The Fractional Quantum Hall Effect: Properties of an IncompressibleQuantum FluidT. Chakraborty, P. Pietiläinen, and Allan H. MacDonald Citation: Phys. Today 43(3), 80 (1990); doi: 10.1063/1.2810494 View online: http://dx.doi.org/10.1063/1.2810494 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v43/i3 Published by the American Institute of Physics. Additional resources for Physics TodayHomepage: http://www.physicstoday.org/ Information: http://www.physicstoday.org/about_us Daily Edition: http://www.physicstoday.org/daily_edition

ics Series, is most suitable for thelatter audience. It could be used forpart of a course on modern physics orfor independent study. While physicsmajors would benefit from the broadsurvey Burge provides, they are likelyto be left dissatisfied by the frequentcasual references to new conceptswith inadequate technical explana-tion. Burge provides references tooriginal papers but not to supplemen-tary pedagogical review articles.Most of the text is accessible to thosewith a basic knowledge of mechanics,electricity and magnetism. Knowl-edge of quantum mechanics is neces-sary to follow the discussions of thedeuteron-bound state and barrierpenetration.

A strength of Burge's text is itssupply of good problems at the end ofeach chapter. Deficiencies includethe characterization of quantum elec-trodynamics as "controversial" andthe confusing brief treatment ofgauge invariance.

BRUCE BERGERUndergraduate student

Princeton UniversityEDMOND L. BERGER

Argonne National Laboratory

The Fractional QuantumHall Effect: Properties ofan IncompressibleQuantum Fluid

T. Chakraborty andP. PietilainenSpringer-Verlag, New York,1988. 175pp. $45.00 heISBN 0-387-19111-9

The quantum Hall effect occurs whena two-dimensional electron gas be-comes incompressible, provided thatthe density at which the incompress-ibility occurs is magnetic field depen-dent. For the integer quantum Halleffect, the incompressibility is easy tounderstand. The quantization of theelectron's cyclotron motion meansthat only a discrete set of kineticenergies is allowed, and both theseparation between allowed energiesand the number of states of a givenenergy are proportional to magneticfield. (The set of states with a givenkinetic energy is called a Landaulevel.) The incompressibility respon-sible for the integer QHE occurs atdensities where an integer number ofLandau levels are filled and the chem-ical potential jumps from one allowedkinetic energy to another.

The incompressibility responsiblefor the fractional QHE is due toelectron-electron interactions. Asthe density is increased above certain

fractional Landau-level fillings, it be-comes impossible for electrons toavoid states of a lower relative angu-lar momentum. Strengthened repul-sive interactions cause the chemicalpotential to jump. At the criticalfilling factor there is only one many-body state in which the electrons canavoid the lower relative angular mo-mentum. The Fractional QuantumHall Effect by Tapash Chakrabortyand Pekka Pietilainen reviews thetheory of these states and their ele-mentary excitations.

Much is understood about the frac-tional quantum Hall effect. The in-compressible states mentioned abovehave unique properties unlike anypreviously known. Their discoveryhas added to the small list of distinctclasses of many-body systems. It istherefore not surprising that theideas developed in trying to under-stand the fractional QHE are havingan impact on other fields of theory,notably the theory of high-Tc super-conductivity.

On the other hand, much remainsto be understood about the fractionalQHE. Many of the incompressiblestates arise in a much more subtleway than that outlined above, andlittle theory exists on the competitionbetween disorder and interaction ef-fects, despite interesting experimen-tal results. It is important that frac-tional QHE theory be communicatedto a broad audience both so that itsnotions can be applied elsewhere inphysics and so that its own develop-ment will continue. That is the objec-tive of this book.

The book succeeds especiallystrongly in providing the technicalbackground necessary for those whowish to push the fractional QHEtheory further ahead. The authorshave gone to some trouble to make thebook accessible to anyone with a solidbackground in statistical physics andquantum mechanics. They providemany details of derivations, omittedin the original references, and thussave many hours for those attemptingto introduce themselves to the sub-ject.

Emphasis is placed on explainingthe properties of the elementary exci-tations of the incompressible states,including detailed accounts of theirfractionally charged quasiparticles.Insights into the nature of theseexcitations have been achieved by theuse of both small-system exact-dia-gonalization studies and trial wave-functions that allow analogies to bemade with classical two-dimensionalplasmas. The authors describe bothapproaches with authority, havingeach made important contributions to

the original research. A succinctappendix on the hypernetted-chainmethod, used for many of the techni-cal calculations, adds to the complete-ness of the presentation and enhancesthe value of the book.

Readers seeking an impressionisticoverview of fractional QHE theoryand hoping for a lucid account ofconceptual elements that they cantake away and fit into another pieceof nature's great puzzle are likely tobe disappointed by this book. Thebook is intended for nonexpert re-searchers who want to begin investi-gating the fractional QHE. For thesepeople, I believe that the book willprove invaluable and I strongly re-commend it. The book can also serveas a useful reference for active re-searchers in either theory or experi-ment. I believe that this book willsucceed in opening up the fractionalQHE theory to a larger community.In writing it the authors have done aservice to the subject, for there ismuch left to do.

ALLAN H. MACDONALDIndiana University

Multiphase Flowin Porous Media:Mechanics, Mathematicsand Numerics

M. B. Allen, G. A. Behie andJ. A. TrangensteinSpringer-Verlag, New York,1988. $44.60pb ISBN0-387-96731-1

Fluid motion in porous media hasbeen an area of great activity inrecent years due to the combination ofits practical importance in petroleumrecovery, the scientific issues it raisesin applied mathematics and numeri-cal analysis, and the microscopicphysics of disordered materials. Thisbook, part of the Springer LectureNotes in Engineering series, is pri-marily devoted to the second of theseareas and gives an introduction to themathematical problems of (hydrocar-bon or water) reservoir simulation.

Multiphase Flow in Porous Media isbased on three sets of lectures pre-sented by the authors at the IBMBergen Scientific Center, Bergen,Norway in 1986. Myron Allen dis-cusses the basic mechanics of fluidflow in reservoirs, as formulated atthe macroscopic level of continuum-averaged partial differential equa-tions. Aside from surveying the es-sential introductory material on thesubject, this lecture presents an ex-tensive treatment of the thermody-namics of phase equilibrium for prob-

80 PHYSICS TODAY MARCH 1990