def reflectionless(l=1):
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "reflectionless-" + str(l)
p0 = 0.8
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = qf.reflectionless(x, l=l)
ss.set_static_potential(V_x)
return ss, x0, p0
def osc_reflectionless(l=1):
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "oscillating_reflectionless"
p0 = 0.75
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
freq = 0.05
amp = 10
V_x = np.zeros((Nt, Nx), dtype=np.complex128)
for i in range(Nt - 1):
V = np.zeros((Nx), dtype=np.complex128)
V += qf.reflectionless(x + amp * np.cos(2 * np.pi * freq * t[i]), l)
V_x[i] = V
ss.set_potential(V_x)
return ss, x0, p0
def invisible_susy(a=1j, c=1):
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "invisible_susy_a" + str(a) + "c" + str(c)
p0 = 1
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = qf.invisible_susy(x, a=a, c=c)
ss.set_static_potential(V_x)
return ss, x0, p0
def osc_barrier():
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "oscillating_barrier"
p0 = 1
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
freq = 0.1
amp = 10
V_x = np.zeros((Nt, Nx))
for i in range(Nt - 1):
V = np.zeros((Nx))
V[x < -99] = 1E6
V[x > 99] = 1E6
V += qf.square_barrier(x + amp * np.cos(2 * np.pi * freq * t[i]), 4, 2)
V_x[i] = V
ss.set_potential(V_x)
return ss, x0, p0
def dancing():
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "dancing"
x = dx * (np.arange(Nx) - 0.5 * Nx)
p0 = 0
d = 3
x0 = 0
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = qf.theta(x + 1) - qf.theta(x - 1)
V_x[x < -20] = 1E6
V_x[x > 20] = 1E6
V_x = np.array([V_x])
ss.set_static_potential(V_x)
return ss, x0, p0
def square_barrier():
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "squar_barrier"
p0 = 1
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = qf.square_barrier(x, 2, 2)
ss.set_static_potential(V_x)
return ss, x0, p0
def tentativo():
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "tentativo"
p0 = 0.8
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = -40
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = 1j * np.imag(qf.kk(x, n=1, a=1j, c=3, A=20))
ss.set_static_potential(V_x)
return ss, x0, p0
def kk_wrong(n, a, c, A):
Nx = 2 ** 13
dx = 0.03
t0 = 0.0
dt = 0.02
Nt = int(105 / dt)
x = dx * (np.arange(Nx) - 0.5 * Nx)
t = t0 + dt * np.arange(Nt)
simname = "kk-wrong_n" + str(n) + "a" + str(a) + "c" + str(c) + "A" + str(A)
p0 = -1
dp2 = p0 * p0 * 1. / 80
d = 1 / np.sqrt(2 * dp2)
x0 = 50
psi_x0 = qf.gauss_x(x, d, x0, p0)
norm = np.sqrt((np.abs(psi_x0) ** 2).sum() * 2 * np.pi / dx)
psi_x0 = psi_x0 / norm
ss = SchrodingerSimulation(Nx=Nx, dx=dx, t0=t0, Nt=Nt, dt=dt,
psi_x0=psi_x0, normalize=False,
simname=simname)
V_x = qf.kk(x=x, n=n, a=a, A=A, c=c)
ss.set_static_potential(V_x)
return ss, x0, p0