def delta(spin, r):
def repulsion(site):
"Compute |U|(sn_jj-n_jj+1/2)"
# FIXME: I'm slow
return self.repulsion * greens[(1 - spin,) + 2 * site] + abs(self.repulsion) * (
0.5 - greens[(spin,) + 2 * site]
)
f = 1 if spin == 1 else copysign(1, -self.repulsion)
result = ndmat(zeros(2 * self.sites))
for i in sites(self.sites):
result[2 * i] = (
-repulsion(i) - f * sqrt(2 * abs(self.repulsion)) * noise[(r,) + i] + self.chemical_potential
)
for i, j in adjacencies(self.sites):
assert i != j
result[i + j] = self.hopping
return result
def derivative(self, time, state, noise):
greens = state.mean
noise = array(noise).reshape((2,) + self.sites)
def greens_dot(spin):
n = greens[spin, ::]
particles = ndmat(n)
holes = ndmat(unit_like(n) - n)
return 0.5 * (holes * delta(spin, 0) * particles + particles * delta(spin, 1) * holes)
def delta(spin, r):
def repulsion(site):
"Compute |U|(sn_jj-n_jj+1/2)"
# FIXME: I'm slow
return self.repulsion * greens[(1 - spin,) + 2 * site] + abs(self.repulsion) * (
0.5 - greens[(spin,) + 2 * site]
)
f = 1 if spin == 1 else copysign(1, -self.repulsion)
result = ndmat(zeros(2 * self.sites))
for i in sites(self.sites):
result[2 * i] = (
-repulsion(i) - f * sqrt(2 * abs(self.repulsion)) * noise[(r,) + i] + self.chemical_potential
)
for i, j in adjacencies(self.sites):
assert i != j
result[i + j] = self.hopping
return result
weight_log_dot = (
self.hopping * sum([greens[(0,) + i + j] + greens[(1,) + i + j] for i, j in adjacencies(self.sites)])
+ self.repulsion * (greens[0, ::] * greens[1, ::]).sum()
- self.chemical_potential * sum([greens[(0,) + i + i] + greens[(1,) + i + i] for i in sites(self.sites)])
)
return Weighting(array([greens_dot(0), greens_dot(1)]), weight=state.weight * weight_log_dot)