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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Phase Space Methods for Degenerate Quantum Gases (Hardcover)
Loot Price: R3,793
Discovery Miles 37 930
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Phase Space Methods for Degenerate Quantum Gases (Hardcover)
Series: International Series of Monographs on Physics, 163
Expected to ship within 12 - 17 working days
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Donate to Against Period Poverty
Total price: R3,813
Discovery Miles: 38 130
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Recent experimental progress has enabled cold atomic gases to be
studied at nano-kelvin temperatures, creating new states of matter
where quantum degeneracy occurs - Bose-Einstein condensates and
degenerate Fermi gases. Such quantum states are of macroscopic
dimensions. This book presents the phase space theory approach for
treating the physics of degenerate quantum gases, an approach
already widely used in quantum optics. However, degenerate quantum
gases involve massive bosonic and fermionic atoms, not massless
photons. The book begins with a review of Fock states for systems
of identical atoms, where large numbers of atoms occupy the various
single particle states or modes. First, separate modes are
considered, and here the quantum density operator is represented by
a phase space distribution function of phase space variables which
replace mode annihilation, creation operators, the dynamical
equation for the density operator determines a Fokker-Planck
equation for the distribution function, and measurable quantities
such as quantum correlation functions are given as phase space
integrals. Finally, the phase space variables are replaced by time
dependent stochastic variables satisfying Langevin stochastic
equations obtained from the Fokker-Planck equation, with stochastic
averages giving the measurable quantities. Second, a quantum field
approach is treated, the density operator being represented by a
distribution functional of field functions which replace field
annihilation, creation operators, the distribution functional
satisfying a functional FPE, etc. A novel feature of this book is
that the phase space variables for fermions are Grassmann
variables, not c-numbers. However, we show that Grassmann
distribution functions and functionals still provide equations for
obtaining both analytic and numerical solutions. The book includes
the necessary mathematics for Grassmann calculus and functional
calculus, and detailed derivations of key results are provided.
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