Application-driven Quantum and Statistical Physics: A Short Course for Future Scientists and Engineers

300 Pages·2018·6.861 MB·English

by  Jean-Michel Gillet

Q0164_9781786345547_TP.indd 1 28/9/18 4:31 PM
Essential Textbooks in Physics
ISSN: 2059-7630
The Essential Textbooks in Physics explores the most important topics in Phys-
ics that all Physical Sciences students need to know to pass their undergraduate
exams (years 1, 2 and 3 of the BSc). Some topics are run-of-the-mill topics, others
introduce students to more applied areas (e.g. Quantum Optics, Microfluidics…).
Written by senior academics as well lecturers recognised for their teaching
skills, they offer in around 200 to 250 pages a theoretical overview of fundamental
concepts backed by problems and worked solutions at the end of each chapter.
Their lively style, focused scope and pedagogical material make them ideal
learning tools at a very affordable price.
Most authors are based at prestigious universities: Imperial College London,
Oxford, UCL, Ecole Polytechnique.
Published
Application-Driven Quantum and Statistical Physics: A Short Course for Future
Scientists and Engineers
Volume 1: Foundations
by Jean-Michel Gillet
A Guide to Mathematical Methods for Physicists: With Problems and Solutions
by Michela Petrini, Gianfranco Pradisi and Alberto Zaffaroni
Introduction to General Relativity and Cosmology
by Christian G. Böhmer
Newtonian Mechanics for Undergraduates
by Vijay Tymms
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World Scientific
Q0164_9781786345547_TP.indd 2 28/9/18 4:31 PM
Published by
World Scientific Publishing Europe Ltd.
57 Shelton Street, Covent Garden, London WC2H 9HE
Head office: 5 Toh Tuck Link, Singapore 596224
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Library of Congress Cataloging-in-Publication Data
Names: Gillet, Jean-Michel, author.
Title: Application-driven quantum and statistical physics : a short course for future scientists and
engineers / Jean-Michel Gillet (CentraleSupâelec, France).
Other titles: Essential textbooks in physics.
Description: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018] |
Series: Essential textbooks in physics Contents: volume 1: Foundations --
volume 2: Equilibrium -- volume 3: Transition.
Identifiers: LCCN 2018023720| ISBN 9781786345547 (hc ; v.1 ; alk. paper) |
ISBN 1786345544 (hc ; v.1 ; alk. paper) | ISBN 9781786345578 (hc ; v.2 ; alk. paper) |
ISBN 1786345579 (hc ; v.2 ; alk. paper)
Subjects: LCSH: Quantum theory--Textbooks. | Statistical physics--Textbooks.
Classification: LCC QC174.12 .G54 2018 | DDC 530.12--dc23
LC record available at https://lccn.loc.gov/2018023720
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
First published 2019 (Hardcover)
Reprinted 2019 (in paperback edition)
ISBN 9781786346902 (pbk)
Copyright © 2019 by Jean-Michel Gillet
The moral right of the author has been asserted.
All rights reserved.
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/Q0164#t=suppl
Desk Editors: V. Vishnu Mohan/Jennifer Brough/Koe Shi Ying
Typeset by Stallion Press
Email: [e-mail]
Printed in Singapore
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Preface
Le concret c’est de l’abstrait rendu familier par l’usage.1
Paul Langevin
“La notion de corpuscules et d’atomes”
16th October 1933
Thisfirstvolumeofatriptychsetsthegeneralquantumlandscape.Itisbuilt
uponthreeconnectedpartsthatcanbeconsideredasageneralintroduction
to quantum physics.
Classical physics had shown all its power and ability to accompany the
industrialrevolutionwiththetremendoussuccessof—inparticular—ther-
modynamics,withthedevelopmentofmoreefficientheatenginesorelectro-
magnetism, with the birth of modern radio-communications. Nevertheless
some scientists at the beginning of the twentieth century were still dissat-
isfied with unexplained experimental results. It is thus the purpose of the
first part to give the general ambiance that led a well-established physical
paradigm to progressively crumble. It then shows how many daring scien-
tistscametoinventthenecessityofanewuniversalphysicalconstant — the
1Theconcreteistheabstractrenderedfamiliarthroughuse.
v
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vi Preface
celebrated Planck constant — that will prove to be the cornerstone of an
alternative way to interpret the physical world.
In the second part, we introduce new rules according to which one
believes the quantum game is played. They are presented as mere pos-
tulates that have — so far — proved to be corroborated by every single
experiment and at any level of accessible precision. Most of these rules
haveliftedformerobstaclesinexplainingphysicalobservations,whilesome
of them have led to develop new methods of investigation at the micro-
scopic scale or even new technologies. It has been stated that a rough25%
oftheUSAgrossnationalproductistheresultofinventionsbasedonquan-
tum physics. It is not to be overoptimisticto foresee anincreasing input of
quantum consequences in the coming years.
Finally,thethirdpartofthisvolumepresentsconnectionsbetweenquan-
tum and classical descriptions. While the quantum paradigm solves many
difficult problems, it also introduces a new level of complexity that is both
cumbersome and unnecessary in most of daily life macroscopic challenges.
We thenraisea quite legitimate question: whendo we reallyneedto resort
toaquantumdescriptionofourphysicalworld?Thelinksbetweenthosetwo
points ofview turnout to be multifaceted andrequirea careful inspection.
Three excellent references, which are not mentioned explicity in the
main text but have guided me throughout my study years and are still of
great inspiration for my daily teaching, are worth being cited here. Quan-
tum Mechanics by C. Cohen-Tanoudji, B. Diu and F. Laloe (Wiley, 1991),
Physique Statistique by B. Diu, C. Guthmann, D. Lederer, B. Roulet
(Hermann, 1989), and Quantics: Rudiments of Quantum Physics by
J.-M. Levy-Leblond and F. Balibard (North-Holland, 1990). I have been
lucky enough to enjoy the very inspiring teaching of Franc¸oise Balibard
and Bernard Diu who gave me the taste for learning, then transmitting
this exciting science. I am sure many readers would benefit from in depth
treatments given by their published work.
The biographical notes, which focus on the human side of some key
actors, are based on a subjective collection of information from several
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Preface vii
historiographic books on post-nineteenth century physics. Remarkable
Physicists by Ioan James [59] is an excellent introduction to many exciting
lives and has served as the backbone of what is too briefly presented here.
Some readers may not be satisfied with pure science
and need torely on possible concrete examples. They will find motivation to
further endure more concepts and calculations in a one-sentence box at the
beginning of each chapter. This gives a glimpse of some applications that
will be treated, or briefly evoked.
To safely wrap up the chapter, another box summarizes the
most important resultsin termsof ideas, expressions or formula. These will
beessentialfor understandingtheremainderofthebook,orarequitesimply
a “must have” for each futu✍re quantum-educated scientist.
Questions marked with include important results which are rele-
vant for better understanding later developments given in the main text.
It is thus advisable to spend the little additional necessary time to work
them out.
Finally, I wishto expressmy deep gratitudeto all the wonderfulpeople
and colleagues without whom this book would have never been anything
but a teacher’s fantasy.
Among them, I am profoundly indebted to thousands of students at
Ecole Centrale Beijing (ECPKn) and CentraleSup´elec (CS) Paris who had
to study hard to keep up with our high expectations in basic sciences.
Their enthusiasm for the Quantum and Statistical Physics course never
ceased to grow over the last 10 years and was the true motivation for
proposing a written version for a much broader and international reader-
ship.Theoriginallecturenotesbenefitedfromstudents’numerousremarks,
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viii Preface
and additions suggested by colleagues and friends in the Physics depart-
ment: Pierre Becker, Pietro Cortona, Bruno Palpant, Thomas Antoni and
Pierre-Eymeric Janolin, to name but a few.
Devinderjit Sivia had the brilliant idea that I should spend some time
as a visiting scholar at St John’s College in Oxford where the project for
this book really took shape. Claude Lecomte, S´ebastien Candel and Julie
McDonald thoughtfully helped me make it happen. In Oxford, Richard
Comptonhadthegenerositytobelieveintheprojectandintroducedmeto
LaurentChaminadeatWorldScientific. Overthe yearsofwriting, Jennifer
Brough constantly provided help and encouragement.
Nevertheless,none of this wouldhave been possible without four amaz-
ing human beings.
JulieMcDonaldatCShasalreadybeenmentionedandhasnowbecome
adearfriend.Butalso,startinglongbeforetheOxfordperiod,shehasbeen
the most supportive English teacher I have ever met. No English version
wouldexistwithoutherencouragementandnever-endingdedicationtospot
and correct my numerous spelling, grammar and stylistic deficiencies.
Guillaume Merle at ECPKn spent hours reading and correcting the
manuscriptwithanincredible ability to detect incoherences,weaknessesin
the explanations and mistakes. He is a true (and generous) master of the
red pen.
Jean-Christophe Pain at CEA was my second reader. His enthusiastic
endorsement,suggestionsandideaswereavaluablesourceofinspirationto
help make this book a real pedagogical tool.
Last, but far from least, my family has been very compassionate and
understanding over the writing period. I am fully aware of how much they
had to endure because of my mental and physical absence. In particular,it
is essential to emphasize the key role played by my wife Nadine who kept
me going with her loving patience and unstinting support.
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Preface ix
Table1. Tableofnotationsusedinthisbook.Notethatvectorsarewritteninboldface.
Notations Descriptions
A(cid:2) operator
{an, |φn(cid:2)} eigenvalues andcorresponding
eigenkets ofA(cid:2)
|ψ(cid:2) stateket
(cid:3)ψ| statebra
−→
∇r “nabla”operatoractingon
variabler,asin:
−→
∇rf(r) gradientoperator withrespectto
variabler
−→
∇r·u(r) divergenceoperatorwithrespectto
variabler
−→
∇r×u(r) curloperatorwithrespecttovariable
r
−→ −→
∇2rf(r)≡ ∇r.(∇rf(r)) Laplacianoperator withrespectto
variabler
−→ −→
∇(cid:3)2ru(r)≡(∇r.∇Tr)u(r) Hessianmatrixwithrespectto
variabler
Table2. Tableofconstants usedinthisbook.
Notations Descriptions Approximatedvalues
c speedoflightinvacuum 2.99792×108 ms−1
(cid:4)0 vacuumdielectricpermittivity 8.854×10−12 A2s4kg−1m−3
μ0 vacuummagneticpermittivity 4π×10−7 kgmA−2s−2
e elementarycharge 1.602×10−19 C
h Planck’sconstant 6.62607×10−34 Js
(cid:2) Planck’sconstant dividedby2π 1.054589×10−34 Js
kB Boltzmann’sconstant 1.38066×10−23 JK−1
NA Avogadro’snumber 6.02214×1023 mol−1
σ Stefan–Boltzmann’s constant 5.67×10−8 Wm−2K−4
me massofelectron 9.1094×10−31 kg
mp massofproton 1.6726×10−27 kg
mn massofneutron 1.6749×10−27 kg
a0 Bohr’sradius 4π(cid:4)0(cid:2)2/(me2)≈0.5292×10−10 m