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about PSI purity #16

jesusmontera started this conversation in General
about PSI purity #16
Sep 8, 2022 * 0 comments
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jesusmontera
Sep 8, 2022

Hello again, when running the example "1D_interactive_fermions" without potential (setting V=0 for both oscillator and coulomb), if I get the PSI purity it always return 0.5 (maximun entangled), when it must be 1, because if there is no potential particles can't be entagled. No matter the method I use, Crack or Split. If I initilize the psi with my own function(without potential and with kinetic move), it shows purity 1 like it must be. So what's going on?

def MyPsi2P(size, e1, e2, packetwidth, dt, barrierenergy, barrierwidth, initpos):
psi = np.zeros((size,size),dtype=complex)
centerX = math.floor(size*initpos)
centerY = size - centerX
k1 = math.sqrt(2*e1)
k2 = - math.sqrt(2*e2)
pw = pow(packetwidth,2)
for y in range (size):
for x in range (size):
x0=x-centerX
y0=y-centerY
envelope=math.exp(-(x0*x0+y0*y0) /pw)

phasemoveReal=math.cos(k1*x0)*math.cos(k2*y0) - math.sin(k1*x0)*math.sin(k2*y0)
phasemoveImag=math.cos(k1*x0)*math.sin(k2*y0) + math.sin(k1*x0)*math.cos(k2*y0);
psi[y][x] = complex(envelope * phasemoveReal, envelope * phasemoveImag)
`
And her is the function that measures purity, (with psi reshaped to 1D):
```
def shcroduingerpurity(psi):

size=int(len(psi)**0.5)
p=0
#xMaxm1 = size - 1
for xp in range(0,size,1):
for x in range(xp,size,1):
rhore = 0.0
rhoim = 0.0
for y in range(0,size,1):
i1 = x + size*y;
i2 = xp + size*y;
rhore =rhore + psi[i1].real * psi[i2].real + psi[i1].imag * psi[i2].imag
rhoim = rhoim + psi[i1].real * psi[i2].imag - psi[i2].real*psi[i1].imag
if x == xp:
p = p + rhore*rhore + rhoim*rhoim
else:
p = p + 2.*(rhore*rhore + rhoim*rhoim)


return p
```
```
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