An Introduction to Quantum Stochastic Calculus

Buch | Softcover
XI, 290 Seiten
2012 | 1992
Springer Basel (Verlag)
978-3-0348-0565-0 (ISBN)

Lese- und Medienproben

An Introduction to Quantum Stochastic Calculus - K.R. Parthasarathy
96,29 inkl. MwSt
This elegantly written text includes a wealth of exercises for students as it weaves classical probability theory into the quantum framework. It deepens our understanding of classical and quantum views on the dynamics of systems subject to the laws of chance.

An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features:

The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle.
Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields.
Many quantum dynamical semigroups as well as classical Markov semigroups are realised through unitary operator evolutions.

The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.

- - -

This is an excellent volume which will be a valuable companion both to those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students.
(Mathematical Reviews)

This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field.
(Zentralblatt MATH)

Elegantly written, withobvious appreciation for fine points of higher mathematics (...) most notable is [the] author's effort to weave classical probability theory into [a] quantum framework.
(The American Mathematical Monthly)

Kalyanapuram Rangachari Parthasarathy was professor of statistics at the University of Manchester (1968-70), the University of Bombay (1970-76) and the Indian Statistical Institute Delhi Centre (1977-96) where he was also CV Raman Professor of INSA (1996-2001). Now he is Emeritus Scientist at the Indian Statistical Institute in New Delhi.

Preface.- I Events, Observables and States.- II Observables and States in Tensor Products of Hilbert Spaces.- III Stochastic Integration and Quantum Ito's Formula.- References.- Index.- Author Index.

Erscheint lt. Verlag 14.12.2012
Reihe/Serie Modern Birkhäuser Classics
Zusatzinfo XI, 290 p.
Verlagsort Basel
Sprache englisch
Maße 155 x 235 mm
Gewicht 465 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Brownian motion • Calculus • differential equation • Fock space • hilbert space • Integration • noncommutative probability • Operator • operator theory • Poisson process • Probability • Probability Theory • Quantenstatistik • quantum dynamical semigroup • quantum Ito's product formula • quantum Ito’s product formula • quantum stochastic differential equations • Stochastic Calculus • stochastic differential equation • Stochastic Integration • Stochastik • Tensor
ISBN-10 3-0348-0565-9 / 3034805659
ISBN-13 978-3-0348-0565-0 / 9783034805650
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Wie bewerten Sie den Artikel?
Bitte geben Sie Ihre Bewertung ein:
Bitte geben Sie Daten ein:
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
79,99