EigenmodePhonon¶
-
class
sisl.physics.
EigenmodePhonon
(state, c, parent=None, **info)[source]¶ Bases:
sisl.physics.phonon.ModeCPhonon
Eigenmodes of phonons with eigenvectors and eigenvalues.
This holds routines that enable the calculation of (projected) density of states.
Attributes
__doc__
__module__
__slots__
The data-type of the state (in str)
Data-type for the state
Eigenmode values in units of \(\hbar \omega\) [eV]
Eigenmodes (states)
Returns the shape of the state
Methods
DOS
(E[, distribution])Calculate DOS for provided energies, E.
PDOS
(E[, distribution])Calculate PDOS for provided energies, E.
__delattr__
Implement delattr(self, name).
__dir__
Default dir() implementation.
__eq__
Return self==value.
__format__
Default object formatter.
__ge__
Return self>=value.
__getattribute__
Return getattr(self, name).
__getitem__
(key)Return a new state with only one associated state
__gt__
Return self>value.
__hash__
Return hash(self).
__init__
(state, c[, parent])Define a state container with a given set of states and coefficients for the states
__init_subclass__
This method is called when a class is subclassed.
__iter__
([asarray])An iterator looping over the states in this system
__le__
Return self<=value.
__len__
()Number of states
__lt__
Return self<value.
__ne__
Return self!=value.
__new__
Create and return a new object.
__reduce__
Helper for pickle.
__reduce_ex__
Helper for pickle.
__repr__
Return repr(self).
__setattr__
Implement setattr(self, name, value).
__sizeof__
Size of object in memory, in bytes.
__str__
()The string representation of this object
__subclasshook__
Abstract classes can override this to customize issubclass().
_sanitize_index
(idx)Ensure indices are transferred to acceptable integers
align_norm
(other[, ret_index])Align other.state with the site-norms for this state, a copy of other is returned with re-ordered states
align_phase
(other[, copy])Align other.state with the phases for this state, a copy of other is returned with rotated elements
asState
()change_gauge
(gauge)In-place change of the gauge of the mode coefficients
copy
()Return a copy (only the coefficients and states are copied),
parent
andinfo
are passed by referencedegenerate
(eps)Find degenerate coefficients with a specified precision
Calculate displacements for the modes
inner
([right, diagonal, align])Return the inner product as \(\mathbf M_{ij} = \langle\psi_i|\psi'_j\rangle\)
iter
([asarray])An iterator looping over the states in this system
norm
()Return a vector with the Euclidean norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
norm2
([sum])Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)
Return a normalized state where each state has \(|\psi|^2=1\)
occupation
([distribution])Calculate the occupations for the states according to a distribution function
outer
([idx])Return the outer product for the indices idx (or all if
None
) by \(\sum_i|\psi_i\rangle c_i\langle\psi_i|\)phase
([method, return_indices])Calculate the Euler angle (phase) for the elements of the state, in the range \(]-\pi;\pi]\)
rotate
([phi, individual])Rotate all states (in-place) to rotate the largest component to be along the angle phi
sort
([ascending])Sort and return a new
StateC
by sorting the coefficients (default to ascending)sub
(idx)Return a new state with only the specified states
velocity
([eps])Calculate velocity for the modes
-
DOS
(E, distribution='gaussian')[source]¶ Calculate DOS for provided energies, E.
This routine calls
sisl.physics.phonon.DOS
with appropriate arguments and returns the DOS.See
DOS
for argument details.
-
PDOS
(E, distribution='gaussian')[source]¶ Calculate PDOS for provided energies, E.
This routine calls
PDOS
with appropriate arguments and returns the PDOS.See
PDOS
for argument details.
-
align_norm
(other, ret_index=False)¶ Align other.state with the site-norms for this state, a copy of other is returned with re-ordered states
To determine the new ordering of other we first calculate the residual norm of the site-norms.
\[\delta N_{\alpha\beta} = \sum_i \big(\langle \psi^\alpha_i | \psi^\alpha_i\rangle - \langle \psi^\beta_i | \psi^\beta_i\rangle\big)^2\]where \(\alpha\) and \(\beta\) correspond to state indices in self and other, respectively. The new states (from other) returned is then ordered such that the index \(\alpha \equiv \beta'\) where \(\delta N_{\alpha\beta}\) is smallest.
- Parameters
- Returns
other_swap (State) – A swapped instance of other
index (array of int) – the indices that swaps other to be
other_swap
, i.e.other_swap = other.sub(index)
Notes
The input state and output state have the same states, but their ordering is not necessarily the same.
See also
align_phase
rotate states such that their phases align
-
align_phase
(other, copy=False)¶ Align other.state with the phases for this state, a copy of other is returned with rotated elements
States will be rotated by \(\pi\) provided the phase difference between the states are above \(|\Delta\theta| > \pi/2\).
- Parameters
See also
align_norm
re-order states such that site-norms have a smaller residual
-
asCoefficient
()¶
-
asState
()¶
-
c
¶
-
change_gauge
(gauge)¶ In-place change of the gauge of the mode coefficients
The two gauges are related through:
\[\tilde C_j = e^{i\mathbf k\mathbf r_j} C_j\]where \(C_j\) belongs to the gauge
R
and \(\tilde C_j\) is in the gauger
.- Parameters
gauge ({'R', 'r'}) – specify the new gauge for the mode coefficients
-
copy
()¶ Return a copy (only the coefficients and states are copied),
parent
andinfo
are passed by reference
-
degenerate
(eps)¶ Find degenerate coefficients with a specified precision
- Parameters
eps (float) – the precision above which coefficients are not considered degenerate
- Returns
a list of indices
- Return type
list of numpy.ndarray
-
displacement
()[source]¶ Calculate displacements for the modes
This routine calls displacements with appropriate arguments and returns the real space displacements for the modes.
Note that the coefficients associated with the
ModeCPhonon
must correspond to the frequencies of the modes.See
displacement
for details.
-
property
dkind
¶ The data-type of the state (in str)
-
property
dtype
¶ Data-type for the state
-
property
hw
¶ Eigenmode values in units of \(\hbar \omega\) [eV]
-
info
¶
-
inner
(right=None, diagonal=True, align=False)¶ Return the inner product as \(\mathbf M_{ij} = \langle\psi_i|\psi'_j\rangle\)
- Parameters
right (State, optional) – the right object to calculate the inner product with, if not passed it will do the inner product with itself. This object will always be the left \(\langle\psi_i|\)
diagonal (bool, optional) – only return the diagonal matrix \(\mathbf M_{ii}\).
align (bool, optional) – first align right with the angles for this state (see align)
Notes
This does not take into account a possible overlap matrix when non-orthogonal basis sets are used.
- Returns
a matrix with the sum of inner state products
- Return type
-
iter
(asarray=False)¶ An iterator looping over the states in this system
- Parameters
asarray (bool, optional) – if true the yielded values are the state vectors, i.e. a numpy array. Otherwise an equivalent object is yielded.
- Yields
state (State) – a state only containing individual elements, if asarray is false
state (numpy.ndarray) – a state only containing individual elements, if asarray is true
-
property
mode
¶ Eigenmodes (states)
-
norm
()¶ Return a vector with the Euclidean norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
- Returns
the Euclidean norm for each state
- Return type
-
norm2
(sum=True)¶ Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)
- Parameters
sum (bool, optional) – for true only a single number per state will be returned, otherwise the norm per basis element will be returned.
- Returns
the squared norm for each state
- Return type
-
normalize
()¶ Return a normalized state where each state has \(|\psi|^2=1\)
This is roughly equivalent to:
>>> state = StateC(np.arange(10), 1) >>> n = state.norm() >>> norm_state = StateC(state.state / n.reshape(-1, 1), state.c.copy()) >>> norm_state.c[0] == 1
- Returns
a new state with all states normalized, otherwise equal to this
- Return type
-
occupation
(distribution='bose_einstein')[source]¶ Calculate the occupations for the states according to a distribution function
- Parameters
distribution (str or func, optional) – distribution used to find occupations
- Returns
len(self)
with occupation values- Return type
-
outer
(idx=None)¶ Return the outer product for the indices idx (or all if
None
) by \(\sum_i|\psi_i\rangle c_i\langle\psi_i|\)- Parameters
idx (int or array_like, optional) – only perform an outer product of the specified indices, otherwise all states are used
- Returns
a matrix with the sum of outer state products
- Return type
-
parent
¶
-
phase
(method='max', return_indices=False)¶ Calculate the Euler angle (phase) for the elements of the state, in the range \(]-\pi;\pi]\)
- Parameters
method ({'max', 'all'}) – for max, the phase for the element which has the largest absolute magnitude is returned, for all, all phases are calculated
return_indices (bool, optional) – return indices for the elements used when
method=='max'
-
rotate
(phi=0.0, individual=False)¶ Rotate all states (in-place) to rotate the largest component to be along the angle phi
The states will be rotated according to:
\[S' = S / S^\dagger_{\phi-\mathrm{max}} \exp (i \phi),\]where \(S^\dagger_{\phi-\mathrm{max}}\) is the phase of the component with the largest amplitude and \(\phi\) is the angle to align on.
-
property
shape
¶ Returns the shape of the state
-
sort
(ascending=True)¶ Sort and return a new
StateC
by sorting the coefficients (default to ascending)- Parameters
ascending (bool, optional) – sort the contained elements ascending, else they will be sorted descending
-
state
¶
-
sub
(idx)¶ Return a new state with only the specified states
-
velocity
(eps=1e-07)¶ Calculate velocity for the modes
This routine calls
velocity
with appropriate arguments and returns the velocity for the modes.Note that the coefficients associated with the
ModeCPhonon
must correspond to the energies of the modes.See
velocity
for details.Notes
The eigenvectors for the modes may have changed after calling this routine. This is because of the velocity un-folding for degenerate modes. I.e. calling
displacement
and/orPDOS
after this method may change the result.- Parameters
eps (float, optional) – precision used to find degenerate modes.
-