LEADER 03948nam 2200505 450 001 9910488723503321 005 20230619183722.0 010 $a3-030-62688-1 035 $a(CKB)5590000000516514 035 $a(MiAaPQ)EBC6676314 035 $a(Au-PeEL)EBL6676314 035 $a(OCoLC)1260347567 035 $a(PPN)258059958 035 $a(EXLCZ)995590000000516514 100 $a20220329d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMarkov processes and quantum theory /$fMasao Nagasawa 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (349 pages) 225 1 $aMonographs in mathematics ;$vVolume 109 311 $a3-030-62687-3 327 $aIntro -- Preface -- Contents -- Chapter 1 Mechanics of Random Motion -- 1.1 Smooth Motion and Random Motion -- 1.2 On Stochastic Processes -- 1.3 Ito?'s Path Analysis -- 1.4 Equation of Motion for a Stochastic Process -- 1.5 Kinematics of Random Motion -- 1.6 Free Random Motion of a Particle -- 1.7 Hooke's Force -- 1.8 Hooke's Force and an Additional Potential -- 1.9 Complex Evolution Functions -- 1.10 Superposition Principle -- 1.11 Entangled Quantum Bit -- 1.12 Light Emission from a Silicon Semiconductor -- 1.13 The Double-Slit Problem -- 1.14 Double-Slit Experiment with Photons -- 1.15 Theory of Photons -- 1.16 Principle of Least Action -- 1.17 Transformation of Probability Measures -- 1.18 Schro?dinger Equation and Path Equation -- Chapter 2 Applications -- 2.1 Motion induced by the Coulomb Potential -- 2.2 Charged Particle in a Magnetic Field -- 2.3 Aharonov-Bohm Effect -- 2.4 Tunnel Effect -- 2.5 Bose-Einstein Distribution -- 2.6 Random Motion and the Light Cone -- 2.7 Origin of the Universe -- 2.8 Classification of Boundary Points -- 2.9 Particle Theory of Electron Holography -- 2.10 Escherichia coli and Meson models -- 2.11 High-Temperature Superconductivity -- Chapter 3 Momentum, Kinetic Energy, Locality -- 3.1 Momentum and Kinetic Energy -- 3.2 Matrix Mechanics -- 3.3 Function Representations of Operators -- 3.4 Expectation and Variance -- 3.5 The Heisenberg Uncertainty Principle -- 3.6 Kinetic Energy and Variance of Position -- 3.7 Theory of Hidden Variables -- 3.8 Einstein's Locality -- 3.9 Bell's Inequality -- 3.10 Local Spin Correlation Model -- 3.11 Long-Lasting Controversy and Random Motion -- Chapter 4 Markov Processes -- 4.1 Time-Homogeneous Markov Proces-ses -- 4.2 Transformations by M-Functionals -- 4.3 Change of Time Scale -- 4.4 Duality and Time Reversal -- 4.5 Time Reversal, Last Occurrence Time. 327 $a4.6 Time Reversal, Equations of Motion -- 4.7 Conditional Expectation -- 4.8 Paths of Brownian Motion -- Chapter 5 Applications of Relative Entropy -- 5.1 Relative Entropy -- 5.2 Variational Principle -- 5.3 Exponential Family of Distributions -- 5.4 Existence of Entrance and Exit Functions -- 5.5 Cloud of Paths -- 5.6 Kac's Phenomenon of Propagation of Chaos -- Chapter 6 Extinction and Creation -- 6.1 Extinction of Particles -- 6.2 Piecing-Together Markov Processes -- 6.3 Branching Markov Processes -- 6.4 Construction of Branching Markov Processes -- 6.5 Markov Processes with Age -- 6.6 Branching Markov Processes with Age -- Bibliography -- Index. 410 0$aMonographs in mathematics ;$vVolume 109. 606 $aQuantum theory 606 $aTeoria quàntica$2thub 606 $aProcessos de Markov$2thub 608 $aLlibres electrònics$2thub 615 0$aQuantum theory. 615 7$aTeoria quàntica 615 7$aProcessos de Markov 676 $a530.12 700 $aNagasawa$b Masao$f1933 August 1-$060497 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910488723503321 996 $aMarkov processes and quantum theory$92819234 997 $aUNINA