BMBPT Diagram

Routines and class for Bogoliubov MBPT diagrams.

class adg.bmbpt.BmbptFeynmanDiagram(nx_graph, tag_num)

Bases: adg.diag.Diagram

Describes a BMBPT Feynman diagram with its related properties.

two_or_three_body

The 2 or 3-body characted of the vertices.

Type:int

time_tag

The tag number associated to the diagram’s associated TSD.

Type:int

tsd_is_tree

The tree or non-tree character of the associated TSD.

Type:bool

feynman_exp

The Feynman expression associated to the diagram.

Type:str

diag_exp

The Goldstone expression associated to the diagram.

Type:str

vert_exp

The expression associated to the vertices.

Type:list

hf_type

The Hartree-Fock, non-Hartree-Fock or Hartree-Fock for the energy operator only character of the graph.

Type:str

attribute_expressions(time_diag)

Attribute the correct Feynman and Goldstone expressions.

Parameters:time_diag (TimeStructureDiagram) – The associated TSD.

attribute_qp_labels()

Attribute the appropriate qp labels to the graph’s propagators.

extract_integral()

Return the integral part of the Feynman expression of the diag.

Returns:The integral part of its Feynman expression. Return type:(str)

extract_numerator()

Return the numerator associated to a BMBPT graph.

Returns:The numerator of the graph. Return type:(str)

has_crossing_sign()

Return True for a minus sign associated with crossing propagators.

Use the fact that all lines propagate upwards and the canonical representation of the diagrams and vertices.

Returns:

Encode for the sign factor associated with crossing

propagators.

Return type:(bool)

multiplicity_symmetry_factor()

Return the symmetry factor associated with propagators multiplicity.

Returns:The symmetry factor associated with equivalent lines. Return type:(str)

time_tree_denominator(time_graph)

Return the denominator for a time-tree graph.

Parameters:time_graph (NetworkX MultiDiGraph) – Its associated time-structure graph. Returns:The denominator of the graph. Return type:(str)

vertex_exchange_sym_factor()

Return the symmetry factor associated with vertex exchange.

Returns:The symmetry factor for vertex exchange. Return type:(str)

vertex_expression(vertex)

Return the expression associated to a given vertex.

Parameters:vertex (int) – The vertex of interest in the graph.

write_diag_exps(latex_file, norder)

Write the expressions associated to a diagram in the LaTeX file.

Parameters:

• latex_file (file) – The LaTeX outputfile of the program.
• norder (int) – The order in BMBPT formalism.

write_graph(latex_file, directory, write_time)

Write the BMBPT graph and its associated TSD to the LaTeX file.

Parameters:

• latex_file (file) – The LaTeX output file of the program.
• directory (str) – The path to the result folder.
• write_time (bool) – True if we want informations on the associated TSDs.

write_section(result, commands, diags_nbs)

Write section and subsections for BMBPT result file.

Parameters:

• result (file) – The LaTeX output file of the program.
• commands (dict) – The flags associated with run management.
• diags_nbs (dict) – The number of diagrams per type.

write_tsd_info(diagrams_time, latex_file)

Write info related to the BMBPT associated TSD to the LaTeX file.

Parameters:

• diagrams_time (list) – The associated TSDs.
• latex_file (file) – The LaTeX output file of the program.

write_vertices_values(latex_file, mapping)

Write the qp energies associated to each vertex of the diag.

Parameters:

• latex_file (file) – The LaTeX output file of the program.
• mapping (dict) – A mapping between the vertices in the diagram and the vertices in its euivalent TSD, since permutations between vertices are possible.

adg.bmbpt.check_unconnected_spawn(matrices, max_filled_vertex, length_mat)

Exclude some matrices that would spawn unconnected diagrams.

Parameters:

• matrices (list) – The adjacency matrices to be checked.
• max_filled_vertex (int) – The furthest vertex until which the matrices have been filled.
• length_mat (int) – The size of the square matrices.

>>> mats = [[[0, 2, 0], [2, 0, 0], [0, 0, 0]],                 [[0, 2, 1], [2, 0, 1], [0, 0, 0]]]
>>>
>>> check_unconnected_spawn(mats, 1, 3)
>>> mats
[[[0, 2, 1], [2, 0, 1], [0, 0, 0]]]

adg.bmbpt.diagrams_generation(p_order, three_body_use, nbody_obs, canonical)

Generate diagrams for BMBPT from bottom up.

Parameters:

• p_order (int) – The BMBPT perturbative order of the studied diagrams.
• three_body_use (bool) – Flag for the use of three-body forces.
• nbody_obs (int) – N-body character of the obervable of interest.
• canonical (bool) – True if one draws only canonical diagrams.

Returns:

NumPy arrays encoding the adjacency matrices of the graphs.

Return type:

(list)

>>> diagrams_generation(1, False, 2, False) #doctest: +NORMALIZE_WHITESPACE
[array([[0, 4], [0, 0]]), array([[0, 2], [0, 0]])]
>>> diagrams_generation(1, True, 3, False)  #doctest: +NORMALIZE_WHITESPACE
[array([[0, 6], [0, 0]]), array([[0, 4], [0, 0]]), array([[0, 2], [0, 0]])]
>>> diagrams_generation(2, False, 2, True)  #doctest: +NORMALIZE_WHITESPACE
[array([[0, 2, 2], [0, 0, 2], [0, 0, 0]]),
 array([[0, 1, 1], [0, 0, 3], [0, 0, 0]])]

adg.bmbpt.order_diagrams(diagrams)

Order the BMBPT diagrams and return number of diags for each type.

Parameters:diagrams (list) – Possibly redundant BmbptFeynmanDiagrams. Returns:

First element is the list of topologically unique, ordered

diagrams. Second element is a dict with the number of diagrams for each major type.

Return type:(tuple)

adg.bmbpt.produce_expressions(diagrams, diagrams_time)

Produce and store the expressions associated to the BMBPT diagrams.

Parameters:

• diagrams (list) – The list of all BmbptFeynmanDiagrams.
• diagrams_time (list) – Their associates TSDs.

adg.bmbpt.write_header(tex_file, commands, diags_nbs)

Write overall header for BMBPT result file.

Parameters:

• tex_file (file) – The ouput LaTeX file of the program.
• commands (Namespace) – Flags for the program run.
• diags_nbs (dict) – The number of diagrams per type.