-
Notifications
You must be signed in to change notification settings - Fork 0
/
N_chaotic_baths.cpp
305 lines (195 loc) · 9.71 KB
/
N_chaotic_baths.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <fstream>
#include <time.h>
#include <sstream>
using namespace std;
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void Evol_Temp(int N_bath, double Lambda, int N_cond, int N_iter, ofstream &arquivo){
double r = (pow(2.0,1.0/3.0) + pow(2.0,-1.0/3.0) -1)/6.0;
double c[4] = {r + 1.0/2.0, -r, -r, r + 1.0/2.0};
double d[4] = {2.0*r + 1.0, -4.0*r - 1.0, 2.0*r + 1.0, 0.0};
double T_step = 0.01;
// system coordinates
double *Q = (double *) calloc(N_cond, sizeof(double));
double *P = (double *) calloc(N_cond, sizeof(double));
// sample coordinates
double *x1 = (double *) calloc(N_cond, sizeof(double));
double *y1 = (double *) calloc(N_cond, sizeof(double));
double *px1 = (double *) calloc(N_cond, sizeof(double));
double *py1 = (double *) calloc(N_cond, sizeof(double));
// heat bath coordinates for each mode
double **X = (double **) calloc(N_bath , sizeof(double*));
//double **X01 = (double **) calloc(N_bath , sizeof(double*));
double **Y = (double **) calloc(N_bath , sizeof(double*));
double **Px = (double **) calloc(N_bath, sizeof(double*));
double **Py = (double **) calloc(N_bath, sizeof(double*));
int i, j, h, l;
for(i = 0; i < N_bath; i++){
X[i] = (double*) calloc(N_cond, sizeof(double));
//X01[i] = (double*) calloc(N_cond, sizeof(double));
Y[i] = (double*) calloc(N_cond, sizeof(double));
Px[i] = (double*) calloc(N_cond, sizeof(double));
Py[i] = (double*) calloc(N_cond, sizeof(double));
}
// quartic parameter 'a'
double A = 0.1;
//double C_qq0;
double E_part = 0.1968*(100);
double E_bath = 0.01/(1000);
double k = 0.3;
double Quant;
double E_Test, E_Harm, Ep_aver, Eb_aver, Ei_aver;
int tau_relax = 100000;
// Sampling initial conditions for each heat bath mode.
for(i = 0; i < N_bath; i++){
//cout << i << " de " << N_cond << "\n";
j = 0;
while(j < N_cond){
double m = rand()%4;
if(m == 0){
y1[j] = (2.0*rand()/RAND_MAX - 1) / pow(A,1.0/4.0);
px1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
py1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
x1[j] = pow(-1,rand()%2) * sqrt(-y1[j]*y1[j] + sqrt(y1[j]*y1[j]*y1[j]*y1[j] - A*(2*px1[j]*px1[j] + 2*py1[j]*py1[j] + A*y1[j]*y1[j]*y1[j]*y1[j] - 4*E_bath)))/sqrt(A);
}
else if(m == 1){
x1[j] = (2.0*rand()/RAND_MAX - 1) * pow(4.0 * E_bath/A, 1.0/4.0);
px1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
py1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
y1[j] = pow(-1,rand()%2) * sqrt(-x1[j]*x1[j] + sqrt(x1[j]*x1[j]*x1[j]*x1[j] -A*(2*px1[j]*px1[j] + 2*py1[j]*py1[j] + A*x1[j]*x1[j]*x1[j]*x1[j] - 4*E_bath)))/sqrt(A);
}
else if(m == 2){
x1[j] = (2.0*rand()/RAND_MAX - 1) * pow(4.0 * E_bath/A, 1.0/4.0);
y1[j] = (2.0*rand()/RAND_MAX - 1) * pow(4.0 * E_bath/A, 1.0/4.0);
py1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
px1[j] = pow(-1,rand()%2) * sqrt(2*E_bath - A*(x1[j]*x1[j]*x1[j]*x1[j] + y1[j]*y1[j]*y1[j]*y1[j])/2 - x1[j]*x1[j]*y1[j]*y1[j] - py1[j]*py1[j]);
}
else{
x1[j] = (2.0*rand()/RAND_MAX - 1) * pow(4.0 * E_bath/A, 1.0/4.0);
y1[j] = (2.0*rand()/RAND_MAX - 1) * pow(4.0 * E_bath/A, 1.0/4.0);
px1[j] = (2.0*rand()/RAND_MAX - 1) * pow(2.0 * E_bath, 1.0/2.0);
py1[j] = pow(-1,rand()%2) * sqrt(2*E_bath - A*(x1[j]*x1[j]*x1[j]*x1[j] + y1[j]*y1[j]*y1[j]*y1[j])/2 - x1[j]*x1[j]*y1[j]*y1[j] - px1[j]*px1[j]);
}
if(!isnan(x1[j]) && !isnan(y1[j]) && !isnan(px1[j]) && !isnan(py1[j])){
X[i][j] = x1[j];
Y[i][j] = y1[j];
Px[i][j] = px1[j];
Py[i][j] = py1[j];
Q[j] = sqrt(2.0 * E_part / k) * sin(j*2.0*M_PI/N_cond);
P[j] = sqrt(2.0 * E_part) * cos(j*2.0*M_PI/N_cond);
j++;
}
}
}
// Picking up the 5th bath mode and testing whether it relaxes into chaotic behavior before coupling to the system
/* With the correlation function for the position of the bath mode it is possible to see if the bath is chaotic
(see ref: "https://iopscience.iop.org/article/10.1088/1751-8121/ab9a78/meta") */
/*for(j = 0; j < N_cond; j++){
X01[5][j] = X[5][j];
}*/
for(i = 0; i < tau_relax ; i++){
/*C_qq0 = 0.0;
for(j = 0; j < N_cond; j++){
C_qq0 += X01[5][j]*X[5][j]/N_cond;
}
arquivo << showpos << fixed << (i)*T_step << " ";
arquivo << showpos << scientific << C_qq0 << "\n" ;*/
// Updating bath coordinates of each mode until it gets chaotic
/* We use fourth-order symplectic integration to integrate Hamilton's equations. See:
"https://www.sciencedirect.com/science/article/abs/pii/016727899090019L?via%3Dihub"*/
for(j = 0; j < N_cond; j++){
for(l = 0; l < 4; l++){
for(h = 0; h < N_bath; h++){
Px[h][j] += - c[l] * T_step * (A * X[h][j]*X[h][j]*X[h][j] + X[h][j]*Y[h][j]*Y[h][j]);
Py[h][j] += - c[l] * T_step * (A * Y[h][j]*Y[h][j]*Y[h][j] + Y[h][j]*X[h][j]*X[h][j]);
}
for(h = 0; h < N_bath; h++){
X[h][j] += + d[l] * T_step * Px[h][j];
Y[h][j] += + d[l] * T_step * Py[h][j];
}
}
}
}
int temp = 0;
for(i = 0; i < N_iter ; i++){
// writting a file with energies during the system interaction with the chaotic bath
E_Test = 0.0;
E_Harm = 0.0;
Ep_aver = 0.0;
Eb_aver = 0.0;
Ei_aver = 0.0;
for(j = 0; j < N_cond; j++){
Quant = 0.0;
for(h= 0; h < N_bath; h++){
Quant += X[h][j];
Eb_aver += ((Px[h][j]*Px[h][j] + Py[h][j]*Py[h][j])/2.0 + A*(X[h][j]*X[h][j]*X[h][j]*X[h][j] + Y[h][j]*Y[h][j]*Y[h][j]*Y[h][j])/4.0 + (Y[h][j]*Y[h][j]*X[h][j]*X[h][j])/2.0)/ N_cond ;
}
E_Harm += (k * Q[j]*Q[j]/(2.0)) / N_cond;
Ep_aver += (P[j]*P[j]/(2.0)) / N_cond;
Ei_aver += (Lambda * (Quant) * Q[j]) / N_cond;
}
E_Test = (Eb_aver + Ep_aver + E_Harm + Ei_aver);
if(i == temp ){
arquivo << showpos << fixed << (i)*T_step << " ";
arquivo << showpos << scientific << E_Test << " " << E_Harm << " " << Ep_aver << " " << Eb_aver << " " << Ei_aver << "\n" ;
// ignoring some data (too heavy)
temp += 100;
}
// Interaction system-bath
for(j = 0; j < N_cond; j++){
for(int l = 0; l < 4; l++){
Quant = 0.0;
for(h= 0; h < N_bath; h++){
Quant += X[h][j];
}
P[j] += - c[l] * T_step * (Lambda * (Quant) + k * Q[j]);
for(h= 0; h < N_bath; h++){
Px[h][j] += - c[l] * T_step * (A * X[h][j]*X[h][j]*X[h][j] + X[h][j]*Y[h][j]*Y[h][j] + Lambda * Q[j]);
Py[h][j] += - c[l] * T_step * (A * Y[h][j]*Y[h][j]*Y[h][j] + Y[h][j]*X[h][j]*X[h][j]);
X[h][j] += + d[l] * T_step * Px[h][j];
Y[h][j] += + d[l] * T_step * Py[h][j];
}
// Position should be the last one to be implemented
Q[j] += + d[l] * T_step * P[j];
}
}
}
free(Q);
free(P);
free(x1);
free(y1);
free(px1);
free(py1);
free(X);
//free(X01);
free(Y);
free(Px);
free(Py);
}
////////////////////////////////////----------Main -----//////////////////////////////////////////////////////
int main(int argn, char **arg){
if(argn != 5){
cout << "\n";
cout << "Entrada Inválida!\n";
cout << "Entre com as seguintes variáveis: Número de Condições Iniciais, Número de Iterações e o parâmetro A.\n\n";
}
// Picking parameters
int N_bath = atoi(arg[1]); // number of bath modes
double Lambda = atof(arg[2]); // coupling constant
int N_cond = atoi(arg[3]); // number of initial samples of the system
int N_iter = atoi(arg[4]); // number of iterations between system and bath
double Lambda1 = Lambda/sqrt(N_bath);
double t_0 = clock();
ofstream arquivo;
arquivo.open (("Teste_" + string(arg[1]) + "_" + string(arg[2]) + "_" + string(arg[3]) + "_" + string(arg[4]) + ".txt").c_str());
Evol_Temp(N_bath, Lambda1, N_cond, N_iter, arquivo);
arquivo.close();
double T_process = (clock()-t_0)/CLOCKS_PER_SEC;
cout << "\n";
cout << "Cálculo Encerrado! ";
cout << "Tempo de Processamento [em segundos]: " << T_process;
cout << "\n\n";
return 0;
}