# Density profile

As a second example of the dwa QMC code, we will study the density profile of an optical lattice in an harmonic trap which resembles the experiment

## Mimicking the experiment

### Preparing and running the simulation from the command line

The parameter file parm2a sets up Monte Carlo simulation of a 1003 optical lattice trap that mimicks the Bloch experiment:

```LATTICE="inhomogeneous simple cubic lattice"
L=100

MODEL='boson Hubbard"
Nmax=20

t=1.
U=8.11
mu="4.05 - (0.0073752*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.0036849*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.0039068155*(z-(L-1)/2.)*(z-(L-1)/2.))"

THERMALIZATION=50000
SWEEPS=200000
SKIP=100

MEASURE[Local Density]=1

{ T=1. }
```

Using the standard sequence of commands you can run the simulation using the quantum dwa code

```parameter2xml parm2a
dwa parm2a.in.xml
```

### Preparing and running the simulation from Python

```import pyalps

parms = [
{
'LATTICE' : 'inhomogeneous simple cubic lattice' ,
'L'       : 100 ,

'MODEL'   : 'boson Hubbard' ,
'Nmax'    : 20 ,

't'  : 1. ,
'U'  : 8.11 ,
'mu' : '4.05 - (0.0073752*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.0036849*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.0039068155*(z-(L-1)/2.)*(z-(L-1)/2.))' ,

'T'  : 1. ,

'THERMALIZATION' : 50000 ,
'SWEEPS'         : 2000000 ,
'SKIP'           : 100 ,

'MEASURE[Local Density]': 1
}
)

input_file = pyalps.writeInputFiles('parm1a', parms)
res = pyalps.runApplication('dwa', input_file, Tmin=5, writexml=True)
```

or simply if existent,

```h5_infiles = pyalps.getInputH5Files(prefix='parm9f');
```

Have a preliminary taste:

```pyalps.runApplication('dwa', h5_infiles[0]);
```

Detailed step by step instruction for running this example is illustrated here.