Generated Dynamics of Markov and Quantum Processes - Rilegato

Janssen, Martin

Rilegato

ISBN 10: 3662496941 ISBN 13: 9783662496947

Casa editrice: Springer Verlag, 2016

Riassunto

This book presents Markov and quantum processes as twosides of a coin called generated stochastic processes. It deals withquantum processes as  reversible stochastic processes generated byone-step unitary operators, while Markov processes are irreversible stochasticprocesses generated by one-step stochastic operators. The characteristicfeature of quantum processes are oscillations, interference, lots of stationarystates in bounded systems and possible asymptotic stationary scattering statesin open systems, while the characteristic feature of Markov processes arerelaxations to a single stationary state. Quantum processes apply to systemswhere all variables, that control reversibility, are taken as relevantvariables, while Markov processes emerge when some of those variables cannot befollowed and are thus irrelevant for the dynamic description. Their absencerenders the dynamic irreversible.

Afurther aim is to demonstrate that almost any subdiscipline of theoretical physicscan conceptually be put into the context of generated stochastic processes.Classical mechanics and classical field theory are deterministic processeswhich emerge when fluctuations in relevant variables are negligible. Quantummechanics and quantum field theory consider genuine quantum processes.Equilibrium and non-equilibrium statistics apply to the regime where relaxingMarkov processes emerge from quantum processes by omission of a large number ofuncontrollable variables. Systems with many variables often self-organize insuch a way that only a few slow variables can serve as relevant variables.Symmetries and topological classes are essential in identifying such relevantvariables.

Thethird aim of this book is to provide conceptually general methods of solutionswhich can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generatingfunctionals.

The potential reader is a graduate student whohas heard already a course in quantum theory and equilibrium statisticalphysics including the mathematics of spectral analysis (eigenvalues,eigenvectors, Fourier and Laplace transformation). The reader should be openfor a unifying look on several topics.

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Informazioni sull?autore

MartinJanßen is a private lecturer at the Institute of Theoretical Physics at theUniversity of Cologne and a high school teacher at theFriedrich-Wilhelm-Gymnasium in Cologne. He gained his doctorate in 1990 inCologne for his work on magneto transport and multifractality in the context ofthe quantum Hall effect and his venia legendi in 1997, on completion of hispost-doctoral thesis on statistics and scaling in mesoscopic electron systems.He held a DFG Postdoctoral Fellowship at Oxford University in 1993 and aMinerva Postdoctoral Fellowship at Haifa University in 1995. He has been amember of academic staff at the University of Cologne from 1992 to 1998 and atBochum University from 1998 to 2001. After working as an environmentalphysicist from 2001 to 2011 he became a high school teacher in physics andmathematics. Since 2001 he gives lectures at the University of Cologne onTheoretical Physics with emphasis on dynamics of stochastic processes. He hasco-written a book on the integer quantum Hall effect and written a book onfluctuations and localization in mesoscopic electron systems. 

Dalla quarta di copertina

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as  reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible.

A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processes which emerge when fluctuations in relevant variables are negligible. Quantum mechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxing Markov processes emerge from quantum processes by omission of a large number of uncontrollable variables. Systems with many variables often self-organize in such a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevant variables.

The third aim of this book is to provide conceptually general methods of solutions which can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generating functionals.

The potential reader is a graduate student who has heard already a course in quantum theory and equilibrium statistical physics including the mathematics of spectral analysis (eigenvalues, eigenvectors, Fourier and Laplace transformation). The reader should be open for a unifying look on several topics.

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3662496941
• ISBN 13: 9783662496947
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 244
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