676 research outputs found
Proof of Bose-Einstein Condensation for Dilute Trapped Gases
The ground state of bosonic atoms in a trap has been shown experimentally to
display Bose-Einstein condensation (BEC). We prove this fact theoretically for
bosons with two-body repulsive interaction potentials in the dilute limit,
starting from the basic Schroedinger equation; the condensation is 100% into
the state that minimizes the Gross-Pitaevskii energy functional. This is the
first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To
appear in Phys. Rev. Let
Von Neumann's Quantization of General Relativity
Von Neumann's procedure is applied for quantization of General Relativity. We
quantize the initial data of dynamical variables at the Planck epoch, where the
Hubble parameter coincides with the Planck mass. These initial data are defined
via the Fock simplex in the tangent Minkowskian space-time and the Dirac
conformal interval. The Einstein cosmological principle is applied for the
average of the spatial metric determinant logarithm over the spatial volume of
the visible Universe. We derive the splitting of the general coordinate
transformations into the diffeomorphisms (as the object of the second N\"other
theorem) and the initial data transformations (as objects of the first N\"other
theorem). Following von Neumann, we suppose that the vacuum state is a quantum
ensemble. The vacuum state is degenerated with respect to quantum numbers of
non-vacuum states with the distribution function that yields the Casimir effect
in gravidynamics in analogy to the one in electrodynamics. The generation
functional of the perturbation theory in gravidynamics is given as a solution
of the quantum energy constraint. We discuss the region of applicability of
gravidynamics and its possible predictions for explanation of the modern
observational and experimental data.Comment: 14 pages, updated version with extended discussio
Dilute Fermi gas: kinetic and interaction energies
A dilute homogeneous 3D Fermi gas in the ground state is considered for the
case of a repulsive pairwise interaction. The low-density (dilution) expansions
for the kinetic and interaction energies of the system in question are
calculated up to the third order in the dilution parameter. Similar to the
recent results for a Bose gas, the calculated quantities turn out to depend on
a pairwise interaction through the two characteristic lengths: the former, ,
is the well-known s-wave scattering length, and the latter, , is related to
by , where stands for the fermion mass.
To take control of the results, calculations are fulfilled in two independent
ways. The first involves the Hellmann-Feynman theorem, taken in conjunction
with a helpful variational theorem for the scattering length. This way is used
to derive the kinetic and interaction energies from the familiar low-density
expansion of the total system energy first found by Huang and Yang. The second
way operates with the in-medium pair wave functions. It allows one to derive
the quantities of interest``from the scratch'', with no use of the total
energy. An important result of the present investigation is that the pairwise
interaction of fermions makes an essential contribution to their kinetic
energy. Moreover, there is a complicated and interesting interplay of these
quantities
Theory of superfluidity and drag force in the one-dimensional Bose gas
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher
spatial dimensions, the existence of non-classical rotational inertia is not
directly linked to the dissipationless motion of infinitesimal impurities.
Recently, experimental tests with ultracold atoms have begun and quantitative
predictions for the drag force experienced by moving obstacles have become
available. This topical review discusses the drag force obtained from linear
response theory in relation to Landau's criterion of superfluidity. Based upon
improved analytical and numerical understanding of the dynamical structure
factor, results for different obstacle potentials are obtained, including
single impurities, optical lattices and random potentials generated from
speckle patterns. The dynamical breakdown of superfluidity in random potentials
is discussed in relation to Anderson localization and the predicted
superfluid-insulator transition in these systems.Comment: 17 pages, 12 figures, mini-review prepared for the special issue of
Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold
Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and
Drummon
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