物理和化学中的随机过程（第3版）

物理和化学中的随机过程（第3版）

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作者: [荷兰] 范卡梅伦著

出版社: 世界图书出版公司

出版时间: 2010-04

版次: 1

ISBN: 9787510005695

定价: 59.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 463页

正文语种: 英语

分类: 自然科学

1 张插图图片

40人买过

　　Definition、Averages、Multivariatedistributions、Additionofstochasticvariables、Transformationofvariables、TheGaussiandistribution、Thecentrallimittheorem、Definition、ThePoissondistribution、Alternativedescriptionofrandomevents、Theinverseformula、Thecorrelationfunctions、Waitingtimes、Factorialcorrelationfunctions等等。 PREFACETOTHEFIRSTEDITION
PREFACETOTHESECONDEDITION
ABBREVIATEDREFERENCES
PREFACETOTHETHIRDEDITION
1.STOCHASTICVARIABLES
1.Definition
2.Averages
3.Multivariatedistributions
4.Additionofstochasticvariables
5.Transformationofvariables
6.TheGaussiandistribution
7.Thecentrallimittheorem

Ⅱ.RANDOMEVENTS
1.Definition
2.ThePoissondistribution
3.Alternativedescriptionofrandomevents
4.Theinverseformula
5.Thecorrelationfunctions
6.Waitingtimes
7.Factorialcorrelationfunctions

Ⅲ.STOCHASTICPROCESSES
1.Definition
2.Stochasticprocessesinphysics
3.Fouriertransformationofstationaryprocesses.
4.Thehierarchyofdistributionfunctions
5.Thevibratingstringandrandomfields
6.Branchingprocesses

Ⅳ.MARKOVPROCESSES
1.TheMarkovproperty
2.TheChapman-Kolmogorovequation
3.StationaryMarkovprocesses
4.Theextractionofasubensemble
5.Markovchains
6.Thedecayprocess

Ⅴ.THEMASTEREQUATION
1.Derivation
2.TheclassofW-matrices
3.Thelong-timelimit
4.Closed，isolated，physicalsystems
5.Theincreaseofentropy
6.Proofofdetailedbalance
7.Expansionineigenfunctions
8.Themacroscopicequation
9.Theadjointequation
10.Otherequationsrelatedtothemasterequation

Ⅵ.ONE-STEPPROCESSES
1.Definition;thePoissonprocess
2.Randomwalkwithcontinuoustime
3.Generalpropertiesofone-stepprocesses
4.Examplesoflinearone-stepprocesses
5.Naturalboundaries
6.Solutionoflinearone-stepprocesseswithnaturalboundaries
7.Artificialboundaries
8.Artificialboundariesandnormalmodes
9.Nonlinearone-stepprocesses

Ⅶ.CHEMICALREACTIONS
1.Kinematicsofchemicalreactions
2.Dynamicsofchemicalreactions.
3.Thestationarysolution
4.Opensystems
5.Unimolecularreactions
6.Collectivesystems
7.CompositeMarkovprocesses

Ⅷ.THEFOKKER-PLANCKEQUATION
1.Introduction
2.DerivationoftheFokker-Planckequation
3.Brownianmotion
4.TheRayleighparticle
5.Applicationtoone-stepprocesses
6.ThemultivariateFokker-Planckequation
7.Kramersequation

Ⅸ.THELANGEVINAPPROACH
1.LangevintreatmentofBrownianmotion
2.Applications
3.RelationtoFokker-Planckequation
4.TheLangevinapproach
5.DiscussionoftheIt6——Stratonovichdilemma
6.Non-Gaussianwhitenoise
7.Colorednoise

Ⅹ.THEEXPANSIONOFTHEMASTEREQUATION
1.Introductiontotheexpansion
2.Generalformulationoftheexpansionmethod，
3.Theemergenceofthemacroscopiclaw
4.Thelinearnoiseapproximation
5.Expansionofamultivariatemasterequation..
6.Higherorders

Ⅺ.THEDIFFUSIONTYPE
1.Masterequationsofdiffusiontype
2.Diffusioninanexternalfield
3.Diffusioninaninhomogeneousmedium
4.Multivariatediffusionequation
5.Thelimitofzerofluctuations

Ⅻ.FIRST-PASSAGEPROBLEMS
1.Theabsorbingboundaryapproach
2.Theapproachthroughtheadjointequation-Discretecase
3.Theapproachthroughtheadjointequation-Continuouscase
4.Therenewalapproach
5.BoundariesoftheSmoluchowskiequation
6.Firstpassageofnon-Markovprocesses
7.Markovprocesseswithlargejumps

ⅩⅢ.UNSTABLESYSTEMS
1.Thebistablesystem
2.Theescapetime
3.Splittingprobability
4.Diffusioninmoredimensions
5.Criticalfluctuations
6.Kramersescapeproblem
7.Limitcyclesandfluctuations.

ⅩⅣ.FLUCTUATIONSINCONTINUOUSSYSTEMS
1.Introduction
2.Diffusionnoise
3.Themethodofcompoundingmoments
4.Fluctuationsinphasespacedensity
5.FluctuationsandtheBoltzmannequation
ⅩⅤ.THESTATISTICSOFJUMPEVENTS
1.Basicformulaeandasimpleexample
2.Jumpeventsinnonlinearsystems
3.Effectofincidentphotonstatistics
4.Effectofincidentphotonstatistics-continued.

ⅩⅥ.STOCHASTICDIFFERENTIALEQUATIONS
1.Definitions
2.Heuristictreatmentofmultiplicativeequations.
3.Thecumulantexpansionintroduced
4.Thegeneralcumulantexpansion
5.Nonlinearstochasticdifferentialequations
6.Longcorrelationtimes

ⅩⅦ.STOCHASTICBEHAVIOROFQUANTUMSYSTEMS
1.Quantumprobability
2.Thedampedharmonicoscillator
3.Theeliminationofthebath
4.Theeliminationofthebath-continued
5.TheSchrodinger-Langevinequationandthequantummasterequation
6.Anewapproachtonoise
7.Internalnoise
SUBJECTINDEX
内容简介:
　　Definition、Averages、Multivariatedistributions、Additionofstochasticvariables、Transformationofvariables、TheGaussiandistribution、Thecentrallimittheorem、Definition、ThePoissondistribution、Alternativedescriptionofrandomevents、Theinverseformula、Thecorrelationfunctions、Waitingtimes、Factorialcorrelationfunctions等等。
目录:
PREFACETOTHEFIRSTEDITION
PREFACETOTHESECONDEDITION
ABBREVIATEDREFERENCES
PREFACETOTHETHIRDEDITION
1.STOCHASTICVARIABLES
1.Definition
2.Averages
3.Multivariatedistributions
4.Additionofstochasticvariables
5.Transformationofvariables
6.TheGaussiandistribution
7.Thecentrallimittheorem

Ⅱ.RANDOMEVENTS
1.Definition
2.ThePoissondistribution
3.Alternativedescriptionofrandomevents
4.Theinverseformula
5.Thecorrelationfunctions
6.Waitingtimes
7.Factorialcorrelationfunctions

Ⅲ.STOCHASTICPROCESSES
1.Definition
2.Stochasticprocessesinphysics
3.Fouriertransformationofstationaryprocesses.
4.Thehierarchyofdistributionfunctions
5.Thevibratingstringandrandomfields
6.Branchingprocesses

Ⅳ.MARKOVPROCESSES
1.TheMarkovproperty
2.TheChapman-Kolmogorovequation
3.StationaryMarkovprocesses
4.Theextractionofasubensemble
5.Markovchains
6.Thedecayprocess

Ⅴ.THEMASTEREQUATION
1.Derivation
2.TheclassofW-matrices
3.Thelong-timelimit
4.Closed，isolated，physicalsystems
5.Theincreaseofentropy
6.Proofofdetailedbalance
7.Expansionineigenfunctions
8.Themacroscopicequation
9.Theadjointequation
10.Otherequationsrelatedtothemasterequation

Ⅵ.ONE-STEPPROCESSES
1.Definition;thePoissonprocess
2.Randomwalkwithcontinuoustime
3.Generalpropertiesofone-stepprocesses
4.Examplesoflinearone-stepprocesses
5.Naturalboundaries
6.Solutionoflinearone-stepprocesseswithnaturalboundaries
7.Artificialboundaries
8.Artificialboundariesandnormalmodes
9.Nonlinearone-stepprocesses

Ⅶ.CHEMICALREACTIONS
1.Kinematicsofchemicalreactions
2.Dynamicsofchemicalreactions.
3.Thestationarysolution
4.Opensystems
5.Unimolecularreactions
6.Collectivesystems
7.CompositeMarkovprocesses

Ⅷ.THEFOKKER-PLANCKEQUATION
1.Introduction
2.DerivationoftheFokker-Planckequation
3.Brownianmotion
4.TheRayleighparticle
5.Applicationtoone-stepprocesses
6.ThemultivariateFokker-Planckequation
7.Kramersequation

Ⅸ.THELANGEVINAPPROACH
1.LangevintreatmentofBrownianmotion
2.Applications
3.RelationtoFokker-Planckequation
4.TheLangevinapproach
5.DiscussionoftheIt6——Stratonovichdilemma
6.Non-Gaussianwhitenoise
7.Colorednoise

Ⅹ.THEEXPANSIONOFTHEMASTEREQUATION
1.Introductiontotheexpansion
2.Generalformulationoftheexpansionmethod，
3.Theemergenceofthemacroscopiclaw
4.Thelinearnoiseapproximation
5.Expansionofamultivariatemasterequation..
6.Higherorders

Ⅺ.THEDIFFUSIONTYPE
1.Masterequationsofdiffusiontype
2.Diffusioninanexternalfield
3.Diffusioninaninhomogeneousmedium
4.Multivariatediffusionequation
5.Thelimitofzerofluctuations

Ⅻ.FIRST-PASSAGEPROBLEMS
1.Theabsorbingboundaryapproach
2.Theapproachthroughtheadjointequation-Discretecase
3.Theapproachthroughtheadjointequation-Continuouscase
4.Therenewalapproach
5.BoundariesoftheSmoluchowskiequation
6.Firstpassageofnon-Markovprocesses
7.Markovprocesseswithlargejumps

ⅩⅢ.UNSTABLESYSTEMS
1.Thebistablesystem
2.Theescapetime
3.Splittingprobability
4.Diffusioninmoredimensions
5.Criticalfluctuations
6.Kramersescapeproblem
7.Limitcyclesandfluctuations.

ⅩⅣ.FLUCTUATIONSINCONTINUOUSSYSTEMS
1.Introduction
2.Diffusionnoise
3.Themethodofcompoundingmoments
4.Fluctuationsinphasespacedensity
5.FluctuationsandtheBoltzmannequation
ⅩⅤ.THESTATISTICSOFJUMPEVENTS
1.Basicformulaeandasimpleexample
2.Jumpeventsinnonlinearsystems
3.Effectofincidentphotonstatistics
4.Effectofincidentphotonstatistics-continued.

ⅩⅥ.STOCHASTICDIFFERENTIALEQUATIONS
1.Definitions
2.Heuristictreatmentofmultiplicativeequations.
3.Thecumulantexpansionintroduced
4.Thegeneralcumulantexpansion
5.Nonlinearstochasticdifferentialequations
6.Longcorrelationtimes

ⅩⅦ.STOCHASTICBEHAVIOROFQUANTUMSYSTEMS
1.Quantumprobability
2.Thedampedharmonicoscillator
3.Theeliminationofthebath
4.Theeliminationofthebath-continued
5.TheSchrodinger-Langevinequationandthequantummasterequation
6.Anewapproachtonoise
7.Internalnoise
SUBJECTINDEX

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