Bose-Einstein condensation and superfluidity / Lev Pitaevskii, Sandro Stringari

Author:: Pitaevskiĭ, L. P. (Lev Petrovich)
Published:: Oxford : Oxford University Press, 2016.
Physical Description:: 1 online resource
Additional Creators:: Stringari, S.

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Machine generated contents note: 1.Introduction -- PART I -- 2.Long-range Order, Symmetry Breaking, and Order Parameter -- 2.1.One-body density matrix and long-range order -- 2.2.Order parameter -- 3.The Ideal Bose Gas -- 3.1.The ideal Bose gas in the grand canonical ensemble -- 3.2.The ideal Bose gas In the box -- 3.3.Fluctuations and two-body density -- 4.Weakly Interacting Bose Gas -- 4.1.Lowest-order approximation: ground state energy and equation of state -- 4.2.Higher-order approximation: excitation spectrum and quantum fluctuations -- 4.3.Particles and elementary excitations -- 5.Nonuniform Bose Gases at Zero Temperature -- 5.1.The Gross--Pitaevskii equation -- 5.2.Thomas--Fermi limit -- 5.3.Vortex line in the weakly interacting Bose gas -- 5.4.Vortex rings -- 5.5.Solitons -- 5.6.Small-amplitude oscillations -- 6.Superfluidity -- 6.1.Landau's criterion of superfluidity -- 6.2.Bose--Einstein condensation and superfluidity -- 6.3.Hydrodynamic theory of superfluids: zero temperature -- 6.4.Quantum hydrodynamics -- 6.5.Beliaev decay of phonons -- 6.6.Two-fluid hydrodynamics: first and second sound -- 6.7.Fluctuations of the phase -- 6.8.Rotation of superfluids -- 7.Linear Response Function -- 7.1.Dynamic structure factor and sum rules -- 7.2.Density response function -- 7.3.Current response function -- 7.4.General inequalities -- 7.5.Response function of the ideal Bose gas -- 7.6.Response function of the weakly interacting Bose gas -- 8.Superfluid 4He -- 8.1.Elementary excitations and dynamic structure factor -- 8.2.Thermodynamic properties -- 8.3.Quantized vortices -- 8.4.Momentum distribution and Bose--Einstein condensation -- 9.Atomic Gases: Collisions and Trapping -- 9.1.Metastability and the role of collisions -- 9.2.Low-energy collisions and scattering length -- 9.3.Low-energy collisions in two dimensions -- 9.4.Zeeman effect and magnetic trapping -- 9.5.Interaction with the radiation field and optical traps -- PART II -- 10.The Ideal Bose Gas in the Harmonic Trap -- 10.1.Condensate fraction and critical temperature -- 10.2.Density of single-particle states and thermodynamics -- 10.3.Density and momentum distribution -- 10.4.Thermodynamic limit -- 10.5.Release of the trap and expansion of the gas -- 10.6.Bose--Einstein condensation in deformed traps -- 10.7.Adiabatic formation of BEC with non-harmonic traps -- 11.Ground State of a Trapped Condensate -- 11.1.An instructive example: the box potential -- 11.2.Interacting condensates in harmonic traps: density and momentum distribution -- 11.3.Energy, chemical potential, and virial theorem -- 11.4.Finite-size corrections to the Thomas--Fermi limit -- 11.5.Beyond-mean-field corrections -- 11.6.Attractive forces -- 12.Dynamics of a Trapped Condensate -- 12.1.Collective oscillations -- 12.2.Repulsive forces and the Thomas--Fermi limit -- 12.3.Sum rule approach: from repulsive to attractive forces -- 12.4.Finite-size corrections to the Thomas--Fermi limit -- 12.5.Beyond-mean-field corrections -- 12.6.Large-amplitude oscillations -- 12.7.Expansion of the condensate -- 12.8.Dynamic structure factor -- 12.9.Collective versus single-particle excitations -- 13.Thermodynamics of a Trapped Bose Gas -- 13.1.Role of interactions, scaling, and thermodynamic limit -- 13.2.The Hartree--Fock approximation -- 13.3.Shift of the critical temperature -- 13.4.Critical region near Tc -- 13.5.Below Tc -- 13.6.Equation of state and density profiles -- 13.7.Collective oscillations at a finite temperature -- 14.Superfluidity and Rotation of a Trapped Bose Gas -- 14.1.Critical velocity of a superfluid -- 14.2.Moment of inertia -- 14.3.Scissors mode -- 14.4.Expanding a rotating condensate -- 14.5.Rotation at higher angular velocities -- 14.6.Quantized vortices -- 14.7.Vortices, angular momentum, and collective oscillations -- 14.8.Stability and precession of the vortex line -- 14.9.Quantized vortices and critical velocity in a toroidal trap -- 15.Coherence, Interference, and the Josephson Effect -- 15.1.Coherence and the one-body density matrix -- 15.2.Interference between two condensates -- 15.3.Double-well potential and the Josephson effect -- 15.4.Quantization of the Josephson equations -- 15.5.Decoherence and phase spreading -- 15.6.Boson Hubbard Hamiltonian -- PART III -- 16.Interacting Fermi Gases and the BCS--BEC Crossover -- 16.1.The ideal Fermi gas -- 16.2.Dilute interacting Fermi gases -- 16.3.The weakly repulsive Fermi gas -- 16.4.Gas of composite bosons -- 16.5.The BCS limit of a weakly attractive gas -- 16.6.Gas at unitarity -- 16.7.The BCS--BEC crossover -- 16.8.The Bogoliubov--de Gennes approach to the BCS--BEC crossover -- 16.9.Equation of state, momentum distribution, and condensate fraction of pairs -- 17.Fermi Gas in the Harmonic Trap -- 17.1.The harmonically trapped ideal Fermi gas -- 17.2.Equation of state and density profiles -- 17.3.Momentum distribution -- 18.Tan Relations and the Contact Parameter -- 18.1.Wave function of a dilute Fermi gas near a Feshbach resonance -- 18.2.Tails of the momentum distribution -- 18.3.Dependence of energy on scattering length -- 18.4.Relation between the energy and the momentum distribution -- 18.5.Static structure factor -- 18.6.The contact of a harmonically trapped gas -- 19.Dynamics and Superfluidity of Fermi Gases -- 19.1.Hydrodynamics at zero temperature: sound and collective oscillations -- 19.2.Expansion of a superfluid Fermi gas -- 19.3.Phonon versus pair-breaking excitations and Landau's critical velocity -- 19.4.Dynamic structure factor -- 19.5.Radiofrequency transitions -- 19.6.Two-fluid hydrodynamics: first and second sound -- 19.7.Rotations and vortices -- 20.Spin-polarized Fermi Gases -- 20.1.Magnetic properties of the weakly repulsive Fermi gas -- 20.2.Superfluidity and magnetization -- 20.3.Phase separation at unitarity -- 20.4.Phase separation in harmonic traps at unitarity -- 20.5.The Fermi polaron -- PART IV -- 21.Quantum Mixtures and Spinor Gases -- 21.1.Mixtures of Bose--Einstein condensates -- 21.2.Spinor Bose--Einstein condensates -- 21.3.Coherently coupled Bose--Einstein condensates -- 21.4.Synthetic gauge fields and spin-orbit coupling -- 21.5.Fermi--Bose mixtures -- 22.Quantum Gases in Optical Lattices -- 22.1.Single-particle properties in an optical lattice -- 22.2.Equilibrium properties of a Bose--Einstein condensate -- 22.3.Localization in one-dimensional quasiperiodic potentials -- 22.4.Equilibrium properties of a Fermi gas in a lattice -- 22.5.Bloch oscillations -- 22.6.Elementary excitations of BEC gases in an optical lattice -- 22.7.Centre-of-mass oscillation of a Fermi gas in an optical lattice -- 22.8.Dimer formation in periodic potentials -- 22.9.Quantum fluctuations in optical lattices and the Bose--Hubbard model -- 23.Quantum Gases in Pancake and Two-dimensional Regimes -- 23.1.From three-dimensional pancakes to the two-dimensional regime -- 23.2.Two-dimensional Bose gas at finite temperatures -- 23.3.Fast-rotating Bose gases and the lowest Landau level regime -- 23.4.Two-dimensional Fermi gas: the BEC--BCS crossover -- 24.Quantum Gases in Cigar and One-dimensional Regimes -- 24.1.Bose gas: from three-dimensional radial cigars to the one-dimensional mean-field regime -- 24.2.Solitons and vortical configurations in cigar traps -- 24.3.Phase fluctuations and long-range behaviour of the off-diagonal one-body density -- 24.4.Lieb--Liniger theory: from the one-dimensional mean field to the Tonks--Girardeau limit -- 24.5.Dynamic structure factor and superfluidity -- 24.6.One-dimensional Fermi gas -- 25.Dipolar Gases -- 25.1.The dipole--dipole force -- 25.2.Harmonic trapping and stability of dipolar BEC gases -- 25.3.Dynamic behaviour of dipolar gases -- 25.4.Dipolar Fermi gases.

Summary:

Ultracold atomic gases is a rapidly developing field of physics that attracts many young researchers around the world. This book gives a comprehensive overview of exciting developments in Bose-Einstein condensation and superfluidity from a theoretical perspective and makes sense of key experiments with a special focus on ultracold atomic gases.

Subject(s):

ISBN:

9780191818721 (ebook)

Bibliography Note:

Includes bibliographical references and index.

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