Beispiel #1
0
def test_contraction():
    i, j, k, l = symbols("i,j,k,l", below_fermi=True)
    a, b, c, d = symbols("a,b,c,d", above_fermi=True)
    p, q, r, s = symbols("p,q,r,s")
    assert contraction(Fd(i), F(j)) == KroneckerDelta(i, j)
    assert contraction(F(a), Fd(b)) == KroneckerDelta(a, b)
    assert contraction(F(a), Fd(i)) == 0
    assert contraction(Fd(a), F(i)) == 0
    assert contraction(F(i), Fd(a)) == 0
    assert contraction(Fd(i), F(a)) == 0
    assert contraction(Fd(i), F(p)) == KroneckerDelta(i, p)
    restr = evaluate_deltas(contraction(Fd(p), F(q)))
    assert restr.is_only_below_fermi
    restr = evaluate_deltas(contraction(F(p), Fd(q)))
    assert restr.is_only_above_fermi
    raises(ContractionAppliesOnlyToFermions, lambda: contraction(B(a), Fd(b)))
Beispiel #2
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def test_contraction():
    i, j, k, l = symbols('i,j,k,l', below_fermi=True)
    a, b, c, d = symbols('a,b,c,d', above_fermi=True)
    p, q, r, s = symbols('p,q,r,s')
    assert contraction(Fd(i), F(j)) == KroneckerDelta(i, j)
    assert contraction(F(a), Fd(b)) == KroneckerDelta(a, b)
    assert contraction(F(a), Fd(i)) == 0
    assert contraction(Fd(a), F(i)) == 0
    assert contraction(F(i), Fd(a)) == 0
    assert contraction(Fd(i), F(a)) == 0
    assert contraction(Fd(i), F(p)) == KroneckerDelta(i, p)
    restr = evaluate_deltas(contraction(Fd(p), F(q)))
    assert restr.is_only_below_fermi
    restr = evaluate_deltas(contraction(F(p), Fd(q)))
    assert restr.is_only_above_fermi
    raises(ContractionAppliesOnlyToFermions, lambda: contraction(B(a), Fd(b)))
def test_contraction():
    i, j, k, l = symbols('i,j,k,l', below_fermi=True)
    a, b, c, d = symbols('a,b,c,d', above_fermi=True)
    p, q, r, s = symbols('p,q,r,s')
    assert contraction(Fd(i), F(j)) == KroneckerDelta(i, j)
    assert contraction(F(a), Fd(b)) == KroneckerDelta(a, b)
    assert contraction(F(a), Fd(i)) == 0
    assert contraction(Fd(a), F(i)) == 0
    assert contraction(F(i), Fd(a)) == 0
    assert contraction(Fd(i), F(a)) == 0
    assert contraction(Fd(i), F(p)) == KroneckerDelta(i, p)
    restr = evaluate_deltas(contraction(Fd(p), F(q)))
    assert restr.is_only_below_fermi
    restr = evaluate_deltas(contraction(F(p), Fd(q)))
    assert restr.is_only_above_fermi
Beispiel #4
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def test_contraction():
    i,j,k,l = symbols('ijkl',below_fermi=True)
    a,b,c,d = symbols('abcd',above_fermi=True)
    p,q,r,s = symbols('pqrs')
    assert contraction(Fd(i),F(j)) == KroneckerDelta(i,j)
    assert contraction(F(a),Fd(b)) == KroneckerDelta(a,b)
    assert contraction(F(a),Fd(i)) == 0
    assert contraction(Fd(a),F(i)) == 0
    assert contraction(F(i),Fd(a)) == 0
    assert contraction(Fd(i),F(a)) == 0
    assert contraction(Fd(i),F(p)) == KroneckerDelta(p,i)
    restr = evaluate_deltas(contraction(Fd(p),F(q)))
    assert restr.is_only_below_fermi
    restr = evaluate_deltas(contraction(F(p),Fd(q)))
    assert restr.is_only_above_fermi
Beispiel #5
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def test_contraction():
    i, j, k, l = symbols("i,j,k,l", below_fermi=True)
    a, b, c, d = symbols("a,b,c,d", above_fermi=True)
    p, q, r, s = symbols("p,q,r,s")
    assert contraction(Fd(i), F(j)) == KroneckerDelta(i, j)
    assert contraction(F(a), Fd(b)) == KroneckerDelta(a, b)
    assert contraction(F(a), Fd(i)) == 0
    assert contraction(Fd(a), F(i)) == 0
    assert contraction(F(i), Fd(a)) == 0
    assert contraction(Fd(i), F(a)) == 0
    assert contraction(Fd(i), F(p)) == KroneckerDelta(i, p)
    restr = evaluate_deltas(contraction(Fd(p), F(q)))
    assert restr.is_only_below_fermi
    restr = evaluate_deltas(contraction(F(p), Fd(q)))
    assert restr.is_only_above_fermi
Beispiel #6
0
#Link to Second quant documentation: https://docs.sympy.org/latest/modules/physics/secondquant.html

pretty_dummies_dict = {
    'above': 'abcdefgh',
    'below': 'ijklmno',
    'general': 'pqrstu'
}

p, q, r, s = symbols('p,q,r,s', cls=Dummy)

#Setup creation and annihilation operators
ap_dagger = Fd(p)
aq = F(q)
#Perform a contraction
contr = evaluate_deltas(contraction(ap_dagger, aq))
print("Example outputs")
print()
print("contraction(a_p^\dagger a_q): ", latex(contr))
print()

#Setup Hamiltonian, not on normal order form
h = AntiSymmetricTensor('h', (p, ), (q, ))
pq = ap_dagger * aq

V = AntiSymmetricTensor('V', (p, q), (r, s))
pqsr = Fd(p) * Fd(q) * F(s) * F(r)

H0 = h * pq
HI = Rational(1, 4) * V * pqsr