6,743 research outputs found
VARs with Mixed Roots Near Unity
Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity -- in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.Common roots, Local to unity, Mildly explosive, Mixed roots, Model selection, Persistence, Tests of common roots
Finite temperature phase diagram of a spin-polarized ultracold Fermi gas in a highly elongated harmonic trap
We investigate the finite temperature properties of an ultracold atomic Fermi
gas with spin population imbalance in a highly elongated harmonic trap.
Previous studies at zero temperature showed that the gas stays in an exotic
spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid
state at the trap center; while moving to the edge, the system changes into
either a non-polarized Bardeen-Cooper-Schriffer superfluid () or a fully
polarized normal gas (), depending on the smallness of the spin
polarization , relative to a critical value . In this work, we show how
these two phase-separation phases evolve with increasing temperature, and
thereby construct a finite temperature phase diagram. For typical interactions,
we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy
temperature, which seems to be accessible in the current experiment. The
density profile, equation of state, and specific heat of the polarized system
have been calculated and discussed in detail. Our results are useful for the
on-going experiment at Rice University on the search for FFLO states in
quasi-one-dimensional polarized Fermi gases.Comment: 9 pages and 8 figures; Published version in Phys. Rev.
Exact few-body results for strongly correlated quantum gases in two dimensions
The study of strongly correlated quantum gases in two dimensions has
important ramifications for understanding many intriguing pheomena in solid
materials, such as high- superconductivity and the fractional quantum
Hall effect. However, theoretical methods are plagued by the existence of
significant quantum fluctuations. Here, we present two- and three-body exact
solutions for both fermions and bosons trapped in a two-dimensional harmonic
potential, with an arbitrary -wave scattering length. These few-particle
solutions link in a natural way to the high-temperature properties of
many-particle systems via a quantum virial expansion. As a concrete example,
using the energy spectrum of few fermions, we calculate the second and third
virial coefficients of a strongly interacting Fermi gas in two dimensions, and
consequently investigate its high-temperature thermodynamics. Our thermodynamic
results may be useful for ongoing experiments on two-dimensional Fermi gases.
These exact results also provide an unbiased benchmark for quantum Monte Carlo
simulations of two-dimensional Fermi gases at high temperatures.Comment: 11 pages, 6 figure
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