Bosonic statistics second quantization#1
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Following WFR implementations in a wrapper way for bosonic commutations relations
Separating the context in files. Added bosonic symbolic algebra functions. Added a loader file to ensure SecondQuantization context loads properly.
Context was seperated in different files
States.m: Adding label to states for circuit display. PhaseSpaceRepresentations.m: Adding symbolic Wigner and HusimiQ.
Closed form for some cases where the bosonic algebra closes
Improvement in FieldVariables for handling different formal symbol variables (not limited to same label). Ease of use of the infinity parameter for DisplacementOperator, both signatures use different ordering as default. In BosonicAlgebra.m added BosonicVEV for vacuum expectation values, and BosonicMatrixElement for the m,n element of Displacement and Squeeze operators.
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Refactor
SecondQuantizationmodule + add bosonic symbolic algebra toolsSummary
SecondQuantization.m(511 lines) into six focused sub-modules underKernel/SecondQuantization/, improving maintainability and making individual components easier to load, test, and extend.BosonicNormalOrder,BosonicBCHTerms,BosonicZassenhausTerms,BosonicBCHExact,BosonicRelations,BosonVEV, andBosonicMatrixElement— all exported from theSecondQuantizationcontext.BosonicNormalOrder.nb,BosonicBCH_Zassenhaus.nb) demonstrating the new tools.Module split
The old
SecondQuantization.mis replaced by:Utils.m$FockSize,SetFockSpaceSize,FieldVariables,OrderVariables,G1Correlation,G2CoherenceStates.mFockState,CoherentState,ThermalState,CatStateOperators.mAnnihilationOperator,DisplacementOperator,SqueezeOperator,QuadratureOperators,BeamSplitterOperator,PhaseShiftOperatorPhaseSpaceRepresentations.mWignerRepresentation,HusimiQRepresentation,WignerFunction,HusimiQFunctionBlasiakFormula.mBlasiakNormalOrder/MultiModeBlasiakOrderengineBosonicAlgebra.mNew symbolic algebra API
BosonicRelations[vars]— constructs the canonical bosonic commutation relations for a given list of mode operators.BosonicNormalOrder[expr, vars]— brings an operator expression into normal order; supportsMethod -> "GrobnerBasis"(default, viaNonCommutativePolynomialReduce) orMethod -> "Blasiak"(Blasiak combinatorial engine for pure bosonic polynomial moments), and"Scalars" -> syms.BosonicBCHTerms[X, Y, n]/BosonicZassenhausTerms[X, Y, n]— BCH / Zassenhaus expansions tonth term reduced with bosonic algebra.BosonicBCHExact[X, Y]— closed-form exact BCH cases for exponentials.BosonVEV[expr, vars]/BosonicMatrixElement[{m, n}, op]— vacuum expectation values and Fock matrix elements.Notes