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:
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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 |
Inhaltsangabe:
- 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
- 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
- 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
- 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
- 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
- 10.2.4.3 Superfluid Fraction