# 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

## Column integrated density

### 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

To set up and run the simulation in Python we use the script tutorial2a.py. The first parts of this script imports the required modules and then prepares the input files as a list of Python dictionaries:

```import pyalps

parms = [
{
'LATTICE' : 'inhomogeneous simple cubic lattice' ,
'L'       : 120 ,

'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' : 1500 ,
'SWEEPS'         : 7000 ,
'SKIP'           : 50 ,

'MEASURE[Local Density]': 1
}
]
```

We next convert this into a job file in XML format and run the worm simulation:

```input_file = pyalps.writeInputFiles('parm2a', parms)
res = pyalps.runApplication('dwa', input_file)
```

We now have the same output files as in the command line version.