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Bose-Condensed Gases at Finite Temperatures

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ISBN-10: 0521837022

ISBN-13: 9780521837026

Edition: 2008

Authors: Allan Griffin, Tetsuro Nikuni, Eugene Zaremba

List price: $189.00
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Description:

The discovery of Bose-Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and non-equilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and two-fluid hydrodynamic regions. Major topics are introduced at an elementary level, before more detailed treatments and microscopic derivations of the underlying equations are given. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics, and condensed matter physics.
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Book details

List price: $189.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 2/19/2009
Binding: Hardcover
Pages: 476
Size: 7.00" wide x 9.75" long x 1.00" tall
Weight: 2.398

Allan Griffin works in theoretical condensed matter theory and is Professor Emeritus of Physics at the University of Toronto. He received his BSc (1960) and MSc (1961) from the University of British Columbia, and his PhD at Cornell University (1965). Dr Griffin has spent research sabbaticals at the KFA Julich (Germany), the Institut Laue-Langevin in Grenoble (France), Kyoto University (Japan), the University of Trento (Italy) and was a JILA Fellow at the University of Colorado (USA). His research has been on superfluid He4, superconductivity and theory of ultracold atoms. He has been a short-term visiting professor at the ANU in Canberra (Australia), the Coll�ge de France in Paris, and the University of Otago (New Zealand). Dr Griffin is a Fellow of the Royal Society of Canada (2003), a Fellow of the American Physical Society (2004), and received the Bronze Medal from the Coll�ge de France (2001). He is the author of a monograph on Bose liquids (1993) and the editor of a well-known book on Bose-Einstein condensation (1995), both published by Cambridge University Press.

Preface
Overview and introduction
Historical overview of Bose superfluids
Summary of chapters
Condensate dynamics at T = 0
Gross-Pitaevskii (GP) equation
Bogoliubov equations for condensate fluctuations
Coupled equations for the condensate and thermal cloud
Generalized GP equation for the condensate
Boltzmann equation for the noncondensate atoms
Solutions in thermal equilibrium
Region of validity of the ZNG equations
Green's functions and self-energy approximations
Overview of Green's function approach
Nonequilibrium Green's functions in normal systems
Green's functions in a Bose-condensed gas
Classification of self-energy approximations
Dielectric formalism
The Beliaev and the time-dependent HFB approximations
Hartree-Fock-Bogoliubov self-energies
Beliaev self-energy approximation
Beliave as time-dependent HFB
Density response in the Beliaev-Popov approximation
Kadanoff-Baym derivation of the ZNG equations
Kadanoff-Baym formalism for Bose superfluids
Hartree-Fock-Bogoliubov equations
Derivation of a kinetic equation with collisions
Collision integrals in the Hartree-Fock approximation
Generalized GP equation
Linearized collision integrals in collisionless theories
Kinetic equation for Bogoliubov thermal excitations
Generalized kinetic equation
Kinetic equation in the Bogoliubov-Popov approximation
Comments on improved theory
Static thermal cloud approximation
Condensate collective modes at finite temperatures
Phenomenological GP equations with dissipation
Relation to Pitaevskii's theory of superfluid relaxation
Vortices and vortex lattices at finite temperatures
Rotating frames of reference: classical treatment
Rotating frames of reference: quantum treatment
Transformation of the kinetic equation
Zaremba-Nikuni-Griffin equations in a rotating frame
Stationary states
Stationary vortex states at zero temperature
Equilibrium vortex state at finite temperatures
Nonequilibrium vortex states
Dynamics at finite temperatures using the moment method
Bose gas above TBEC
Scissors oscillations in a two-component superfluid
The moment of inertia and superfluid response
Numerical simulation of the ZNG equations
The generalized Gross-Pitaevskii equation
Collisionless particle evolution
Collisions
Self-consistent equilibrium properties
Equilibrium collision rates
Simulation of collective modes at finite temperature
Equilibration
Dipole oscillations
Radial breathing mode
Scissors mode oscillations
Quadrupole collective modes
Transverse breathing mode
Landau damping in trapped Bose-condensed gases
Landau damping in a uniform Bose gas
Landau damping in a trapped Bose gas
Numerical results for Landau damping
Landau's theory of superfluidity
History of two-fluid equations
First and second sound
Dynamic structure factor in the two-fluid region
Two-fluid hydrodynamics in a dilute Bose gas
Equations of motion for local equilibrium
Equivalence to the Landau two-fluid equations
First and second sound in a Bose-condensed gas
Hydrodynamic modes in a trapped normal Bose gas
Variational formulation of the Landau two-fluid equations
Zilsel's variational formulation
The action integral for two-fluid hydrodynamics
Hydrodynamic modes in a trapped gas
Two-fluid modes in the BCS-BEC crossover at unitarity
The Landau-Khalatnikov two-fluid equations
The Chapman-Enskog solution of the kinetic equation
Deviation from local equilibrium
Equivalence to Landau-Khalatnikov two-fluid equations
The C12 collisions and the second viscosity coefficients
Transport coefficients and relaxation times
Transport coefficients in trapped Bose gases
Relaxation times for the approach to local equilibrium
Kinetic equations versus Kubo formulas
General theory of damping of hydrodynamic modes
Review of coupled equations for hydrodynamic modes
Normal mode frequencies
General expression for damping of hydrodynamic modes
Hydrodynamic damping in a normal Bose gas
Hydrodynamic damping in a superfluid Bose gas
Monte Carlo calculation of collision rates
Evaluation of transport coefficients: technical details
Frequency-dependent transport coefficients
Derivation of hydrodynamic damping formula
References
Index