Dynamics of Dissipation

ISBN-13: 9783642079078 / Angielski / Miękka / 2010 / 516 str.

Piotr Garbaczewski; Robert Olkiewicz

Opis

The present volume contains expanded and substantially reworked records of invitedlecturesdeliveredduringthe38thKarpaczWinterSchoolofTheoretical Physics on Dynamical Semigroups: Dissipation, Chaos, Quanta, which took placeinLadek, Zdr oj, (Poland)intheperiod6 15February2002. Themainpurposeoftheschoolwastocreateaplatformfortheconfrontation ofviewpointsandresearchmethodologiesrepresentedbytwogroupsofexperts actually working in the very same area of theoretical physics. This situation is quite distinct in non-equilibrium statistical physics of open systems, where classicalandquantumaspectsareaddressedseparatelybymeansofverydi?erent andevenincompatibleformaltools. TheschooltopicsselectionbytheLecturersreads: dissipativedynamicsand chaoticbehaviour, modelsofenvironment systemcouplingandmodelsofth- mostats;non-equilibriumstatisticalmechanicsandfarfromequilibriumphen- ena;quantumopensystems, decoherenceandlinkstoquantumchaos;quantum andclassicalapplicationsofMarkovsemigroupsandthevalidityofMarkovian approximations. Theorganizingprincipleforthewholeendeavourwastheissueofthedyn- ics of open systems and more speci?cally thedynamics of dissipation. Since this research area is extremely broad and varied, no single book can cover all importantdevelopments. Therefore, linkswithdynamicalchaoswerechosento representasupplementaryconstraint. Theprogrammeoftheschoolandits?naloutcomeintheformofthepresent volumehasbeenshapedwiththehelpofthescienti?ccommitteecomprising: R. Alicki, Ph. Blanchard, J. R. Dorfman, G. Gallavotti, P. Gaspard, I. Guarneri, ? F. Haake, M. Kus, A. Lasota, B. Zegarlinski and K. Zyczkowski. Some of the committeememberstookchargeoflecturingtoo. Weconveyourthankstoall ofthem. Wewouldliketoexpresswordsofgratitudetomembersofthelocalorgan- ingcommittee, W. Ceg laandP. Lugiewicz, fortheirhelp. Specialthanksmust beextendedtoMrsAnnaJadczykforherhelpatvariousstagesoftheschool organizationandthecompetenteditorialassistance. Theschoolwas?nanciallysupportedbytheUniversityofWroc law, Univ- sityofZielonaG ora, PolishMinistryofEducation, PolishAcademyofSciences, FoundationfortheKarpaczWinterSchoolofTheoreticalPhysicsandthe- nationfromtheDrWilhelmHeinrichHeraeusundElseHeraeusStiftung. Wrocla wandZielonaG ora, Poland PiotrGarbaczewski June2002 RobertOlkiewicz TableofContents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ChapterI NonequilibriumDynamics SomeRecentAdvancesinClassicalStatisticalMechanics E. G. D. Cohen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 DeterministicThermostatsandFluctuationRelations L. Rondoni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 WhatIstheMicroscopicResponseofaSystem DrivenFarFromEquilibrium? C. Jarzynski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Non-equilibriumStatisticalMechanics ofClassicalandQuantumSystems D. Kusnezov, E. Lutz, K. Aoki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 ChapterII DynamicsofRelaxationandChaoticBehaviour DynamicalTheoryofRelaxation inClassicalandQuantumSystems P. Gaspard. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 RelaxationandNoiseinChaoticSystems S. Fishman, S. Rahav. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 FractalStructuresinthePhaseSpace ofSimpleChaoticSystemswithTransport J. R. Dorfman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 ChapterIII DynamicalSemigroups MarkovSemigroupsandTheirApplications R. Rudnicki, K. Pichor, M. Tyran-Kaminska . . . . . . . . . . . . . . . . . . . . . . . . . 215 VIII TableofContents InvitationtoQuantumDynamicalSemigroups R. Alicki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 FiniteDissipativeQuantumSystems M. Fannes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 CompletePositivityinDissipativeQuantumDynamics F. Benatti, R. Floreanini, R. Romano. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 QuantumStochasticDynamicalSemigroup W. A. Majewski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 ChapterIV Driving, DissipationandControlinQuantumSystems DrivenChaoticMesoscopicSystems, DissipationandDecoherence D. Cohen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 QuantumStateControlinCavityQED T. WellensandA. Buchleitner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 SolvingSchr]odinger sEquationforanOpenSystem andItsEnvironment W. T. Strunz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 ChapterV DynamicsofLargeSystems ThermodynamicBehaviorofLargeDynamicalSystems Quantum1dConductorandClassicalMultibakerMap S. Tasaki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 CoherentandDissipativeTransport inAperiodicSolids: AnOverview J. Bellissard. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Recenzje

"The value of this volume is that it helps give students and other researchers a view of 'the big picture' in nonequilibrium statistical mechanics." (The Physicist, 40/5, 2003)

Spis treści

Nonequilibrium Dynamics.- Some Recent Advances in Classical Statistical Mechanics.- Deterministic Thermostats and Flctuation Relations.- What Is the Microscopic Response of a System Driven Far From Equilibrium?.- Non-equilibrium Statistical Mechanics of Classical and Quantum Systems.- Dynamics of Relaxation and Chaotic Behaviour.- Dynamical Theory of Relaxation in Classical and Quantum Systems.- Relaxation and Noise in Chaotic Systems.- Fractal Structures in the Phase Space of Simple Chaotic Systems with Transport.- Dynamical Semigroups.- Markov Semigroups and Their Applications.- Invitation to Quantum Dynamical Semigroups.- Finite Dissipative Quantum Systems.- Complete Positivity in Dissipative Quantum Dynamics.- Quantum Stochastic Dynamical Semigroup.- Driving, Dissipation and Control in Quantum Systems.- Driven Chaotic Mesoscopic Systems, Dissipation and Decoherence.- Quantum State Control in Cavity QED.- Solving Schrödinger’s Equation for an Open System and Its Environment.- Dynamics of Large Systems.- Thermodynamic Behavior of Large Dynamical Systems.- Coherent and Dissipative Transport in Aperiodic Solids: An Overview.- Scaling Limits of Schrödinger Quantum Mechanics.

Blurb

This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical mechanics, environment-system coupling (decoherence) and applications of Markov semi-groups to name but a few. The book addresses not only experienced researchers in the field but also nonspecialists from related areas of research, postgraduate students wishing to enter the field and lecturers searching for advanced textbook material.