Functional renormalization and ultracold quantum gases
Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic prop...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Book/Monograph Hochschulschrift |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer-Verlag Berlin Heidelberg
2010
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| Schriftenreihe: | Springer Theses
SpringerLink Bücher |
| DOI: | 10.1007/978-3-642-14113-3 |
| Schlagworte: | |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1007/978-3-642-14113-3 Resolving-System, lizenzpflichtig, Volltext: http://dx.doi.org/10.1007/978-3-642-14113-3 Verlag, Inhaltsverzeichnis: https://swbplus.bsz-bw.de/bsz330933396inh.htm Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:1208.81002 
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| Verfasserangaben: | by Stefan Flörchinger |
MARC
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| 245 | 1 | 0 | |a Functional renormalization and ultracold quantum gases |c by Stefan Flörchinger |
| 264 | 1 | |a Berlin, Heidelberg |b Springer-Verlag Berlin Heidelberg |c 2010 | |
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| 505 | 8 | |a Functional Renormalization andUltracold Quantum Gases; Supervisor's Foreword; Contents; 1 Introduction; 1.1…Flow Equations to Solve an Integral; 1.2…Functional Integral Representation of Quantum Field Theory; 1.2.1 From the Lattice to Field Theory; 1.2.2 Expectation Values, Correlation Functions; 1.2.3 Functional Derivatives, Generating Functionals; 1.2.4 Microscopic Actions in Real Time and Analytic Continuation; 1.2.5 Matsubara Formalism; References; 2 The Wetterich Equation; 2.1…Scale Dependent Schwinger Functional; 2.2…The Average Action and its Flow Equation | |
| 505 | 8 | |a 2.3…Functional Integral Representation and Initial ConditionReference; 3 Generalized Flow Equation; 3.1…Scale-dependent Bosonization; 3.2…Flowing Action; 3.3…General Coordinate Transformations; References; 4 Truncations; 4.1…Symmetries as a Guiding Principles; 4.2…Separation of Scales; 4.3…Derivative Expansion; 5 Cutoff Choices; References; 6 Investigated Models; 6.1…Bose Gas in Three Dimensions; 6.1.1 Lagrangian; 6.2…Bose Gas in Two Dimensions; 6.3…BCS--BEC Crossover; 6.3.1 Lagrangian; 6.4…BCS--Trion--BEC Transition; 6.4.1 Lagrangian; References; 7 Symmetries | |
| 505 | 8 | |a 7.1…Derivative Expansion and Ward Identities7.1.1 Propagator and Dispersion; 7.2…Noethers Theorem; References; 8 Truncated Flow Equations; 8.1…Bose Gas; 8.1.1 Flow Equations for the Effective Potential; 8.1.2 Kinetic Coefficients; 8.2…BCS--BEC Crossover; 8.2.1 Flow of the Effective Potential; 8.3…BCS--Trion--BEC Transition; References; 9 Few-Body Physics; 9.1…Repulsive Interacting Bosons; 9.1.1 Vacuum Flow Equations and their Solution for d = 3; 9.1.2 Logarithmic Running in Two Dimensions; 9.2…Two Fermion Species: Dimer Formation; 9.2.1 Two-body Problem; 9.2.2 Renormalization | |
| 505 | 8 | |a 9.2.3 Binding Energy9.2.4 Dimer--Dimer Scattering; 9.3…Three Fermion Species: Efimov Effect; 9.3.1 SU(3) Symmetric Model; 9.3.1.1 Flow Equations for Two-body Sector; 9.3.1.2 Three-body Problem; 9.3.1.3 Limit Cycle Scaling; 9.3.2 Experiments with Lithium; References; 10 Many-Body Physics; 10.1…Bose--Einstein Condensation in Three Dimensions; 10.1.1 Different Methods to Determine the Density; 10.1.2 Quantum Depletion of Condensate; 10.1.3 Quantum Phase Transition; 10.1.4 Thermal Depletion of Condensate; 10.1.5 Critical Temperature; 10.1.6 Zero Temperature Sound Velocity | |
| 505 | 8 | |a 10.1.7 Thermodynamic Observables10.1.7.1 Density, Superfluid Density, Condensate and Correlation Length; 10.1.7.2 Entropy Density, Energy Density, and Specific Heat; 10.1.7.3 Compressibility; 10.1.7.4 Isothermal and Adiabatic Sound Velocity; 10.1.7.5 First and Second Velocity of Sound; 10.2…Superfluid Bose Gas in Two Dimensions; 10.2.1 Flow Equations at Zero Temperature; 10.2.2 Quantum Depletion of Condensate; 10.2.3 Dispersion Relation and Sound Velocity; 10.2.4 Kosterlitz--Thouless Physics; 10.2.4.1 Superfluidity and Order Parameter; 10.2.4.2 Critical Temperature | |
| 505 | 8 | |a 10.2.4.3 Superfluid Fraction | |
| 520 | |a Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics. | ||
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