sciforge 0.0.3

A comprehensive scientific computing library in pure Rust with zero dependencies
Documentation 
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

use crate::maths::complex::Complex;

pub fn pauli_x() -> [[Complex; 2]; 2] {
    [
        [Complex::new(0.0, 0.0), Complex::new(1.0, 0.0)],
        [Complex::new(1.0, 0.0), Complex::new(0.0, 0.0)],
    ]
}

pub fn pauli_y() -> [[Complex; 2]; 2] {
    [
        [Complex::new(0.0, 0.0), Complex::new(0.0, -1.0)],
        [Complex::new(0.0, 1.0), Complex::new(0.0, 0.0)],
    ]
}

pub fn pauli_z() -> [[Complex; 2]; 2] {
    [
        [Complex::new(1.0, 0.0), Complex::new(0.0, 0.0)],
        [Complex::new(0.0, 0.0), Complex::new(-1.0, 0.0)],
    ]
}

pub fn identity_2() -> [[Complex; 2]; 2] {
    [
        [Complex::new(1.0, 0.0), Complex::new(0.0, 0.0)],
        [Complex::new(0.0, 0.0), Complex::new(1.0, 0.0)],
    ]
}

pub fn spin_up() -> [Complex; 2] {
    [Complex::new(1.0, 0.0), Complex::new(0.0, 0.0)]
}

pub fn spin_down() -> [Complex; 2] {
    [Complex::new(0.0, 0.0), Complex::new(1.0, 0.0)]
}

pub fn spin_plus_x() -> [Complex; 2] {
    let s = 1.0 / 2.0_f64.sqrt();
    [Complex::new(s, 0.0), Complex::new(s, 0.0)]
}

pub fn spin_minus_x() -> [Complex; 2] {
    let s = 1.0 / 2.0_f64.sqrt();
    [Complex::new(s, 0.0), Complex::new(-s, 0.0)]
}

pub fn spin_plus_y() -> [Complex; 2] {
    let s = 1.0 / 2.0_f64.sqrt();
    [Complex::new(s, 0.0), Complex::new(0.0, s)]
}

pub fn spin_minus_y() -> [Complex; 2] {
    let s = 1.0 / 2.0_f64.sqrt();
    [Complex::new(s, 0.0), Complex::new(0.0, -s)]
}

pub fn dirac_gamma0() -> [[Complex; 4]; 4] {
    let z = Complex::new(0.0, 0.0);
    let p = Complex::new(1.0, 0.0);
    let m = Complex::new(-1.0, 0.0);
    [[p, z, z, z], [z, p, z, z], [z, z, m, z], [z, z, z, m]]
}

pub fn dirac_gamma1() -> [[Complex; 4]; 4] {
    let z = Complex::new(0.0, 0.0);
    let p = Complex::new(1.0, 0.0);
    let m = Complex::new(-1.0, 0.0);
    [[z, z, z, p], [z, z, p, z], [z, m, z, z], [m, z, z, z]]
}

pub fn dirac_gamma2() -> [[Complex; 4]; 4] {
    let z = Complex::new(0.0, 0.0);
    let pi = Complex::new(0.0, 1.0);
    let mi = Complex::new(0.0, -1.0);
    [[z, z, z, mi], [z, z, pi, z], [z, mi, z, z], [pi, z, z, z]]
}

pub fn dirac_gamma3() -> [[Complex; 4]; 4] {
    let z = Complex::new(0.0, 0.0);
    let p = Complex::new(1.0, 0.0);
    let m = Complex::new(-1.0, 0.0);
    [[z, z, p, z], [z, z, z, m], [m, z, z, z], [z, p, z, z]]
}

pub fn gamma5() -> [[Complex; 4]; 4] {
    let z = Complex::new(0.0, 0.0);
    let p = Complex::new(1.0, 0.0);
    [[z, z, p, z], [z, z, z, p], [p, z, z, z], [z, p, z, z]]
}

pub fn rotation_operator(angle: f64, pauli: &[[Complex; 2]; 2]) -> [[Complex; 2]; 2] {
    let cos_half = (angle / 2.0).cos();
    let sin_half = (angle / 2.0).sin();
    let i = Complex::new(0.0, 1.0);
    let mut result = [[Complex::new(0.0, 0.0); 2]; 2];
    for r in 0..2 {
        for c in 0..2 {
            let id = if r == c {
                Complex::new(1.0, 0.0)
            } else {
                Complex::new(0.0, 0.0)
            };
            result[r][c] =
                id * Complex::new(cos_half, 0.0) - i * pauli[r][c] * Complex::new(sin_half, 0.0);
        }
    }
    result
}

pub fn ladder_operator_plus(j: f64) -> Vec<Vec<Complex>> {
    let dim = (2.0 * j + 1.0) as usize;
    let mut op = vec![vec![Complex::new(0.0, 0.0); dim]; dim];
    for idx in 0..dim - 1 {
        let m = -j + idx as f64;
        let val = (j * (j + 1.0) - m * (m + 1.0)).sqrt();
        op[idx + 1][idx] = Complex::new(val, 0.0);
    }
    op
}

pub fn ladder_operator_minus(j: f64) -> Vec<Vec<Complex>> {
    let dim = (2.0 * j + 1.0) as usize;
    let mut op = vec![vec![Complex::new(0.0, 0.0); dim]; dim];
    for idx in 1..dim {
        let m = -j + idx as f64;
        let val = (j * (j + 1.0) - m * (m - 1.0)).sqrt();
        op[idx - 1][idx] = Complex::new(val, 0.0);
    }
    op
}

pub fn jz_operator(j: f64) -> Vec<Vec<Complex>> {
    let dim = (2.0 * j + 1.0) as usize;
    let mut op = vec![vec![Complex::new(0.0, 0.0); dim]; dim];
    for (idx, op_row) in op.iter_mut().enumerate() {
        let m = -j + idx as f64;
        op_row[idx] = Complex::new(m, 0.0);
    }
    op
}