國立虎尾科技大學 |

Generated Dynamics of Markov and Quantum Processes

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Generated Dynamics of Markov and Quantum Processes/ by Martin Janßen.
Author:	Janßen, Martin.
Description:	XVII, 226 p. 36 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical physics. -
Online resource:	https://doi.org/10.1007/978-3-662-49696-1
ISBN:	9783662496961

Generated Dynamics of Markov and Quantum Processes
Janßen, Martin.

Generated Dynamics of Markov and Quantum Processes[electronic resource] /by Martin Janßen. - 1st ed. 2016. - XVII, 226 p. 36 illus., 1 illus. in color.online resource.

Introduction - Dynamics of Relevant Variables- Generated Dynamics -- Formal Solutions -- Special Solutions -- Observables, States, Entropy and Generating Functionals -- Symmetries and Breaking of Symmetries -- Topology -- Selected Applications.

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.

ISBN: 9783662496961

Standard No.: 10.1007/978-3-662-49696-1doiSubjects--Topical Terms:

527831
Mathematical physics.

LC Class. No.: QC19.2-20.85

Dewey Class. No.: 530.1

Generated Dynamics of Markov and Quantum Processes
LDR:03854nam a22003975i 4500 001 977809
003 DE-He213
005 20200705230201.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783662496961 $9 978-3-662-49696-1
024 7 $a 10.1007/978-3-662-49696-1 $2 doi
035 $a 978-3-662-49696-1
050 4 $a QC19.2-20.85
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.1 $2 23
100 1 $a Janßen, Martin. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1271442
245 1 0 $a Generated Dynamics of Markov and Quantum Processes $h [electronic resource] / $c by Martin Janßen.
250 $a 1st ed. 2016.
264 1 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2016.
300 $a XVII, 226 p. 36 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Introduction - Dynamics of Relevant Variables- Generated Dynamics -- Formal Solutions -- Special Solutions -- Observables, States, Entropy and Generating Functionals -- Symmetries and Breaking of Symmetries -- Topology -- Selected Applications.
520 $a 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.
650 0 $a Mathematical physics. $3 527831
650 0 $a Engineering. $3 561152
650 0 $a Economics, Mathematical . $3 1253712
650 1 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 2 4 $a Engineering, general. $3 669723
650 2 4 $a Quantitative Finance. $3 669372
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783662496947
776 0 8 $i Printed edition: $z 9783662496954
776 0 8 $i Printed edition: $z 9783662570289
856 4 0 $u https://doi.org/10.1007/978-3-662-49696-1
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)