentialBase.

Definition at line 2077 of file potential.cpp.

{
 
    double r1 = sqrt(dot(sep1,sep1));
    double r2 = sqrt(dot(sep2,sep2));
 
    if ((r1 <= a ) || (r2 <= a)) 
        return LBIG;
 
    double cosTheta = dot(sep1,sep2)/(r1*r2);
 
    double t1 = -(r1*r2 + a*a - a*(r1 + r2)) * (1.0 + cosTheta);
    t1 /= (4.0*constants()->lambda()*constants()->tau());
 
    double t2 = (a*(r1+r2) - a*a)/(r1*r2);
    double t3 = 1.0 - t2*exp(t1);
 
    return -log(t3);
}

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

• include/potential.h
• src/potential.cpp