• General info
• Defining reference scales for static calculation
  • Fermi momentum
  • Chemical potentials
  • Examples
    • Fermi momentum is fixed by density in the box center
• Defining reference scales for time dependent calculations

General info

During the computation process W-SLDA codes exploit information about typical scales present in the problem. Precisely, reference scales define typical orders of magnitude for computed quantities. The most important reference scale is:

• k_F=(3\pi^2 n)^{1/3} - Fermi momentum.

Other reference scales computed automatically from k_F are:

• \varepsilon_F=\frac{1}{2}k_F^2 - Fermi energy,
• E_{\textrm{ffg}}=\frac{3}{5}N\varepsilon_F - energy of free Fermi gas.

Finally, chemical potentials also serve as reference scales for static problems:

• \mu_{\uparrow} - chemical potential is spin-up particles (particles of type a),
• \mu_{\downarrow} - chemical potential is spin-down particles (particles of type b).

Defining reference scales for static calculation

Fermi momentum

There are the following methods of defining the k_F reference scale:

• automatic: in each iteration code checks what is maximal density n=\max[n_{\uparrow}(\bm{r})+n_{\downarrow}(\bm{r})] and next Fermi momentum is computed as k_F=(3\pi^2 n)^{1/3},
• via input file: k_F is provided by user in input file. To activate this mode you need to uncomment tag referencekF:

referencekF             1.0    # hard set for reference value of kF

• via process_params() function: you can code value of reference scales in problem-definition.h file

void process_params(double *params, double *kF, double *mu, size_t extra_data_size, void *extra_data)
{
    // ...
    (*kF) = MY_VALUE_FOR_KF; 
    // ... 
}

Chemical potentials

Chemical potentials are adjusted automatically when mode with fixed particle number is executed. For mode with fixed chemical potential see here.

Examples

Fermi momentum is fixed by density in the box center

// Set kF via process_params function
void process_params(double *params, double *kF, double *mu, size_t extra_data_size, void *extra_data)
{
    // set kF
    double *dens=(double *)extra_data;
    if(dens[0]>0.0) // do it only if central density has been computed
    {
        (*kF) = pow(3.0*M_PI*M_PI*dens[0],1./3.);
        if(wsldapid==0) wprintf("# UPDATE OF kF=%f\n", (*kF)); // print to stdout
    }

}

// here you can extract needed data, like central density
void modify_potentials(int it, wslda_density h_densities, wslda_potential h_potentials, double *params, size_t extra_data_size, void *extra_data)
{    
    // DETERMINE LOCAL SIZES OF ARRAYS (CODE DIMENSIONALITY DEPENDENT)
    int lNX=h_densities.nx, lNY=h_densities.ny, lNZ=h_densities.nz; // local sizes
    int ixyz;
    
    // take value of density in box center and save it to extra_data
    ixyz = lNZ/2 + lNZ*lNY/2 + lNZ*lNY*lNX/2;
    double *dens=(double *)extra_data;
    dens[0] = h_densities.rho_a[ixyz]+h_densities.rho_b[ixyz];
}

// since you want to pass data between functions, use extra_data buffer
size_t get_extra_data_size(double *params)
{
    return sizeof(double); // I need buffer for density
}

// here you initialize the buffer
int load_extra_data(size_t size, void *extra_data, double *params)
{
    double *dens=(double *)extra_data;
    dens[0]=0.0; // set initial value to zero
    return 0;
}

Defining reference scales for time dependent calculations

All reference scales are provided together with an initial state, i.e. binary files produced by static codes contain this information. Presently there is no option of changing values for reference scales.