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量子混沌導(dǎo)論

量子混沌導(dǎo)論

定 價:¥79.00

作 者: 斯托克曼H-J Stockmaon著
出版社: 世界圖書出版公司北京公司
叢編項:
標 簽: 物理學(xué)中的數(shù)學(xué)方法

ISBN: 9787506260053 出版時間: 2003-01-01 包裝: 膠版紙
開本: 22cm 頁數(shù): 368頁 字數(shù):  

內(nèi)容簡介

  This book introduces the quantum mechanics of classically chaotic systems, or Quantum Chaos for short. The basic concepts of quantum chaos can be grasped easily by any student of physics, but the underlying physical prin-ciples tend to be obscured by the mathematical apparatus used to describe it. The author's philosophy, therefore, has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. A basic knowledge of quantum mechanics is assumed.

作者簡介

  H-J Stockmann was born in 1945 in Gottingen, Germany. He started his studies in physics and mathematics in 1964 at the University of Heidelberg. He performed his diploma work in experimental physics, on Optical spectroscopy which the finished in 1969. For his doctoral work he changed to nuclear solid state physics, with experiments at the research reactor of the Kernforschungszentrum karlsruhe.

圖書目錄

Preface.
1Introduction
2Billiardexperiments
2.1Wavepropagationinsolidsandliquids
2.1.1Chladnifigures
2.1.2Watersurfacewaves
2.1.3Vibratingblocks
2.1.4Ultrasonicfieldsinwater-filledcavities
2.2Microwavebilliards
2.2.1Basicprinciples
2.2.2Fielddistributionsinmicrowavecavities
2.2.3Billiardswithbrokentime-reversalsymmetry
2.2.4Josephsonjunctions
2.3Mesoscopicstructures
2.3.1Antidotlattices
2.3.2Quantumdotbilliards
2.3.3Quantumwellbilliards
2.3.4Quantumcorrals
3Randommatrices
3.1Gaussianensembles
3.1.1Symmetries
3.1.2Universalityclasses
3.1.3DefinitionoftheGaussianensembles
3.1.4Correlatedeigenenergydistribution
3.1.5Averageddensityofstates
3.2Spectralcorrelations
3.2.1Nearestneighbourdistancedistribution
3.2.2Fromtheintegrabletothenonintegrableregime
3.2.3n-pointcorrelationfunction
3.2.4∑2and△3statistics
3.2.5Spectralformfactor
3.3Supersymmetrymethod
3.3.1Replicatrick
3.3.2Anticommutingvariables
3.3.3Hubbard-Stratonovitchtransformation
3.3.4Saddlepointintegration
4Floquetandfight-bindingsystems
4.1Hamiltonianswithperiodictimedependences
4.1.1Floquetoperator
4.1.2Circularensembles
4.2Dynamicallocalization
4.2.1Kickedrotator
4.2.2Hydrogenatomsinstrongradiofrequencyfields
4.2.3Ultra-coldatomsinmagneto-opticaltraps
4.3Tight-bindingsystems
4.3.1Andersonmodel
4.3.2Transfermatrixmethod
4.3.3Harperequation
5Eigenvaluedynamics
5.1Pechukas-Yukawamodel
5.1.1Equationsofmotion
5.1.2Constantsofmotion..
5.1.3Phasespacedensity
5.1.4Pechukas-Yukawamodelandrandommatrixtheory
5.2Billiardleveldynamics
5.2.1BilliardandPechukas-Yukawaleveldynamics
5.2.2TestsoftheYukawaconjecture
5.3Geometricalphases
6Scatteringsystems
6.1Billiardsasscatteringsystems
6.1.1Scatteringmatrix
6.1.2BilliardBreit-Wignerformula
6.1.3Coupled-channelHamiltonian
6.1.4Perturbingbeadmethod
6.2Amplitudedistributionfunctions
6.2.1Randomsuperpositionsofplanewaves
6.2.2Porter-Thomasdistributions
6.3Fluctuationpropertiesofthescatteringmatrix
6.3.1Ericsonfluctuations
6.3.2ConductancefluctuationsinmesoscopicsystemsSemiclassicalquantummechanics
7.1Integrablesystems
7.1.1One-dimensionalcase
7.1.2Multidimensionalintegrablesystems
7.2Gutzwillertraceformula
7.2.1Feynmanpathintegral
7.2.2Ashortexcursioninclassicalmechanics
7.2.3Semiclassicalpropagator
7.2.4SemiclassicalGreenfunction
7.2.5Monodromymatrix
7.2.6Traceformula
7.3Contributionstothedensityofstates
7.3.1Smoothpartofthedensityofstates
7.3.2Oscillatorypartofthedensityofstates
7.3.3Bouncing-ballcontributions
8Applicationsofperiodicorbittheory
8.1Periodicorbitanalysisofspectraandwavefunctions
8.1.1Periodicorbitsinthespectra
8.1.2Hydrogenatominastrongmagneticfield
8.1.3Scars
8.2Semiclassicaltheoryofspectralrigidity
8.2.1Rigidityforintegrablesystems
8.2.2Semiclassicalsumrule
8.2.3Rigidityfornonintegrablesystems
8.3Periodicorbitcalculationofspectra
8.3.1Dynamicalzetafunction
8.3.2Riemannzetafunction
8.4Surfaceswithconstantnegativecurvature
8.4.1Selbergtraceformula
8.4.2Non-Euclidianbilliards
References
Index...

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