Classical Analogies in the Solution of Quantum Many-Body Problems

110 Pages·2018·1.64 MB·English

by  Aydın Cem Keser

Springer Theses
Recognizing Outstanding Ph.D. Research
Aydın Cem Keser

Classical Analogies
in the Solution
of Quantum
Many-Body
Problems
Springer Theses
Recognizing Outstanding Ph.D. Research
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Aydın Cem Keser
Classical Analogies in the
Solution of Quantum
Many-Body Problems
Doctoral Thesis accepted by
University of Maryland, College Park, MD, USA
123
AydınCemKeser
SchoolofPhysics
UNSWAustralia
Sydney,NSW,Australia
ISSN2190-5053 ISSN2190-5061 (electronic)
SpringerTheses
ISBN978-3-030-00487-3 ISBN978-3-030-00488-0 (eBook)
https://doi.org/10.1007/978-3-030-00488-0
LibraryofCongressControlNumber:2018957080
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Tomyfather
Supervisor’s Foreword
AydınC.Keser’sthesisaddressesseeminglyunrelatedproblemsinthreeimportant
recent developments in modern condensed matter physics, namely, topological
superconductivity, many-body localization, and strongly interacting superfluids.
Thesedisparatequantummodelsarelinkedtogetherbyemployingfruitfulanalogies
fromclassicalmechanicsthatareusedtosolvethem.Thisstrategyhasledtosome
tangibleandsurprisingresults.
Firstly,therehasbeenanincredibleamountofrecentresearchactivityinsuper-
conductingnanowiresproposedasaplatformtorealizeMajoranazeromodes.The
thesis uses quasiclassical methods of superconductivity to calculate the density of
states—akeypropertyofthesetopologicalsystems,rathereffortlessly,bymapping
the problem to a textbook-level classical point-particle problem. In addition, the
leakageoftopologicalsuperconductivityintoadisorderedmetalleadispredictedto
belongrange,despitethenaiveexpectationsthatarebasedonbulkconsiderations—
animportantandunexpectedresult.
Anotherdevelopmentinrecentyearsisthepredictionofanon-thermalizingstate
ofmatter,aphenomenondubbedmany-bodylocalization,thatchallengesthebasic
assumptions of statistical mechanics. In localization theory, even the simplest toy
models that exhibit this property are mathematically cumbersome, and the results
rely on simulations limited by computational power. In the thesis, an alternative
viewpoint is developed by describing many-body localization in an analytically
solvable model of quantum rotors that have incommensurate rotation frequencies.
This allows describing localization in terms of integrals of motion that can be
constructed exactly by considering the classical limit of the model. Furthermore,
inthismodel,onecanseparatetheinteractionanddisordereffects,twocompeting
factorsinlocalization,andstudytheeffectsoftheseontheintegralsofmotion.
Finally,thefluctuationsinastronglyinteractingBosecondensateandsuperfluid,
a notoriously difficult system to analyze from first principles, are shown to mimic
stochastic fluctuations of space-time due to quantum fields. A number of authors
have already pointed out the surprising similarity between the trajectory of light
waves in the space curved by a massive object and the trajectory of sound waves
vii
viii Supervisor’sForeword
inamovingsuperfluid.First,thethesisretracesthestepsthatleadtothisanalogy,
butthistimehavingthequantummechanicalandstochasticaspectoftheproblem
in mind from the very beginning. Then, it shows that the so-called covariant
descriptionofphononssatisfiesconservationlawsthataresummarizedinLandau-
Khalatnikov equations for a superfluid. Finally, the thermal fluctuations of the
phonons and their backreaction on the superfluid “spacetime” are studied. This
analogy not only allows for computation of physical properties of the fluctuations
in an elegant way; it also sheds light on the deep connections between statistical
mechanics,generalrelativity,andcondensedmatterphysics.
Overall, the thesis is a valuable contribution to mathematical methods of
condensed matter theory. Its use of elegant mathematical models and techniques
producesnewandinterestingresultsandalongthewayinvitesthereadertoexplore
enjoyableanalogiesandfurtherresearchdirections.
JointQuantumInstitute ProfessorVictorGalitski
UniversityofMaryland
CollegePark,MD,USA
August2018
Acknowledgments
This thesis would not have been possible without people who contributed with
their ideas to my research projects and people who accompanied me throughout
mygraduateschoolyears.
First and foremost, I would like to thank my advisor, Victor Galitski. He gave
me a chance to join his group and to work on a set of diverse, interesting, and
challenging problems. He taught me that being a scientist is about forging a
character that exhibits courage in the face of the unknown, candid curiosity and
integrity,inadditiontoacquiringknowledgeandskills.
I would like to thank my collaborators, Valentin Stanev, Sriram Ganeshan, and
GilRefael.Theirideas,guidance,andsupportwereessentialfortheresearchIam
presenting in this thesis. In addition, I would like to thank Gökçe Bas¸ar, Dmitry
Efimkin, Bei-Lok Hu, Theodore Jacobson, Efim Rozenbaum, Raman Sundrum,
Dmitry D. Sokoloff, and Grigorii E. Volovik for valuable discussions and/or
contributing to this thesis with their ideas. I am also grateful to the Condensed
Matter Theory Center, and its director, Sankar Das Sarma, and the Joint Quantum
Institute for providing great environment for doing physics. The people who
work here and the frequent seminars and talks were very inspiring and helpful. I
also want to mention my officemates (chronologically): Sergey Pershoguba, Juraj
Radic, Hilary Hurst, and Yahya Alavirad. I enjoyed our time together and all the
conversationsanddiscussionsaboutphysicsorlifeingeneral.Iamalsogratefulto
alltheotherGalitskigroupmemberswithwhomIspentmytimeatUMD.
I would like to thank the members of the dissertation committee, Theodore
Einstein, Theodore Jacobson, Ian Spielman and Dionisios Margetis, for their
detailedreadingandcriticalevaluationofthisthesis.
I would like to thank Natalia Budyldina for all the years we spent together and
forcarryingtheemotionalburdenofgraduateschoolwithme.
Likewise,Iwouldliketothankmyroommates.Ithasbeengreatsharingthesame
livingspacewiththem.
I would also like to thank my friends in the area: Ali and Helen and of course
BenjaminYapıcıformakingmeamemberoftheirfamily,BerkGürakanandMaya
Kabkab,CanerÇelikandSinemKılıç,BurakÇes¸me,Ug˘urÇetiner,BahromOripov,
ix
x Acknowledgments
LoriS¸en,GökçeBas¸arandTaniaMarie,andallthemembersoftheMETUalumni
associationinDCandthePirSultanAbdalCulturalAssociationofDC.
IwouldliketothankMonashUniversityandMannixCollegefortheirgenerous
hospitalityandSimonCaterson,whomIhadthechancetomeetduringtheamazing
timeIspentinAustralia.
I would also like to thank Dimitrie Culcer who provided me the employment
opportunity as a postdoctoral research associate in Australian Research Council
Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET),
UniversityofNewSouthWales(UNSW)node,shortlyafterthesubmissionofthis
thesis. I would like to thank FLEET and UNSW School of Physics where part of
thisthesiswaseditedforpublicationasabook.
Finally, I would like to mention my endless gratitude to Sarah Black for
transformingmefromahesitantandriskaverseyoungdreamertowardaresolutely
persistentman.
Sydney,NSW,Australia AydınCemKeser
July2018