vo2solve

package
v1.0.0 Latest Latest
Warning

This package is not in the latest version of its module.

 Go to latest Published: Nov 30, 2016 License: MIT Imports: 11 Imported by: 0

Documentation

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func AbsErrorM 

func AbsErrorM(env *Environment, Ds *HoppingEV, variables []string) solve.Diffable

Return the absolute error and gradient of the M equation w.r.t. the given variables (which should be fixed to ["M", "W", "Mu"] for this case).

func AbsErrorMu 

func AbsErrorMu(env *Environment, variables []string) solve.Diffable

Return the absolute error and gradient of the Mu equation w.r.t. the given variables (which should be fixed to ["M", "W", "Mu"] for this case).

func AbsErrorW 

func AbsErrorW(env *Environment, Ds *HoppingEV, variables []string) solve.Diffable

Return the absolute error and gradient of the W equation w.r.t. the given variables (which should be fixed to ["M", "W", "Mu"] for this case).

func ElHamiltonian 

func ElHamiltonian(env *Environment, k vec.Vector) cmatrix.CMatrix

Calculate 4x4 electronic Hamiltonian. k is in the Cartesian basis, with each component scaled by the corresponding lattice constant; i.e. k = (a kx, a ky, c kz) and a kx, a ky, c kz range over [-pi, pi) and periodic copies of this interval.

func EpsilonAE 

func EpsilonAE(env *Environment, k vec.Vector) complex128

Cubic axes, even symmetry (k, p; k, p)

func EpsilonAO 

func EpsilonAO(env *Environment, k vec.Vector) complex128

Cubic axes, odd symmetry (k, p; k+Q, p)

func EpsilonBE 

func EpsilonBE(env *Environment, k vec.Vector) complex128

Body diagonal, even symmetry (k, p; k, pbar)

func EpsilonBO 

func EpsilonBO(env *Environment, k vec.Vector) complex128

Body diagonal, odd symmetry (k, p; k+Q, pbar)

func GetEV_K0_K0 

func GetEV_K0_K0(env *Environment, k vec.Vector) complex128

Evaluate <c^{\dagger}_{k,0} c_{k,0}>.

func GetEV_K0_K1 

func GetEV_K0_K1(env *Environment, k vec.Vector) complex128

Evaluate <c^{\dagger}_{k,0} c_{k,1}>.

func GetEV_KQ0_K0 

func GetEV_KQ0_K0(env *Environment, k vec.Vector) complex128

Evaluate <c^{\dagger}_{k+Q,0} c_{k,0}>.

func GetEV_KQ0_K1 

func GetEV_KQ0_K1(env *Environment, k vec.Vector) complex128

Evaluate <c^{\dagger}_{k+Q,0} c_{k,1}>.

func MWMuSolve 

func MWMuSolve(env *Environment, Ds *HoppingEV, epsAbs, epsRel float64) (vec.Vector, error)

func MWMuSolve_Iterative 

func MWMuSolve_Iterative(env *Environment, Ds *HoppingEV, epsAbs, epsRel float64) (vec.Vector, error)

func MWMuSystem 

func MWMuSystem(env *Environment, Ds *HoppingEV) (solve.DiffSystem, []float64)

func MWSolve 

func MWSolve(env *Environment, Ds *HoppingEV, epsAbs, epsRel float64) (vec.Vector, error)

func MWSystem 

func MWSystem(env *Environment, Ds *HoppingEV) (solve.DiffSystem, []float64)

func MuSystem 

func MuSystem(env *Environment) (solve.DiffSystem, []float64)

Types

type Environment 

type Environment struct {
	// Size of BZ on one edge (total number of BZ points is this cubed).
	BZPointsPerDim int
	// Hopping parameters, even symmetry (a, c, diagonal axes).
	Tae, Tce, Tbe float64
	// Hopping parameters, odd symmetry (a, c, diagonal axes).
	Tao, Tco, Tbo float64
	// Order parameter <S>.
	M float64
	// Order parameter <S^2>.
	W float64
	// Chemical potential.
	Mu float64
	// Inverse temperature, 1 / (k_B * T).
	Beta float64
	// One-spin term for BEG model: coefficient for (S_i)^2.
	B float64
	// Exchange parameters for BEG model: coefficients to S_i dot S_j.
	// Jb is excluded since it does not contribute to results.
	Ja, Jc float64
	// Biquadratic exchange parameters for BEG model: coefficients to (S_i)^2 * (S_j)^2.
	Ka, Kc, Kb float64
	// On-site energies in M and R phases.
	EpsilonM, EpsilonR float64
	// Consider only ionic part of the problem:
	// only ions contribute to free energy; should solve
	// for (M, W).
	// If this is set to true, need to also set the following to 0:
	// Tae, Tce, Tbe, Tao, Tco, Tbo, EpsilonM, EpsilonR, Mu.
	// (maybe don't need to fix Mu = 0 -- large negative value could
	// be better).
	IonsOnly bool
}

Contains parameters necessary to characterize electronic and ionic systems. The ionic order parameters M and W and the electronic chemical potential Mu must be determined self-consistently.

func LoadEnv 

func LoadEnv(envFilePath string) (*Environment, error)

Load an Environment from the JSON file at envFilePath.

func LoadIonEnv 

func LoadIonEnv(envFilePath string) (*Environment, error)

Load an Environment from the JSON file at envFilePath. Set all electronic parameters to 0 to restrict to ionic system.

func NewEnvironment 

func NewEnvironment(jsonData string) (*Environment, error)

Create an Environment from the given serialized data.

func (*Environment) DeltaS 

func (env *Environment) DeltaS() float64

func (*Environment) Fermi 

func (env *Environment) Fermi(energy float64) float64

Fermi distribution function.

func (*Environment) FiniteHoppings 

func (env *Environment) FiniteHoppings() bool

Are electronic hopping finite? If not, don't need to calculate D's.

func (*Environment) FreeEnergy 

func (env *Environment) FreeEnergy(Ds *HoppingEV) float64

Free energy per cell value (Ncell = 2Nsite). Points on the phase diagram include the state with minimum free energy (may not reach this state, depending on initial conditions - need to consider a set of initial conditions and look for minimum).

func (*Environment) FreeEnergyElectrons 

func (env *Environment) FreeEnergyElectrons() float64

func (*Environment) FreeEnergyIons 

func (env *Environment) FreeEnergyIons(Ds *HoppingEV) float64

func (*Environment) Marshal 

func (env *Environment) Marshal() string

func (*Environment) QJ 

func (env *Environment) QJ(Ds *HoppingEV) float64

Combined renormalized 'exchange' coefficient (S_i S_j) favoring dimers.

func (*Environment) QK 

func (env *Environment) QK() float64

Combined biquadratic coefficient (S_i^2 S_j^2).

func (*Environment) Qele 

func (env *Environment) Qele(Ds *HoppingEV) float64

func (*Environment) Set 

func (env *Environment) Set(v vec.Vector, vars []string)

Iterate through v and vars simultaneously. vars specifies the names of fields to change in env (they are set to the values given in v). Panics if vars specifies a field not contained in env (or a field of non-float type).

func (*Environment) String 

func (env *Environment) String() string

Convert to string by marshalling to JSON

func (*Environment) Z1 

func (env *Environment) Z1(Ds *HoppingEV) float64

type FinalEnvironment 

type FinalEnvironment struct {
	Environment
	Dae, Dce, Dbe, Dao, Dco, Dbo float64
	FreeEnergy                   float64
}

Environment with all self-consistent values converged. Includes additional data for exporting to outside programs.

func NewFinalEnvironment 

func NewFinalEnvironment(env *Environment, Ds *HoppingEV) *FinalEnvironment

Create a FinalEnvironment from the given solved Environment and associated HoppingEV.

func (*FinalEnvironment) Marshal 

func (env *FinalEnvironment) Marshal() string

func (*FinalEnvironment) String 

func (env *FinalEnvironment) String() string

type HoppingEV 

type HoppingEV struct {
	// contains filtered or unexported fields
}

func NewHoppingEV 

func NewHoppingEV() *HoppingEV

func (*HoppingEV) Dae 

func (Ds *HoppingEV) Dae(env *Environment) float64

func (*HoppingEV) Dao 

func (Ds *HoppingEV) Dao(env *Environment) float64

func (*HoppingEV) Dbe 

func (Ds *HoppingEV) Dbe(env *Environment) float64

func (*HoppingEV) Dbo 

func (Ds *HoppingEV) Dbo(env *Environment) float64

func (*HoppingEV) Dce 

func (Ds *HoppingEV) Dce(env *Environment) float64

func (*HoppingEV) Dco 

func (Ds *HoppingEV) Dco(env *Environment) float64

func (*HoppingEV) MarshalEnv 

func (Ds *HoppingEV) MarshalEnv(env *Environment) string

func (*HoppingEV) StringEnv 

func (Ds *HoppingEV) StringEnv(env *Environment) string

Convert to string by marshalling to JSON. Leave out internal cache data.

Source Files

View all Source files

Directories

Path Synopsis

Jump to

Keyboard shortcuts

? : This menu
/ : Search site
f or F : Jump to
y or Y : Canonical URL
go.dev uses cookies from Google to deliver and enhance the quality of its services and to analyze traffic. Learn more.