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Resurgent Theta-functions: A Conjectures Gateway into Dimension D>1 Quantum Mechanics

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Voros, André

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Resurgent Theta-functions: A Conjectures Gateway into Dimension D>1 Quantum Mechanics
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Resurgent Theta-functions: a conjectured gateway into dimension D superior at 1 quantum mechanics Resurgent analysis of the stationary Schrödinger equation (exact-WKB method) has remained exclusivelyconfined to 1D systems due to its underlying linear-ODE techniques.Here, building on a solvable 2D case (a Selberg trace formula, as analyzed with P. CARTIER), and on a Balian-Bloch abstract quantum framework in any dimension using complex orbits, we isolate a very special generalized-heat-trace function as best candidate to start some resurgent description of quantum mechanics in general dimension. The latter statement is still quite embryonic and speculative - our main hope is to encourage future research.
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Thermal expansionOperator (mathematics)HomomorphismusSinguläres IntegralFunction (mathematics)QuantumSpectrum (functional analysis)SurfaceAsymptoteParameter (computer programming)Hamiltonian (quantum mechanics)Borel-MengeAnalytic setMany-sorted logicCorrespondence (mathematics)Nichtlineares GleichungssystemMathematical singularityEigenvalues and eigenvectorsFunktionalgleichungOrdinary differential equationMathematicsNumerical analysisQuantum mechanicsRiemann surfaceOscillationTransformation (genetics)Descriptive statisticsFunction (mathematics)Mathematical singularityAsymptotic analysisModulformDimensional analysisIntegerInfinityFlow separationPartial differential equationLimit (category theory)Complex (psychology)Power (physics)TheoryQuantumResultantTerm (mathematics)TheoremThermal expansionLogical constantNichtlineares GleichungssystemFormal power seriesParameter (computer programming)PropagatorSpectrum (functional analysis)Vector potentialObservational studyFocus (optics)Correspondence (mathematics)RadiusClassical physicsSymmetric functionMultiplication signInverse elementSpacetimePosition operatorSolid geometryINTEGRALComputer animation
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Operator (mathematics)Time domainComplex (psychology)Mathematical analysisMathematical singularityWell-formed formulaPoisson processBloch waveWKB-MethodeSaddle pointINTEGRALQuantumManifoldNichtlineares GleichungssystemMathematical analysisDifferential equationComplex analysisOrdinary differential equationManifoldQuantum mechanicsNetwork topologyFunction (mathematics)Mathematical singularityTime domainINTEGRALPhase transitionWell-formed formulaDimensional analysisInfinityLine (geometry)Planck constantResultantTable (information)WKB-MethodeAreaNichtlineares GleichungssystemReal numberSaddle pointOperator (mathematics)Point (geometry)Arithmetic progressionMany-sorted logicSurfaceBlock (periodic table)Archaeological field surveyComputer programmingExponentiationEqualiser (mathematics)Complex numberLecture/Conference
12:41
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Well-formed formulaFunction (mathematics)Spectrum (functional analysis)Geometric quantizationTerm (mathematics)Fermat's Last TheoremPoisson processSummierbarkeitBorel-MengeMathematical singularityPole (complex analysis)Algebraic structureMathematical analysisHolomorphic functionQuantum mechanicsTransformation (genetics)Function (mathematics)Mathematical singularityCubePositional notationAsymptotic analysisModulformPerturbation theoryVariable (mathematics)Well-formed formulaPower seriesSeries (mathematics)Plane (geometry)Power (physics)LogarithmMereologyPotenz <Mathematik>ResultantTerm (mathematics)ThetafunktionReal numberOrbitSpectrum (functional analysis)Presentation of a groupResidual (numerical analysis)Heaviside step functionDistribution (mathematics)SummierbarkeitFilm editingDivergenceCoefficient of determinationBlock (periodic table)Pole (complex analysis)Multiplication signRight angleGroup representationWeightComputer animation
25:29
Borel-MengeFunction (mathematics)Well-formed formulaPoisson processSummierbarkeitGeometric quantizationTerm (mathematics)Fermat's Last TheoremMassSpectrum (functional analysis)Mathematical singularityEnergy levelConstraint (mathematics)Geometric quantizationGroup actionPhysicalismTraverse (surveying)TrajectoryOrbitFood energyCondition numberClassical physicsTransformation (genetics)Function (mathematics)INTEGRALWell-formed formulaState of matterReal numberOperator (mathematics)Parameter (computer programming)Spectrum (functional analysis)SummierbarkeitComputer animation
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Spectrum (functional analysis)EllipseSign (mathematics)ManifoldRiemannian geometryCompact spacePoisson processRelation <Mathematik>Laplace-OperatorOperator (mathematics)Mathematical singularityFrequencyDistribution (mathematics)ModulformGeodesicMereologyAlgebraic structureDifferential equationDifferential operatorEigenvalues and eigenvectorsPseudodifferentialoperatorRational numberTransformation (genetics)Function (mathematics)Mathematical singularityFrequencyCategory of beingTime domainDimensional analysisIntegerDoubling the cubeDifferential (mechanical device)Series (mathematics)Plane (geometry)Grothendieck topologySphereLaplace-OperatorPower (physics)Moment (mathematics)MultiplicationTheoryPotenz <Mathematik>ResultantTerm (mathematics)ThetafunktionThermal expansionEllipseReal numberSimilarity (geometry)Operator (mathematics)OrbitPropagatorSpectrum (functional analysis)RootResidual (numerical analysis)Musical ensembleGamma functionDistribution (mathematics)SummierbarkeitPoint (geometry)CoefficientEqualiser (mathematics)Process (computing)Film editingCharacteristic polynomialClosed setPole (complex analysis)LengthRule of inferenceStandard deviationRight angleWeyl, HermannAsymptotic analysisMeromorphe FunktionConnected spaceComplete metric spaceBoltzmann constantLecture/Conference
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Operator (mathematics)Spectrum (functional analysis)Well-formed formulaHyperbolischer RaumCompact spaceSurfaceAlgebraic structureOscillationMeromorphe FunktionGeometric quantizationFrequencyComplex (psychology)Mathematical singularityLaplace-OperatorLogical constantCurvatureNegative numberHarmonic analysisDifferential equationHolomorphic functionMathematicsTheory of relativityTransformation (genetics)Descriptive statisticsFunction (mathematics)Mathematical singularityPositional notationFrequencyShift operatorAsymptotic analysisPerturbation theoryInvariant (mathematics)Variable (mathematics)Well-formed formulaIntegerComputabilityEnergy levelAnalytic continuationAxiom of choiceBijectionSeries (mathematics)Connected spaceGeodesicHyperbolischer RaumSphereLaplace-OperatorPower (physics)MereologyNormal-form gameTheoryPoisson processPotenz <Mathematik>QuantumTerm (mathematics)ThetafunktionPolarization (waves)Thermal expansionFormal power seriesOrbitSpectrum (functional analysis)RootGamma functionSquare numberSummierbarkeitMany-sorted logicCoefficientFilm editingSurfaceSign (mathematics)Different (Kate Ryan album)Object (grammar)Pole (complex analysis)LengthSymmetric functionDiagramDimensional analysisFinitismusLine (geometry)Group actionSampling (statistics)Inverse functionGaussian curvatureGoodness of fitReal numberDivisorMusical ensembleTowerCorrespondence (mathematics)Numerical digitLecture/Conference
52:35
FrequencyComplex (psychology)OrbitOrder (biology)Series (mathematics)QuantumCue sportsHarmonic analysisOscillationHyperbolischer RaumLaplace-OperatorGroup representationGroup actionTrajectoryFood energyClassical physicsMathematical singularityTime domainSpectrum (functional analysis)INTEGRALNichtlineares GleichungssystemSign (mathematics)Algebraic structureDiagramDifferential equationNatural numberQuantum mechanicsTheory of relativityTransformation (genetics)Mathematical singularityFrequencyTime domainWell-formed formulaSeries (mathematics)Plane (geometry)GeodesicLine (geometry)Harmonic oscillatorComplex (psychology)SphereExtension (kinesiology)Planck constantQuantumResultantTerm (mathematics)Logical constantOrbitCurvatureSpectrum (functional analysis)SummierbarkeitComplex numberSign (mathematics)Imaginary numberBlock (periodic table)Pole (complex analysis)Multiplication signGeschlossene MannigfaltigkeitGroup representationPhysicistNetwork topologyFlow separationAnalytic continuationBoiling pointSineThetafunktionPoint (geometry)Cartesian coordinate systemDirection (geometry)Film editingSurfaceCue sportsPosition operatorDiagram
57:25
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