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Solid state physics
lectures
Commits
d1e86a14
Verified
Commit
d1e86a14
authored
3 years ago
by
Anton Akhmerov
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improve and speed up drude animation
parent
fd1ec3cb
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!108
rework plots
Pipeline
#60424
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3 years ago
Stage: build
Stage: deploy
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src/3_drude_model.md
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View file @
d1e86a14
```
python tags=["initialize"]
```
python tags=["initialize"]
from matplotlib import pyplot
from matplotlib import pyplot
import matplotlib.animation as animation
from IPython.display import HTML
import numpy as np
import numpy as np
from common import draw_classic_axes, configure_plotting
from common import draw_classic_axes, configure_plotting
...
@@ -61,21 +62,21 @@ Even under these simplistic assumptions, the trajectory of the electrons is hard
...
@@ -61,21 +62,21 @@ Even under these simplistic assumptions, the trajectory of the electrons is hard
Due to the random scattering, each trajectory is different, and this is how several example trajectories look:
Due to the random scattering, each trajectory is different, and this is how several example trajectories look:
```
python
```
python
%
matplotlib
inline
# Use colors from the default color cycle
import
matplotlib.pyplot
as
plt
default_colors
=
pyplot
.
rcParams
[
'
axes.prop_cycle
'
].
by_key
()[
'
color
'
]
import
numpy
as
np
blue
,
red
=
default_colors
[
0
],
default_colors
[
3
]
import
matplotlib.animation
as
animation
from
IPython.display
import
HTML
walkers
=
20
# number of particles
walkers
=
20
# number of particles
tau
=
1
# relaxation time
tau
=
1
# relaxation time
gamma
=
.
3
# dissipation strength
gamma
=
.
3
# dissipation strength
a
=
1
# acceleration
a
=
1
# acceleration
dt
=
.
1
# infinitesimal
dt
=
.
1
# infinitesimal
T
=
2
0
# simulation time
T
=
1
0
# simulation time
v
=
np
.
zeros
((
2
,
int
(
T
//
dt
),
walkers
),
dtype
=
float
)
#
v
=
np
.
zeros
((
2
,
int
(
T
//
dt
),
walkers
),
dtype
=
float
)
#
# Select random time steps and scattering angles
np
.
random
.
seed
(
1
)
scattering_events
=
np
.
random
.
binomial
(
1
,
dt
/
tau
,
size
=
v
.
shape
[
1
:])
scattering_events
=
np
.
random
.
binomial
(
1
,
dt
/
tau
,
size
=
v
.
shape
[
1
:])
angles
=
np
.
random
.
uniform
(
high
=
2
*
np
.
pi
,
size
=
scattering_events
.
shape
)
*
scattering_events
angles
=
np
.
random
.
uniform
(
high
=
2
*
np
.
pi
,
size
=
scattering_events
.
shape
)
*
scattering_events
rotations
=
np
.
array
(
rotations
=
np
.
array
(
...
@@ -97,47 +98,33 @@ r = np.cumsum(v * dt, axis=1)
...
@@ -97,47 +98,33 @@ r = np.cumsum(v * dt, axis=1)
scattering_positions
=
np
.
copy
(
r
)
scattering_positions
=
np
.
copy
(
r
)
scattering_positions
[:,
~
scattering_events
.
astype
(
bool
)]
=
np
.
nan
scattering_positions
[:,
~
scattering_events
.
astype
(
bool
)]
=
np
.
nan
fig
=
plt
.
figure
()
scatter_pts
=
scattering_positions
scatter_pts
=
scattering_positions
[:,
:
100
]
trace
=
r
[:,
:
100
]
nz_scatters
=
tuple
((
np
.
hstack
(
scatter_pts
[
0
])[
~
np
.
isnan
(
np
.
hstack
(
scatter_pts
[
0
]))],
r_min
=
np
.
min
(
r
.
reshape
(
2
,
-
1
),
axis
=
1
)
-
1
np
.
hstack
(
scatter_pts
[
1
])[
~
np
.
isnan
(
np
.
hstack
(
scatter_pts
[
1
]))]))
r_max
=
np
.
max
(
r
.
reshape
(
2
,
-
1
),
axis
=
1
)
+
1
plt
.
axis
([
min
(
nz_scatters
[
0
])
-
1
,
fig
=
py
pl
o
t
.
figure
(
figsize
=
(
9
,
6
))
max
(
nz_scatters
[
0
])
+
1
,
ax
=
fig
.
add_subplot
(
1
,
1
,
1
)
min
(
nz_scatters
[
1
])
-
1
,
ax
.
axis
(
"
off
"
)
max
(
nz_scatters
[
1
])
+
1
]
)
ax
.
set
(
xlim
=
(
r_min
[
0
],
r_max
[
0
]),
ylim
=
(
r_min
[
1
],
r_max
[
1
]))
lines
=
[]
trajectories
=
ax
.
plot
([],[],
lw
=
1
,
color
=
blue
,
alpha
=
0.5
)[
0
]
scatterers
=
[]
scatterers
=
ax
.
scatter
([],
[],
s
=
20
,
c
=
red
)
for
index
in
range
(
walkers
):
lobj
=
plt
.
plot
([],[],
lw
=
1
,
color
=
'
b
'
,
alpha
=
0.5
)[
0
]
lines
.
append
(
lobj
)
scatterers
.
append
(
plt
.
scatter
([],
[],
s
=
10
,
c
=
'
r
'
))
def
animate
(
i
):
def
frame
(
i
):
for
lnum
,
line
in
enumerate
(
lines
):
concatenated_lines
=
np
.
concatenate
(
line
.
set_data
(
trace
[
0
][:
i
,
lnum
],
trace
[
1
][:
i
,
lnum
])
(
r
[:,
:
i
],
np
.
nan
*
np
.
ones
((
2
,
1
,
walkers
))),
data
=
np
.
stack
((
scatter_pts
[
0
][:
i
,
lnum
],
scatter_pts
[
1
][:
i
,
lnum
])).
T
axis
=
1
scatterers
[
lnum
].
set_offsets
(
data
)
).
transpose
(
0
,
2
,
1
).
reshape
(
2
,
-
1
)
trajectories
.
set_data
(
*
concatenated_lines
)
scatterers
.
set_offsets
(
scatter_pts
[:,
:
i
].
reshape
(
2
,
-
1
).
T
)
anim
=
animation
.
FuncAnimation
(
fig
,
animat
e
,
interval
=
100
)
anim
=
animation
.
FuncAnimation
(
fig
,
fram
e
,
interval
=
100
)
def
remove_axes
(
ax
):
pyplot
.
close
()
ax
.
spines
[
'
bottom
'
].
set_color
(
'
white
'
)
ax
.
spines
[
'
top
'
].
set_color
(
'
white
'
)
ax
.
spines
[
'
right
'
].
set_color
(
'
white
'
)
ax
.
spines
[
'
left
'
].
set_color
(
'
white
'
)
ax
.
tick_params
(
axis
=
'
x
'
,
colors
=
'
white
'
)
ax
.
tick_params
(
axis
=
'
y
'
,
colors
=
'
white
'
)
remove_axes
(
plt
.
gca
());
plt
.
close
();
HTML
(
anim
.
to_html5_video
())
HTML
(
anim
.
to_html5_video
())
```
```
---
### Equations of motion
### Equations of motion
Our goal is finding the
*electric current density*
$j$.
Our goal is finding the
*electric current density*
$j$.
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