kwant.operator.Density

class kwant.operator.Density(syst, onsite=1, where=None, check_hermiticity=True, *, sum=False)

Bases: _LocalOperator

An operator for calculating general densities.

An instance of this class can be called like a function to evaluate the expectation value with a wavefunction. See __call__ for details.

Parameters:

• syst (System) –

• onsite (scalar or square matrix or dict or callable) – The onsite matrix that defines the operator. If a dict is given, it maps from site families to square matrices. If a function is given it must take the same arguments as the onsite Hamiltonian functions of the system.

• where (sequence of int or Site, or callable, optional) – Where to evaluate the operator. If syst is not a finalized Builder, then this should be a sequence of integers. If a function is provided, it should take a single int or Site (if syst is a finalized builder) and return True or False. If not provided, the operator will be calculated over all sites in the system.

• check_hermiticity (bool) – Check whether the provided onsite is Hermitian. If it is not Hermitian, then an error will be raised when the operator is evaluated.

• sum (bool, default: False) – If True, then calling this operator will return a single scalar, otherwise a vector will be returned (see __call__ for details).

Notes

In general, if there is a certain “density” (e.g. charge or spin) that is represented by a square matrix \(M_i\) associated with each site \(i\) then an instance of this class represents the tensor \(Q_{iαβ}\) which is equal to \(M_i\) when α and β are orbitals on site \(i\), and zero otherwise.

Methods

act(self, ket, args=(), *, params=None)

Act with the operator on a wavefunction.

For an operator \(Q_{iαβ}\) and ket \(ψ_β\) this computes \(∑_{iβ} Q_{iαβ} ψ_β\).

Parameters:

• ket (sequence of complex) – Wavefunctions defined over all the orbitals of the system.

• args (tuple) – The extra arguments to the Hamiltonian value functions and the operator onsite function. Deprecated in favor of ‘params’ (and mutually exclusive with it).

• params (dict, optional) – Dictionary of parameter names and their values. Mutually exclusive with ‘args’.

Return type:

Array of complex.

bind(self, args=(), *, params=None)

Bind the given arguments to this operator.

Returns a copy of this operator that does not need to be passed extra arguments when subsequently called or when using the act method.

Providing positional arguments via ‘args’ is deprecated, instead provide named parameters as a dictionary via ‘params’.

tocoo(self, args=(), *, params=None)

Convert the operator to coordinate format sparse matrix.

Providing positional arguments via ‘args’ is deprecated, instead provide named parameters as a dictionary via ‘params’.

__call__()

Return the matrix elements of the operator.

An operator A can be called like

>>> A(psi)

to compute the expectation value \(\bra{ψ} A \ket{ψ}\), or like

>>> A(phi, psi)

to compute the matrix element \(\bra{φ} A \ket{ψ}\).

If sum=True was provided when constructing the operator, then a scalar is returned. If sum=False, then a vector is returned. The vector is defined over the sites of the system if the operator is a Density, or over the hoppings if it is a Current or Source. By default, the returned vector is ordered in the same way as the sites (for Density) or hoppings in the graph of the system (for Current or Density). If the keyword parameter where was provided when constructing the operator, then the returned vector is instead defined only over the sites or hoppings specified, and is ordered in the same way as where.

Alternatively stated, for an operator \(Q_{iαβ}\), bra \(φ_α\) and ket \(ψ_β\) this computes \(q_i = ∑_{αβ} φ^*_α Q_{iαβ} ψ_β\) if self.sum is False, otherwise computes \(q = ∑_{iαβ} φ^*_α Q_{iαβ} ψ_β\). where \(i\) runs over all sites or hoppings, and \(α\) and \(β\) run over all the degrees of freedom.

Parameters:

• bra (sequence of complex) – Must have the same length as the number of orbitals in the system. If only one is provided, both bra and ket are taken as equal.

• ket (sequence of complex) – Must have the same length as the number of orbitals in the system. If only one is provided, both bra and ket are taken as equal.

• args (tuple, optional) – The arguments to pass to the system. Used to evaluate the onsite elements and, possibly, the system Hamiltonian. Deprecated in favor of ‘params’ (and mutually exclusive with it).

• params (dict, optional) – Dictionary of parameter names and their values. Mutually exclusive with ‘args’.

Returns:

• float if check_hermiticity is True, and ket is None,

• otherwise complex. If this operator was created with sum=True,

• then a single value is returned, otherwise an array is returned.

Attributes

check_hermiticity

onsite

sum

syst

where