In [1]:
using Pkg
Pkg.add("NBInclude")
Updating registry at `~/.julia/registries/General` Updating git-repo `https://github.com/JuliaRegistries/General.git` [1mFetching: [========================================>] 100.0 %.0 %12.5 %> ] 25.1 %Fetching: [================> ] 37.6 %> ] 50.0 % [==========================> ] 62.6 %75.0 %79.8 %=====================================> ] 92.3 % Resolving package versions... Installed OffsetArrays ─ v0.9.1 Installed NBInclude ──── v2.1.0 Updating `~/.julia/environments/v1.0/Project.toml` [0db19996] + NBInclude v2.1.0 Updating `~/.julia/environments/v1.0/Manifest.toml` [0db19996] + NBInclude v2.1.0 [6fe1bfb0] ↑ OffsetArrays v0.9.0 ⇒ v0.9.1
In [2]:
using NBInclude
┌ Info: Precompiling NBInclude [0db19996-df87-5ea3-a455-e3a50d440464] └ @ Base loading.jl:1186
In [306]:
@nbinclude("quantum_electrodynamical_ground_state_calculator_routines_and_how_to.ipynb")
Out[306]:
photonic(10000, 3, [1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7, 1.0e-7 … 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935, 0.000759935], Complex{Float64}[0.0+0.0im 0.0+0.0im … 3.76236e-8+0.0im 3.85377e-8+0.0im; 0.0+0.0im 0.0+0.0im … -9.6601e-9+0.0im -4.86844e-9+0.0im; 0.0+0.0im 0.0+0.0im … 0.0+3.8844e-8im 0.0+3.8844e-8im])
Example I: Finding the changes in electromagnetic field response due to strong coupling with a single emitter¶
In [13]:
N_el = 200;
electron_1d = construct_matter(zeros(N_el),0.25*ev_hartree,5,N_el)
N_cav = 100;
d_cav = 1; # spatial dimension of the cavity mode, corresponds to number of vector components used to describe mode
L_cav = 18904.0; # 1 micron in atomic units
S_cav = (10.0*nm)^2; #area of cavity
emitter_pos = L_cav/2; # position where the emitter is located
freqs_cav = pi*(1:N_cav)*c/L_cav;
modes_cav = zeros(d_cav,N_cav);
for counter = 1:N_cav
modes_cav[1,counter] = sqrt(2.0/L_cav/S_cav)*sin(freqs_cav[counter]*emitter_pos/c); # for 2d or 3d, want two extra lines specifying those components
end
pt_cav = photonic(N_cav,d_cav,freqs_cav,modes_cav)
sample_ωs = 0:1e-3:2.5;
green_cav = [green!(1,1,ω,pt_cav) for ω in sample_ωs];
In [18]:
plot(sample_ωs[1:200],green_cav[1:200])
xlabel("Frequency (Hartree)")
ylabel("Green's function (*bohr)")
Out[18]:
PyObject Text(24.000000000000007, 0.5, "Green's function (*bohr)")
In [32]:
weight = 40000*qe^2/me/ϵ0/c^2;
freqs_int = construct_coupled_freqs(pt_cav,weight);
plot(1:10,freqs_bare[1:10],1:10,freqs_int[1:10],marker="o",linewidth=0)
xlabel("Mode number")
ylabel("Frequency (Hartree)")
title("Change in photon frequencies due to coupling")
Out[32]:
PyObject Text(0.5, 1.0, 'Change in photon frequencies due to coupling')
In [41]:
weight = 500000*qe^2/me/ϵ0/c^2;
freqs_int = construct_coupled_freqs(pt_cav,weight);
plot(1:30,freqs_bare[1:30],1:30,freqs_int[1:30],marker="o",linewidth=0)
xlabel("Mode number")
ylabel("Frequency (Hartree)")
title("Change in photon frequencies due to coupling")
Out[41]:
PyObject Text(0.5, 1.0, 'Change in photon frequencies due to coupling')
In [60]:
# setting a cavity mode with position dependence
N_cav = 100;
Npts_cav = 1000;
d_cav = 1;
L_cav = 18904.0; # may want to set basic unit in other routines to L_cav if I want.
freqs_cav = pi*(1:N_cav)*c/L_cav;
positions_cav = 0:L_cav/Npts_cav:L_cav;
num_positions_cav = size(positions_cav,1);
modes_cav = zeros(num_positions_cav,N_cav,d_cav);
for counter = 1:size(modes_cav,2)
modes_cav[:,counter,1] = sqrt(2.0/L_cav)*sin.(freqs_cav[counter]*positions_cav/c); #the last argument 1 is hard-coded in
end
pt_cav = photonic(N_cav,d_cav,freqs_cav,modes_cav)
Out[60]:
photonic(100, 1, [0.0227676, 0.0455351, 0.0683027, 0.0910703, 0.113838, 0.136605, 0.159373, 0.182141, 0.204908, 0.227676 … 2.07185, 2.09462, 2.11738, 2.14015, 2.16292, 2.18569, 2.20845, 2.23122, 2.25399, 2.27676], [0.0 0.0 … 0.0 0.0; 3.23137e-5 6.46272e-5 … 0.00314774 0.00317849; … ; 3.23137e-5 -6.46272e-5 … 0.00314774 -0.00317849; 1.25965e-18 -2.51929e-18 … -1.31092e-16 2.02053e-17])
In [69]:
plot(positions_cav,-mode(freqs_bare[1]),positions_cav,-mode(freqs_int[1]))
xlabel("Axial position in cavity")
ylabel("Electric field strength")
title("Change in photon mode profiles due to coupling")
legend(["Bare","Int"])
Out[69]:
PyObject <matplotlib.legend.Legend object at 0x7f95b7fd9438>
In [72]:
plot(positions_cav,-mode(freqs_bare[3]),positions_cav,-mode(freqs_int[3]))
xlabel("Axial position in cavity")
ylabel("Electric field strength")
title("Change in photon mode profiles due to coupling")
legend(["Bare","Int"])
Out[72]:
PyObject <matplotlib.legend.Legend object at 0x7f95b7b100f0>
In [78]:
plot(positions_cav,-mode(freqs_bare[31]),positions_cav,-mode(freqs_int[31]))
xlabel("Axial position in cavity")
ylabel("Electric field strength")
title("Change in photon mode profiles due to coupling")
legend(["Bare","Int"])
Out[78]:
PyObject <matplotlib.legend.Legend object at 0x7f95b78884a8>
Example II: Finding the self-consistent change in the electron energy levels due to coupling with quantized electromagnetic fields.¶
I: With a cavity¶
In [89]:
# photon
N_cav = 100;
d_cav = 1; # spatial dimension of the cavity mode, corresponds to number of vector components used to describe mode
L_cav = 18904.0; # 1 micron in atomic units
S_cav = (10.0*nm)^2; #area of cavity
emitter_pos = L_cav/2; # position where the emitter is located
freqs_cav = pi*(1:N_cav)*c/L_cav;
modes_cav = zeros(d_cav,N_cav);
for counter = 1:N_cav
modes_cav[1,counter] = sqrt(2.0/L_cav/S_cav)*sin(freqs_cav[counter]*emitter_pos/c); # for 2d or 3d, want two extra lines specifying those components
end
pt_cav = photonic(N_cav,d_cav,freqs_cav,modes_cav)
# electron
N_el = 4;
electron_1d = construct_matter(zeros(N_el),0.25*ev_hartree,5,N_el)
# initializing parameters
E = electron_1d;
X0 = E.X
P = pt_cav;
Interaction strengths where the iterates converge rapidly and easily¶
In [91]:
str = 1;
sol_el= fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=100);
[-0.0148064, -0.00565678, 0.00565768, 0.0148133] [-0.0148064, -0.00565678, 0.00565768, 0.0148133] [-0.0148064, -0.00565678, 0.00565768, 0.0148133]
In [93]:
str = 100;
sol_el= fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=100);
[-0.0143492, -0.00560667, 0.00569666, 0.0150416] [-0.0143492, -0.00560612, 0.00569698, 0.0150424] [-0.0143492, -0.00560612, 0.00569698, 0.0150424] [-0.0143492, -0.00560612, 0.00569698, 0.0150424] [-0.0143492, -0.00560612, 0.00569698, 0.0150424] [-0.0143492, -0.00560612, 0.00569698, 0.0150424] [-0.0143492, -0.00560612, 0.00569698, 0.0150424]
In [179]:
str = 1000;
sol_el= fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=100);
[-0.0101936, -0.0051511, 0.00605098, 0.0171173] [-0.0101936, -0.00508895, 0.00608577, 0.0172037] [-0.0101936, -0.00509002, 0.00608545, 0.0172003] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004] [-0.0101936, -0.00509, 0.00608545, 0.0172004]
In [180]:
str = 10000;
sol_el= fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=100);
[-0.000595386, 0.00959421, 0.0313629, 0.0378742] [0.00107939, 0.00744818, 0.010586, 0.0351307] [0.00107939, 0.0106729, 0.0226441, 0.036402] [0.00107939, 0.0106616, 0.011624, 0.0360179] [0.00107939, 0.0106631, 0.01867, 0.0361323] [0.00107939, 0.0106629, 0.0137465, 0.0360981] [0.00107939, 0.0106629, 0.0169925, 0.0361083] [0.00107939, 0.0106629, 0.014765, 0.0361052] [0.00107939, 0.0106629, 0.0162533, 0.0361062] [0.00107939, 0.0106629, 0.0152406, 0.0361059] [0.00107939, 0.0106629, 0.0159213, 0.036106] [0.00107939, 0.0106629, 0.0154599, 0.0361059] [0.00107939, 0.0106629, 0.0157709, 0.0361059] [0.00107939, 0.0106629, 0.0155605, 0.0361059] [0.00107939, 0.0106629, 0.0157025, 0.0361059] [0.00107939, 0.0106629, 0.0156065, 0.0361059] [0.00107939, 0.0106629, 0.0156713, 0.0361059] [0.00107939, 0.0106629, 0.0156275, 0.0361059] [0.00107939, 0.0106629, 0.0156571, 0.0361059] [0.00107939, 0.0106629, 0.0156371, 0.0361059] [0.00107939, 0.0106629, 0.0156506, 0.0361059] [0.00107939, 0.0106629, 0.0156415, 0.0361059] [0.00107939, 0.0106629, 0.0156476, 0.0361059] [0.00107939, 0.0106629, 0.0156435, 0.0361059] [0.00107939, 0.0106629, 0.0156463, 0.0361059] [0.00107939, 0.0106629, 0.0156444, 0.0361059] [0.00107939, 0.0106629, 0.0156457, 0.0361059] [0.00107939, 0.0106629, 0.0156448, 0.0361059] [0.00107939, 0.0106629, 0.0156454, 0.0361059] [0.00107939, 0.0106629, 0.015645, 0.0361059] [0.00107939, 0.0106629, 0.0156453, 0.0361059] [0.00107939, 0.0106629, 0.0156451, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156451, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059] [0.00107939, 0.0106629, 0.0156452, 0.0361059]
Interaction strengths where the iterates don't converge in 1000 iterations¶
In [173]:
str = 100000;
sol_el= fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=1000);
[0.0449617, 0.0450264, 0.245443, 0.446928] [0.0275396, 0.0617095, 0.0728607, 0.0865826] [0.0257903, 0.0328685, 0.175692, 0.446928] [0.026012, 0.0592096, 0.0617095, 0.103138] [0.0251222, 0.0375476, 0.151865, 0.446928] [0.0259609, 0.0523226, 0.0617095, 0.113987] [0.0251004, 0.0411155, 0.140945, 0.446928] [0.0259592, 0.0487142, 0.0617095, 0.120202] [0.0250997, 0.0433967, 0.135543, 0.446928] [0.0259592, 0.0467307, 0.0617095, 0.123618] [0.0250997, 0.0448011, 0.13279, 0.446928] [0.0259592, 0.0456097, 0.0617095, 0.125457] [0.0250997, 0.0456491, 0.131365, 0.446928] [0.0259592, 0.0449659, 0.0617095, 0.126436] [0.0250997, 0.0461554, 0.130622, 0.446928] [0.0259592, 0.0445926, 0.0617095, 0.126954] [0.0250997, 0.0464556, 0.130232, 0.446928] [0.0259592, 0.0443751, 0.0617095, 0.127228] [0.0250997, 0.046633, 0.130028, 0.446928] [0.0259592, 0.0442478, 0.0617095, 0.127372] [0.0250997, 0.0467376, 0.129921, 0.446928] [0.0259592, 0.0441733, 0.0617095, 0.127448] [0.0250997, 0.0467991, 0.129864, 0.446928] [0.0259592, 0.0441295, 0.0617095, 0.127488] [0.0250997, 0.0468353, 0.129835, 0.446928] [0.0259592, 0.0441039, 0.0617095, 0.127509] [0.0250997, 0.0468566, 0.129819, 0.446928] [0.0259592, 0.0440888, 0.0617095, 0.12752] [0.0250997, 0.0468691, 0.129811, 0.446928] [0.0259592, 0.04408, 0.0617095, 0.127526] [0.0250997, 0.0468764, 0.129807, 0.446928] [0.0259592, 0.0440748, 0.0617095, 0.127529] [0.0250997, 0.0468808, 0.129804, 0.446928] [0.0259592, 0.0440717, 0.0617095, 0.127531] [0.0250997, 0.0468833, 0.129803, 0.446928] [0.0259592, 0.0440699, 0.0617095, 0.127531] [0.0250997, 0.0468848, 0.129802, 0.446928] [0.0259592, 0.0440689, 0.0617095, 0.127532] [0.0250997, 0.0468857, 0.129802, 0.446928] [0.0259592, 0.0440682, 0.0617095, 0.127532] [0.0250997, 0.0468862, 0.129802, 0.446928] [0.0259592, 0.0440679, 0.0617095, 0.127532] [0.0250997, 0.0468865, 0.129802, 0.446928] [0.0259592, 0.0440677, 0.0617095, 0.127532] [0.0250997, 0.0468867, 0.129802, 0.446928] [0.0259592, 0.0440675, 0.0617095, 0.127532] [0.0250997, 0.0468868, 0.129802, 0.446928] [0.0259592, 0.0440675, 0.0617095, 0.127532] [0.0250997, 0.0468868, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] 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[0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532] [0.0250997, 0.0468869, 0.129802, 0.446928] [0.0259592, 0.0440674, 0.0617095, 0.127532]
In [193]:
strengths = [10^0.0, 10^0.5, 10^1.0, 10^1.5, 10^2.0, 10^2.5, 10^3.0, 10^3.5, 10^4.0, 10^4.5]
gs_energies = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
for i=1:10
str = strengths[i]
sol_el = fixedpoint(f_el2!, X0; method = :anderson, m=0,beta=1.0,iterations=1000);
gs_energies[i] = sol_el.zero[17]
end
In [197]:
plot(strengths,gs_energies,marker="o",linewidth=0)
xlabel("Coupling strength [arb]")
ylabel("Lowest energy eigenvalue (Hartree)")
title("Change in electronic ground state energies due to coupling")
Out[197]:
PyObject Text(0.5, 1.0, 'Change in electronic ground state energies due to coupling')
In [ ]:
#### I: With a cavity
Example III: Finding the change in the electron density and the electromagnetic field due to coupling of matter with quantized electromagnetic fields -- mean field method.¶
One-dimensional example¶
In [200]:
N_el_l = 200;
R = 8;
xgrid = -R:(2*R)/(N_el_l-1):R
Δx = (2*R)/(N_el_l-1);
V = 0.5*10*(xgrid).^2+0.005*(xgrid).^3+0.0001*(xgrid).^4;
H = SymTridiagonal((1/Δx)^2*2*ones(N_el_l)+V,-(1/Δx)^2*ones(N_el_l-1))
F = eigen(H);
tmp1 = reshape(F.vectors,(N_el_l.^2,1));
tmp2 = reshape(F.values,(N_el_l,1));
X = [tmp1
tmp2];
electron_1d = electronic_r(N_el_l,N_el_l-1,H,Diagonal(xgrid),X);
N_cav = 100;
d_cav = 1; # spatial dimension of the cavity mode, corresponds to number of vector components used to describe mode
L_cav = 18904.0; # 1 micron in atomic units
S_cav = (10.0*nm)^2; #area of cavity
emitter_pos = L_cav/2; # position where the emitter is located
freqs_cav = pi*(1:N_cav)*c/L_cav;
modes_cav = zeros(d_cav,N_cav);
for counter = 1:N_cav
modes_cav[1,counter] = sqrt(2.0/L_cav/S_cav)*sin(freqs_cav[counter]*emitter_pos/c); # for 2d or 3d, want two extra lines specifying those components
end
pt_cav = photonic(N_cav,d_cav,freqs_cav,modes_cav)
E = electron_1d;
P = pt_cav;
X0 = electron_1d.X
str = 100000;
#print("$(real(E.X[end-E.N+1:end])) \n")
In [201]:
sol_el= fixedpoint(f_el_meanfield!, X0; method = :anderson, m=0,beta=1.0,iterations=10);
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476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 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777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572] [2.23406, 6.69816, 11.1542, 15.6022, 20.042, 24.4737, 28.8973, 33.3127, 37.7199, 42.1189, 46.5096, 50.8921, 55.2663, 59.6321, 63.9896, 68.3387, 72.6794, 77.0118, 81.3356, 85.651, 89.9579, 94.2562, 98.546, 102.827, 107.1, 111.364, 115.619, 119.866, 124.103, 128.333, 132.553, 136.764, 140.967, 145.161, 149.346, 153.521, 157.688, 161.846, 165.995, 170.135, 174.266, 178.387, 182.5, 186.603, 190.697, 194.782, 198.857, 202.923, 206.98, 211.027, 215.065, 219.093, 223.112, 227.121, 231.121, 235.11, 239.091, 243.061, 247.022, 250.973, 254.914, 258.845, 262.766, 266.678, 270.579, 274.472, 278.355, 282.229, 286.097, 289.96, 293.82, 297.683, 301.552, 305.434, 309.336, 313.263, 317.221, 321.214, 325.247, 329.32, 333.435, 337.591, 341.787, 346.021, 350.291, 354.595, 358.931, 363.297, 367.69, 372.108, 376.548, 381.01, 385.49, 389.987, 394.499, 399.023, 403.559, 408.104, 412.656, 417.214, 421.777, 426.341, 430.907, 435.471, 440.033, 444.591, 449.142, 453.687, 458.223, 462.748, 467.261, 471.76, 476.245, 480.712, 485.161, 489.59, 493.998, 498.383, 502.743, 507.077, 511.382, 515.659, 519.904, 524.116, 528.294, 532.435, 536.539, 540.602, 544.624, 548.602, 552.535, 556.42, 560.255, 564.039, 567.768, 571.44, 575.053, 578.604, 582.09, 585.508, 588.853, 592.123, 595.312, 598.415, 601.426, 604.337, 607.139, 609.817, 612.365, 614.688, 617.016, 618.385, 621.221, 621.907, 625.902, 626.709, 631.295, 632.209, 637.249, 638.262, 643.704, 644.813, 650.631, 651.835, 658.018, 659.319, 665.865, 667.266, 674.177, 675.683, 682.971, 684.585, 692.265, 693.995, 702.088, 703.94, 712.476, 714.457, 723.473, 725.592, 735.136, 737.404, 747.538, 749.964, 760.77, 763.37, 774.957, 777.744, 790.263, 793.258, 806.926, 810.15, 825.303, 828.785, 845.983, 849.763, 870.098, 874.235, 900.572]
In [207]:
plot(xgrid,(sol_el.zero[1:N_el_l].^2 - X0[1:N_el_l].^2),xgrid,X0[1:N_el_l].^2/10000)
xlabel("Position along atomic potential [bohr]")
ylabel("Change in electron ground state density [*bohr^3]")
title("Change in electronic ground state densities due to coupling")
Out[207]:
PyObject Text(0.5, 1.0, 'Change in electronic ground state densities due to coupling')
Two-dimensional example¶
In [220]:
N_el_l = 50;
R = 8;
xgrid = -R:(2*R)/(N_el_l-1):R
Δx = (2*R)/(N_el_l-1);
V = 0.5*10*(xgrid).^2+0.5*(xgrid).^3+0.01*(xgrid).^4;
Tx = SymTridiagonal((1/Δx)^2*2*ones(N_el_l),-(1/Δx)^2*ones(N_el_l-1));
rsep = kron(Diagonal(xgrid),Diagonal(ones(N_el_l)))
Hsep=kron(Tx,Diagonal(ones(N_el_l)))+kron(Diagonal(ones(N_el_l)),Tx)+kron(Diagonal(V),Diagonal(ones(N_el_l)))
Hsep=sparse(Hsep)
Out[220]:
2500×2500 SparseMatrixCSC{Float64,Int64} with 12300 stored entries:
[1 , 1] = 142.476
[2 , 1] = -9.37891
[51 , 1] = -9.37891
[1 , 2] = -9.37891
[2 , 2] = 142.476
[3 , 2] = -9.37891
[52 , 2] = -9.37891
[2 , 3] = -9.37891
[3 , 3] = 142.476
[4 , 3] = -9.37891
[53 , 3] = -9.37891
[3 , 4] = -9.37891
â‹®
[2498, 2497] = -9.37891
[2448, 2498] = -9.37891
[2497, 2498] = -9.37891
[2498, 2498] = 654.476
[2499, 2498] = -9.37891
[2449, 2499] = -9.37891
[2498, 2499] = -9.37891
[2499, 2499] = 654.476
[2500, 2499] = -9.37891
[2450, 2500] = -9.37891
[2499, 2500] = -9.37891
[2500, 2500] = 654.476
In [330]:
D,V = eigs(Hsep,which=:SM,nev=10)
tmp1 = reshape(V,(N_el_l^2*10,1));
tmp2 = reshape(D,(10,1));
X0 = [tmp1
tmp2];
pcolormesh(reshape(V[:,10],(N_el_l,N_el_l)).^2,cmap="inferno",shading="gouraud")
colorbar()
Out[330]:
PyObject <matplotlib.colorbar.Colorbar object at 0x7f959586f710>
In [222]:
electron_2d = electronic_r(N_el_l^2,10,Hsep,rsep,X0)
E = electron_2d;
P = pt_cav;
X0 = electron_2d.X
str = 100000;
#print("$(real(E.X[end-E.N+1:end])) \n")
sol_el= fixedpoint(f_el_meanfield!, X0; method = :anderson, m=0,beta=1.0,iterations=20);
[2.23244, 2.33903, 2.51625, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00646, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446] [2.23243, 2.33903, 2.51624, 2.7634, 3.07956, 3.46353, 3.91385, 4.42881, 5.00645, 5.6446]
In [243]:
pcolormesh(xgrid,xgrid,reshape(sol_el.zero[1:2500],(50,50)).^2-reshape(X0[1:2500],(50,50)).^2,cmap="seismic",shading="gouraud")
colorbar()
xlabel("x")
ylabel("y")
title("Change in ground state electron density due to coupling")
Out[243]:
PyObject Text(0.5, 1.0, 'Change in ground state electron density due to coupling')
Studying the changes in the fields in the mean-field approximation¶
In [307]:
alphas=scf_photon_meanfield(electron_2d,pt_cav);
In [312]:
plot(1:100,reshape(alphas,(100,1)))
xlabel("Mode number")
ylabel("Mode coefficients")
Out[312]:
PyObject Text(24.0, 0.5, 'Mode coefficients')