2,261 research outputs found
The two-body problem of ultra-cold atoms in a harmonic trap
We consider two bosonic atoms interacting with a short-range potential and
trapped in a spherically symmetric harmonic oscillator. The problem is exactly
solvable and is relevant for the study of ultra-cold atoms. We show that the
energy spectrum is universal, irrespective of the shape of the interaction
potential, provided its range is much smaller than the oscillator length.Comment: Final version accepted for publication in Am. Journ. Phy
The virial expansion of a classical interacting system
We consider N particles interacting pair-wise by an inverse square potential
in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically,
its classical canonical partition function for the repulsive regime is known in
the literature. We start by presenting a concise re-derivation of this result.
The equation of state is then calculated both for the trapped and the
homogeneous gas. Finally, the classical limit of Wu's distribution function for
fractional exclusion statistics is obtained and we re-derive the classical
virial expansion of the homogeneous gas using this distribution function.Comment: 9 pages; added references to some earlier work on this problem; this
has led to a significant shortening of the paper and a changed titl
Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
We derive simple analytical expressions for the particle density
and the kinetic energy density for a system of noninteracting
fermions in a dimensional isotropic harmonic oscillator potential. We test
the Thomas-Fermi (TF, or local-density) approximation for the functional
relation using the exact and show that it locally
reproduces the exact kinetic energy density , {\it including the shell
oscillations,} surprisingly well everywhere except near the classical turning
point. For the special case of two dimensions (2D), we obtain the unexpected
analytical result that the integral of yields the {\it
exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio
Chiral symmetry breaking and stability of quark droplets
We discuss the stability of strangelets -- quark droplets with strangeness --
in the Nambu--Jona-Lasinio model supplemented by a boundary condition for quark
confinement. Effects of dynamical chiral symmetry breaking are considered
properly inside quark droplets of arbitrary baryon number. We obtain the energy
per baryon number of quark droplets with baryon number from one to thousands.
It is shown that strangelets are not the ground states as compared with nuclei,
though they can be locally stable
Zeta Function Zeros, Powers of Primes, and Quantum Chaos
We present a numerical study of Riemann's formula for the oscillating part of
the density of the primes and their powers. The formula is comprised of an
infinite series of oscillatory terms, one for each zero of the zeta function on
the critical line and was derived by Riemann in his paper on primes assuming
the Riemann hypothesis. We show that high resolution spectral lines can be
generated by the truncated series at all powers of primes and demonstrate
explicitly that the relative line intensities are correct. We then derive a
Gaussian sum rule for Riemann's formula. This is used to analyze the numerical
convergence of the truncated series. The connections to quantum chaos and
semiclassical physics are discussed
Cost and benefits of intermediate water storage structures: case study of diggies in Rajasthan
Water storageWater deliveryIrrigation schedulingWater controlIrrigation canalsWatercoursesFarmsCrop productionCost benefit analysis
Relativistic Harmonic Oscillator with Spin Symmetry
The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal
scalar and vector harmonic oscillator potentials are derived. Equal scalar and
vector potentials may be applicable to the spectrum of an antinucleion imbedded
in a nucleus. Triaxial, axially deformed, and spherical oscillator potentials
are considered. The spectrum has a spin symmetry for all cases and, for the
spherical harmonic oscillator potential, a higher symmetry analogous to the
SU(3) symmetry of the non-relativistic harmonic oscillator is discussed
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