BMBPT Diagram¶
Routines and class for Bogoliubov MBPT diagrams.

class
adg.bmbpt.
BmbptFeynmanDiagram
(nx_graph, tag_num)[source]¶ Bases:
adg.diag.Diagram
Describes a BMBPT Feynman diagram with its related properties.

two_or_three_body
¶ The 2 or 3body 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 nontree 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 HartreeFock, nonHartreeFock or HartreeFock for the energy operator only character of the graph.
Type: str

attribute_expressions
(time_diag)[source]¶ Attribute the correct Feynman and Goldstone expressions.
Parameters: time_diag (TimeStructureDiagram) – The associated TSD.

extract_integral
()[source]¶ Return the integral part of the Feynman expression of the diag.
Returns: The integral part of its Feynman expression. Return type: (str)

extract_numerator
()[source]¶ Return the numerator associated to a BMBPT graph.
Returns: The numerator of the graph. Return type: (str)

has_crossing_sign
()[source]¶ 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
()[source]¶ Return the symmetry factor associated with propagators multiplicity.
Returns: The symmetry factor associated with equivalent lines. Return type: (str)

time_tree_denominator
(time_graph)[source]¶ Return the denominator for a timetree graph.
Parameters: time_graph (NetworkX MultiDiGraph) – Its associated timestructure graph. Returns: The denominator of the graph. Return type: (str)

vertex_exchange_sym_factor
()[source]¶ Return the symmetry factor associated with vertex exchange.
Returns: The symmetry factor for vertex exchange. Return type: (str)

vertex_expression
(vertex)[source]¶ Return the expression associated to a given vertex.
Parameters: vertex (int) – The vertex of interest in the graph.

write_diag_exps
(latex_file, norder)[source]¶ 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)[source]¶ 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)[source]¶ 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)[source]¶ 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)[source]¶ 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)[source]¶ 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)[source]¶ 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 threebody forces.
 nbody_obs (int) – Nbody 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)[source]¶ 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)