def hamiltonian(self) -> csc_matrix:
"""
Returns Hamiltonian in basis obtained by employing harmonic basis for
:math:`\\phi, \\zeta` and charge basis for :math:`\\theta`.
"""
phi_osc_mat = self._kron3(
op.number_sparse(self._dim_phi(), self.phi_plasma()),
self._identity_zeta(),
self._identity_theta(),
)
zeta_osc_mat = self._kron3(
self._identity_phi(),
op.number_sparse(self._dim_zeta(), self.zeta_plasma()),
self._identity_theta(),
)
cross_kinetic_mat = (
2 * self._disordered_ecj() *
(self.n_theta_operator() - self.total_identity() * self.ng -
self.n_zeta_operator())**2)
phi_flux_term = self._cos_phi_operator() * np.cos(
self.flux * np.pi) - self._sin_phi_operator() * np.sin(
self.flux * np.pi)
junction_mat = (-2 * self.EJ * self._kron3(
phi_flux_term, self._identity_zeta(), self._cos_theta_operator()) +
2 * self.EJ * self.total_identity())
disorder_l = (-2 * self._disordered_el() * self.dL *
self._kron3(self._phi_operator(), self._zeta_operator(),
self._identity_theta()))
dis_phi_flux_term = self._sin_phi_operator() * np.cos(
self.flux * np.pi) + self._cos_phi_operator() * np.sin(
self.flux * np.pi)
disorder_j = (2 * self.EJ * self.dEJ *
self._kron3(dis_phi_flux_term, self._identity_zeta(),
self._sin_theta_operator()))
dis_c_opt = (
self._kron3(self._n_phi_operator(), self._identity_zeta(),
self._n_theta_operator()) -
self.n_phi_operator() * self.ng -
self._kron3(self._n_phi_operator(), self._n_zeta_operator(),
self._identity_theta()))
disorder_c = -4 * self._disordered_ecj() * self.dCJ * dis_c_opt
return (phi_osc_mat + zeta_osc_mat + cross_kinetic_mat + junction_mat +
disorder_l + disorder_j + disorder_c)
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()