smash::Potentials Class Reference

#include <potentials.h>

A class that stores parameters of potentials, calculates potentials and their gradients.

Potentials are responsible for long-range interactions and stand in the left part of Boltzmann equation. Short-range interactions are taken into account in the right part of it - in the collision term.

Definition at line 31 of file potentials.h.

Collaboration diagram for smash::Potentials:

Public Member Functions
	Potentials (Configuration conf, const DensityParameters &parameters)
	Potentials constructor. More...
	~Potentials ()
	Standard destructor. More...
double	skyrme_pot (const double baryon_density) const
	Evaluates skyrme potential given a baryon density. More...
double	symmetry_pot (const double baryon_isospin_density) const
	Evaluates symmetry potential given baryon isospin density. More...
double	potential (const ThreeVector &r, const ParticleList &plist, const ParticleType &acts_on) const
	Evaluates potential at point r. More...
std::pair< double, int >	force_scale (const ParticleType &data) const
	Evaluates the scaling factor of the forces acting on the particles. More...
std::pair< ThreeVector, ThreeVector >	skyrme_force (const double density, const ThreeVector grad_rho, const ThreeVector dj_dt, const ThreeVector rot_j) const
	Evaluates the electrical and magnetic components of the skyrme force. More...
std::pair< ThreeVector, ThreeVector >	symmetry_force (const ThreeVector grad_rho, const ThreeVector dj_dt, const ThreeVector rot_j) const
	Evaluates the electrical and magnetic components of the symmetry force. More...
virtual std::tuple< ThreeVector, ThreeVector, ThreeVector, ThreeVector >	all_forces (const ThreeVector &r, const ParticleList &plist) const
	Evaluates the electrical and magnetic components of the forces at point r. More...
virtual bool	use_skyrme () const
virtual bool	use_symmetry () const

Private Attributes
const DensityParameters	param_
	Struct that contains the gaussian smearing width \(\sigma\), the distance cutoff \(r_{\rm cut}\) and the testparticle number needed for the density calculation. More...
bool	use_skyrme_
	Skyrme potential on/off. More...
bool	use_symmetry_
	Symmetry potential on/off. More...
double	skyrme_a_
	Parameter of skyrme potentials: the coefficient in front of \(\frac{\rho}{\rho_0}\) in GeV. More...
double	skyrme_b_
	Parameters of skyrme potentials: the coefficient in front of \((\frac{\rho}{\rho_0})^\tau\) in GeV. More...
double	skyrme_tau_
	Parameters of skyrme potentials: the power index. More...
double	symmetry_s_
	coefficent in front of the symmetry term. More...

Constructor & Destructor Documentation

smash::Potentials::Potentials	(	Configuration	conf,
		const DensityParameters &	parameters
	)

Potentials constructor.

Parameters

[in]	conf	Configuration which contains the switches determining whether to turn on the Skyrme or the symmetry potentials, and the coefficents controlling how strong the potentials are.
[in]	parameters	Struct that contains the gaussian smearing factor \(\sigma\), the distance cutoff \(r_{\rm cut}\) and the testparticle number needed for the density calculation.

smash::Potentials::~Potentials

(

)

Standard destructor.

Definition at line 94 of file potentials.cc.

{}

Member Function Documentation

double smash::Potentials::skyrme_pot

(

const double

baryon_density

)

const

Evaluates skyrme potential given a baryon density.

Parameters

[in]

baryon_density

Baryon density \(\rho\) evaluated in the local rest frame in fm \(^{-3}\).

Returns

Skyrme potential

\[U_B=10^{-3}\times\frac{\rho}{|\rho|} (A\frac{\rho}{\rho_0}+B(\frac{\rho}{\rho_0})^\tau)\]

in GeV

Definition at line 96 of file potentials.cc.

                                                               {
  const double tmp = baryon_density / nuclear_density;
  /* U = U(|rho|) * sgn , because the sign of the potential changes
   * under a charge reversal transformation. */
  const int sgn = tmp > 0 ? 1 : -1;
  // Return in GeV
  return 1.0e-3 * sgn *
         (skyrme_a_ * std::abs(tmp) +
          skyrme_b_ * std::pow(std::abs(tmp), skyrme_tau_));
}

Here is the call graph for this function:

Here is the caller graph for this function:

double smash::Potentials::symmetry_pot

(

const double

baryon_isospin_density

)

const

Evaluates symmetry potential given baryon isospin density.

Parameters

[in]

baryon_isospin_density

The difference between the proton and the neutron density in the local rest frame in fm \(^{-3}\).

Returns

Symmetry potential

\[U_I=2\times 10^{-3}S_{\rm sym} \frac{\rho_n-\rho_p}{\rho_0}\]

in GeV

Definition at line 107 of file potentials.cc.

                                                                         {
  return 1.0e-3 * 2. * symmetry_s_ * baryon_isospin_density / nuclear_density;
}

Here is the caller graph for this function:

double smash::Potentials::potential	(	const ThreeVector &	r,
		const ParticleList &	plist,
		const ParticleType &	acts_on
	)		const

Evaluates potential at point r.

Potential is always taken in the local Eckart rest frame, but point r is in the computational frame.

Parameters

[in]	r	Arbitrary space point where potential is calculated
[in]	plist	List of all particles to be used in \(j^{\mu}\) calculation. If the distance between particle and calculation point r, \( |r-r_i| > r_{cut} \) then particle input to density will be ignored.
[in]	acts_on	Type of particle on which potential is going to act. It gives the charges (or more precisely, the scaling factors) of the particle moving in the potential field.

Returns

Total potential energy acting on the particle:

\[U_{\rm tot} =Q_BU_B+2I_3U_I\]

in GeV, where \(Q_B\) is the baryon charge scaled by the ratio of the light (u, d) quark to the total quark number and \(I_3\) is the third compnent of the isospin.

Definition at line 111 of file potentials.cc.

                                                                {
  double total_potential = 0.0;
  const bool compute_gradient = false;
  const bool smearing = true;
  const auto scale = force_scale(acts_on);

  if (!acts_on.is_baryon()) {
    return total_potential;
  }

  if (use_skyrme_) {
    const double rho_eck = std::get<0>(current_eckart(
        r, plist, param_, DensityType::Baryon, compute_gradient, smearing));
    total_potential += scale.first * skyrme_pot(rho_eck);
  }
  if (use_symmetry_) {
    const double rho_iso = std::get<0>(
        current_eckart(r, plist, param_, DensityType::BaryonicIsospin,
                       compute_gradient, smearing));
    const double sym_pot = symmetry_pot(rho_iso) * acts_on.isospin3_rel();
    total_potential += scale.second * sym_pot;
  }
  return total_potential;
}

Here is the call graph for this function:

std::pair< double, int > smash::Potentials::force_scale

(

const ParticleType &

data

)

const

Evaluates the scaling factor of the forces acting on the particles.

The forces are equal to the product of the scaling factor and the gradient of the potential. We need these scaling factors to describe the motions of the hyperons as well as the anti-particles in the potentials. For Lambda and Sigma, since they carry 2 light (u or d) quarks, they are affected by 2/3 of the Skyrme force. Xi carries 1 light quark, it is affected by 1/3 of the Skyrme force. Omega carries no light quark, so it's not affected by the Skyrme force. Anti-baryons are affected by the force as large as the force acting on baryons but with an opposite direction.

Parameters

[in]

data

Type of particle on which potential is going to act.

Returns

( \(Q_B(1-\frac{Q_S}{3}), 2I_3\)) where \(Q_B\) is the baryon charge, \(Q_S\) is the strangeness, and \(I_3\) is the third component of the isospin.

Definition at line 137 of file potentials.cc.

                                                                           {
  double skyrme_scale = data.is_baryon() ? 1.0 : 0.0;
  if (data.pdgcode().is_hyperon()) {
    if (data.pdgcode().is_Xi()) {
      skyrme_scale = 1. / 3.;
    } else if (data.pdgcode().is_Omega()) {
      skyrme_scale = 0.;
    } else {
      skyrme_scale = 2. / 3.;
    }
  }
  skyrme_scale = skyrme_scale * data.pdgcode().baryon_number();
  const int symmetry_scale = data.pdgcode().baryon_number();
  return std::make_pair(skyrme_scale, symmetry_scale);
}

Here is the call graph for this function:

Here is the caller graph for this function:

std::pair< ThreeVector, ThreeVector > smash::Potentials::skyrme_force	(	const double	density,
		const ThreeVector	grad_rho,
		const ThreeVector	dj_dt,
		const ThreeVector	rot_j
	)		const

Evaluates the electrical and magnetic components of the skyrme force.

Parameters

[in]	density	Eckart density [fm \(^{-3}\)].
[in]	grad_rho	Gradient of density [fm \(^{-4}\)]. This density is evaluated in the computational frame.
[in]	dj_dt	Time derivative of the current density [fm \(^{-4}\)
[in]	rot_j	Curl of the current density [fm \(^{-4}\)

Returns

( \(E_B, B_B\)), where

\[E_B = -V_B^\prime(\rho^\ast)(\nabla\rho_B + \partial_t \vec j_B)\]

is the electro component of Skyrme force and

\[B_B = V_B^\prime(\rho^\ast) \nabla\times\vec j_B\]

is the magnetic component of the Skyrme force with \(\rho^\ast\) being the Eckart density.

Definition at line 153 of file potentials.cc.

                                   {
  const double MeV_to_GeV = 1.0e-3;
  ThreeVector E_component(0.0, 0.0, 0.0), B_component(0.0, 0.0, 0.0);
  if (use_skyrme_) {
    const double dV_drho =
        (skyrme_a_ + skyrme_b_ * skyrme_tau_ *
                         std::pow(density / nuclear_density, skyrme_tau_ - 1)) *
        MeV_to_GeV / nuclear_density;
    E_component -= dV_drho * (grad_rho + dj_dt);
    B_component += dV_drho * rot_j;
  }
  return std::make_pair(E_component, B_component);
}

Here is the caller graph for this function:

std::pair< ThreeVector, ThreeVector > smash::Potentials::symmetry_force	(	const ThreeVector	grad_rho,
		const ThreeVector	dj_dt,
		const ThreeVector	rot_j
	)		const

Evaluates the electrical and magnetic components of the symmetry force.

Parameters

[in]	grad_rho	Gradient of density [fm \(^{-4}\)]. This density is evaluated in the computational frame.
[in]	dj_dt	Time derivative of the current density [fm \(^{-4}\)
[in]	rot_j	Curl of the current density [fm \(^{-4}\)

Returns

( \(E_I3, B_I3\)) [GeV/fm], where

\[E_{I3} = -V_{I3}^\prime(\rho^\ast)(\nabla\rho_{I3} + \partial_t \vec j_{I3})\]

is the electrical component of symmetry force and

\[B_{I3} = V_I^\prime(\rho^\ast) \nabla\times\vec j_{I3}\]

is the magnetic component of the symmetry force with \(\rho^\ast\) being the Eckart density.

Definition at line 169 of file potentials.cc.

                                   {
  const double MeV_to_GeV = 1.0e-3;
  ThreeVector E_component(0.0, 0.0, 0.0), B_component(0.0, 0.0, 0.0);
  if (use_symmetry_) {
    const double dV_drho = MeV_to_GeV * 2. * symmetry_s_ / nuclear_density;
    E_component -= dV_drho * (grad_rho + dj_dt);
    B_component += dV_drho * rot_j;
  }
  return std::make_pair(E_component, B_component);
}

Here is the caller graph for this function:

std::tuple< ThreeVector, ThreeVector, ThreeVector, ThreeVector > smash::Potentials::all_forces ( const ThreeVector &  r, const ParticleList &  plist  ) const

virtual

Evaluates the electrical and magnetic components of the forces at point r.

Point r is in the computational frame.

Parameters

[in]	r	Arbitrary space point where potential gradient is calculated
[in]	plist	List of all particles to be used in \(j^{\mu}\) calculation. If the distance between particle and calculation point r, \( |r-r_i| > r_{cut} \) then particle input to density will be ignored.

Returns

( \(E_B, B_B, E_{I3}, B_{I3}\)) [GeV/fm], where \(E_B\): the electric component of the Skyrme force \(B_B\): the magnetic component of the Skyrme force \(E_{I3}\): the electric component of the symmetry force \(B_{I3}\): the magnetic component of the symmetry force

Definition at line 183 of file potentials.cc.

                                                                            {
  const bool compute_gradient = true;
  const bool smearing = true;
  auto F_skyrme =
      std::make_pair(ThreeVector(0., 0., 0.), ThreeVector(0., 0., 0.));
  auto F_symmetry =
      std::make_pair(ThreeVector(0., 0., 0.), ThreeVector(0., 0., 0.));

  if (use_skyrme_) {
    const auto density_and_gradient = current_eckart(
        r, plist, param_, DensityType::Baryon, compute_gradient, smearing);
    const double rho = std::get<0>(density_and_gradient);
    const ThreeVector grad_rho = std::get<2>(density_and_gradient);
    const ThreeVector dj_dt = std::get<3>(density_and_gradient);
    const ThreeVector rot_j = std::get<4>(density_and_gradient);
    F_skyrme = skyrme_force(rho, grad_rho, dj_dt, rot_j);
  }

  if (use_symmetry_) {
    const auto density_and_gradient =
        current_eckart(r, plist, param_, DensityType::BaryonicIsospin,
                       compute_gradient, smearing);
    const ThreeVector grad_rho = std::get<2>(density_and_gradient);
    const ThreeVector dj_dt = std::get<3>(density_and_gradient);
    const ThreeVector rot_j = std::get<4>(density_and_gradient);
    F_symmetry = symmetry_force(grad_rho, dj_dt, rot_j);
  }

  return std::make_tuple(F_skyrme.first, F_skyrme.second, F_symmetry.first,
                         F_symmetry.second);
}

Here is the call graph for this function:

Here is the caller graph for this function:

virtual bool smash::Potentials::use_skyrme ( ) const

inlinevirtual

Returns

Is Skyrme potential on?

Definition at line 164 of file potentials.h.

{ return use_skyrme_; }

Here is the caller graph for this function:

virtual bool smash::Potentials::use_symmetry ( ) const

inlinevirtual

Returns

Is symmetry potential on?

Definition at line 166 of file potentials.h.

{ return use_symmetry_; }

Here is the caller graph for this function:

Member Data Documentation

const DensityParameters smash::Potentials::param_

private

Struct that contains the gaussian smearing width \(\sigma\), the distance cutoff \(r_{\rm cut}\) and the testparticle number needed for the density calculation.

Definition at line 174 of file potentials.h.

bool smash::Potentials::use_skyrme_

private

Skyrme potential on/off.

Definition at line 177 of file potentials.h.

bool smash::Potentials::use_symmetry_

private

Symmetry potential on/off.

Definition at line 180 of file potentials.h.

double smash::Potentials::skyrme_a_

private

Parameter of skyrme potentials: the coefficient in front of \(\frac{\rho}{\rho_0}\) in GeV.

Definition at line 186 of file potentials.h.

double smash::Potentials::skyrme_b_

private

Parameters of skyrme potentials: the coefficient in front of \((\frac{\rho}{\rho_0})^\tau\) in GeV.

Definition at line 192 of file potentials.h.

double smash::Potentials::skyrme_tau_

private

Parameters of skyrme potentials: the power index.

Definition at line 198 of file potentials.h.

double smash::Potentials::symmetry_s_

private

coefficent in front of the symmetry term.

Definition at line 201 of file potentials.h.

---

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

• src/include/smash/potentials.h
• src/potentials.cc