def _n_zeta_operator(self) -> csc_matrix:
"""
Returns
-------
`n_\zeta` operator in the harmonic oscillator basis"""
dimension = self._dim_zeta()
return (1j * (op.creation_sparse(dimension) -
op.annihilation_sparse(dimension)) /
(self.zeta_osc() * math.sqrt(2)))
def _zeta_operator(self) -> csc_matrix:
"""
Returns
-------
`zeta` operator in the harmonic oscillator basis"""
dimension = self._dim_zeta()
return ((op.creation_sparse(dimension) +
op.annihilation_sparse(dimension)) * self.zeta_osc() /
math.sqrt(2))
def hamiltonian(
self,
return_parts: bool = False
) -> Union[csc_matrix, Tuple[csc_matrix, ndarray, ndarray, float]]:
"""Returns Hamiltonian in basis obtained by discretizing phi, employing charge basis for theta, and Fock
basis for zeta.
Parameters
----------
return_parts:
If set to true, `hamiltonian` returns [hamiltonian, evals, evecs, g_coupling_matrix]
"""
zeropi_dim = self.zeropi_cutoff
zeropi_evals, zeropi_evecs = self._zeropi.eigensys(
evals_count=zeropi_dim)
zeropi_diag_hamiltonian = sparse.dia_matrix((zeropi_dim, zeropi_dim),
dtype=np.complex_)
zeropi_diag_hamiltonian.setdiag(zeropi_evals)
zeta_dim = self.zeta_cutoff
prefactor = self.E_zeta
zeta_diag_hamiltonian = op.number_sparse(zeta_dim, prefactor)
hamiltonian_mat = sparse.kron(
zeropi_diag_hamiltonian,
sparse.identity(zeta_dim, format="dia", dtype=np.complex_),
)
hamiltonian_mat += sparse.kron(
sparse.identity(zeropi_dim, format="dia", dtype=np.complex_),
zeta_diag_hamiltonian,
)
gmat = self.g_coupling_matrix(zeropi_evecs)
zeropi_coupling = sparse.dia_matrix((zeropi_dim, zeropi_dim),
dtype=np.complex_)
for l1 in range(zeropi_dim):
for l2 in range(zeropi_dim):
zeropi_coupling += gmat[l1, l2] * op.hubbard_sparse(
l1, l2, zeropi_dim)
hamiltonian_mat += sparse.kron(
zeropi_coupling, op.annihilation_sparse(zeta_dim)) + sparse.kron(
zeropi_coupling.conjugate().T, op.creation_sparse(zeta_dim))
if return_parts:
return (hamiltonian_mat.tocsc(), zeropi_evals, zeropi_evecs, gmat)
return hamiltonian_mat.tocsc()
def hamiltonian(self, return_parts=False):
"""Returns Hamiltonian in basis obtained by discretizing phi, employing charge basis for theta, and Fock
basis for zeta.
Parameters
----------
return_parts: bool, optional
If set to true, `hamiltonian` returns [hamiltonian, evals, evecs, g_coupling_matrix]
Returns
-------
scipy.sparse.csc_matrix or list
"""
zeropi_dim = self.zeropi_cutoff
zeropi_evals, zeropi_evecs = self._zeropi.eigensys(
evals_count=zeropi_dim)
zeropi_diag_hamiltonian = sparse.dia_matrix((zeropi_dim, zeropi_dim),
dtype=np.complex_)
zeropi_diag_hamiltonian.setdiag(zeropi_evals)
zeta_dim = self.zeta_cutoff
prefactor = self.omega_zeta()
zeta_diag_hamiltonian = op.number_sparse(zeta_dim, prefactor)
hamiltonian_mat = sparse.kron(
zeropi_diag_hamiltonian,
sparse.identity(zeta_dim, format='dia', dtype=np.complex_))
hamiltonian_mat += sparse.kron(
sparse.identity(zeropi_dim, format='dia', dtype=np.complex_),
zeta_diag_hamiltonian)
gmat = self.g_coupling_matrix(zeropi_evecs)
zeropi_coupling = sparse.dia_matrix((zeropi_dim, zeropi_dim),
dtype=np.complex_)
for l1 in range(zeropi_dim):
for l2 in range(zeropi_dim):
zeropi_coupling += gmat[l1, l2] * op.hubbard_sparse(
l1, l2, zeropi_dim)
hamiltonian_mat += sparse.kron(
zeropi_coupling,
op.annihilation_sparse(zeta_dim) + op.creation_sparse(zeta_dim))
if return_parts:
return [hamiltonian_mat.tocsc(), zeropi_evals, zeropi_evecs, gmat]
return hamiltonian_mat.tocsc()