3,504 research outputs found
Quantum scattering in one dimension
A self-contained discussion of nonrelativistic quantum scattering is
presented in the case of central potentials in one space dimension, which will
facilitate the understanding of the more complex scattering theory in two and
three dimensions. The present discussion illustrates in a simple way the
concept of partial-wave decomposition, phase shift, optical theorem and
effective-range expansion.Comment: 8 page
Conditions for the Thermal Instability in the Galactic Centre Mini-spiral region
We explore the conditions for the thermal instability to operate in the
mini-spiral region of the Galactic centre (Sgr A*), where both the hot and cold
media are known to coexist. The photoionisation Cloudy calculations are
performed for different physical states of plasma. We neglect the dynamics of
the material and concentrate on the study of the parameter ranges where the
thermal instability may operate, taking into account the past history of Sgr A*
bolometric luminosity. We show that the thermal instability does not operate at
the present very low level of the Sgr A* activity. However, Sgr A* was much
more luminous in the past. For the highest luminosity states the two-phase
medium can be created up to 1.4 pc from the centre. The presence of dust grains
tends to suppress the instability, but the dust is destroyed in the presence of
strong radiation field and hot plasma. The clumpiness is thus induced in the
high activity period, and the cooling/heating timescales are long enough to
preserve later the past multi-phase structure. The instability enhances the
clumpiness of the mini-spiral medium and creates a possibility of episodes of
enhanced accretion of cold clumps towards Sgr A*. The mechanism determines the
range of masses and sizes of clouds; under the conditions of Sgr A*, the likely
values come out - for the cloud typical mass.Comment: Accepted for publication in MNRAS, 10 pages, 7 figure
Efimov states in asymmetric systems
The conditions for occurrence of the Efimov effect is briefly described using
hyperspherical coordinates. The strength of the effective hyperradial
potential appearing for two or three large scattering lengths is
computed and discussed as function of two independent mass ratios of the three
constituent particles. The effect is by far most pronounced for asymmetric
systems with three very different masses. One Efimov state may by chance appear
in nuclei. Many states could be present for systems with one electron and two
neutral atoms or molecules. Estimates of the number of states and their sizes
and energies are given.Comment: 7 pages, 3 figure
Quantum Size Effect and Biased Diffusion of Gravitationally Bound Neutrons in a Rough Waveguide
A comprehensive theory of gravitational quantum states of ultracold neutrons in a rough waveguide is presented. The theory covers recent experiments in which the ultracold neutrons were beamed between a mirror and a rough scatterer and absorber. The results are in very good agreement with experimental data. The analysis is based on a recently developed theory of quantum transport in waveguides with rough absorbing and scattering walls. The calculation is done using two methods: an exact transport equation and a simplified model of biased scattering-driven diffusion of neutrons between quantum states. Both sets of results are in excellent agreement with each other. The exit neutron count is sensitive to the amplitude and the correlation radius (lateral size) of surface inhomogeneities and to the overall time of flight (length of the waveguide). The results indicate that it is possible to choose the waveguide parameters in such a way so to observe the quantum size effect in neutron count—the quantum steps that correspond to individual quantum states—even in a weak roughness regime. Away from the obvious limiting cases, the results are not very sensitive to the ratio of the particle energy to the absorption threshold. The main unresolved issue, which is related to a complexity of required calculations for a “real” experimental cell, is the lack of accurate information on the occupation numbers of neutrons entering the waveguide. Our analysis indicates that the initial occupancies of all gravitational states are expected to be the same except for the smallest values of the waveguide width
Weakly bound atomic trimers in ultracold traps
The experimental three-atom recombination coefficients of the atomic states
Na, Rb and Rb,
together with the corresponding two-body scattering lengths, allow predictions
of the trimer bound state energies for such systems in a trap. The
recombination parameter is given as a function of the weakly bound trimer
energies, which are in the interval for large
positive scattering lengths, . The contribution of a deep-bound state to our
prediction, in the case of Rb, for a particular trap, is
shown to be relatively small.Comment: 5 pages, 1 figur
Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
We study spontaneous symmetry breaking in a system of two parallel
quasi-one-dimensional traps, equipped with optical lattices (OLs) and filled
with a Bose-Einstein condensate (BEC). The cores are linearly coupled by
tunneling. Analysis of the corresponding system of linearly coupled
Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single
GPE split into subgaps. Symmetry breaking in two-component BEC solitons is
studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both
traps; the mixed situation, with repulsion in one trap and attraction in the
other (RA), is considered too. In all the cases, stable asymmetric solitons are
found, bifurcating from symmetric or antisymmetric ones (and destabilizing
them), in the AA and RR systems, respectively. In either case, bi-stability is
predicted, with a nonbifurcating stable branch, either antisymmetric or
symmetric, coexisting with asymmetric ones. Solitons destabilized by the
bifurcation tend to rearrange themselves into their stable asymmetric
counterparts. The impact of a phase mismatch, between the OLs in the two cores
is also studied. Also considered is a related model, for a binary BEC in a
single-core trap with the OL, assuming that the two species (representing
different spin states of the same atom) are coupled by linear interconversion.
In that case, the symmetry-breaking bifurcations in the AA and RR models switch
their character, if the inter-species nonlinear interaction becomes stronger
than the intra-species nonlinearity.Comment: 21 pages + 24 figs, accepted to Phys. Rev.
Scaling limit of virtual states of triatomic systems
For a system with three identical atoms, the dependence of the wave
virtual state energy on the weakly bound dimer and trimer binding energies is
calculated in a form of a universal scaling function. The scaling function is
obtained from a renormalizable three-body model with a pairwise Dirac-delta
interaction. It was also discussed the threshold condition for the appearance
of the trimer virtual state.Comment: 9 pages, 3 figure
Effective Nonlinear Schr\"odinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
In the case of tight transverse confinement (cigar-shaped trap) the
three-dimensional (3D) nonlinear Schr\"odinger equation, describing superfluid
Fermi atoms at unitarity (infinite scattering length ), is
reduced to an effective one-dimensional form by averaging over the transverse
coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger
equation, which produces results in good agreement with the original 3D one. In
the limit of small and large fermion number the nonlinearity is of simple
power-law type. A similar reduction of the 3D theory to a two-dimensional form
is also performed for a tight axial confinement (disk-shaped trap). The
resultant effective 2D nonpolynomial equation also produces results in
agreement with the original 3D equation and has simple power-law nonlinearity
for small and large . For both cigar- and disk-shaped superfluids our
nonpolynomial Schr\"odinger equations are quite attractive for phenomenological
application.Comment: 22 pages, 5 figure
Mean-field description of collapsing and exploding Bose-Einstein condensates
We perform numerical simulation based on the time-dependent mean-field
Gross-Pitaevskii equation to understand some aspects of a recent experiment by
Donley et al. on the dynamics of collapsing and exploding Bose-Einstein
condensates of Rb atoms. They manipulated the atomic interaction by an
external magnetic field via a Feshbach resonance, thus changing the repulsive
condensate into an attractive one and vice versa. In the actual experiment they
changed suddenly the scattering length of atomic interaction from positive to a
large negative value on a pre-formed condensate in an axially symmetric trap.
Consequently, the condensate collapses and ejects atoms via explosion. We find
that the present mean-field analysis can explain some aspects of the dynamics
of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical
Review A, minor changes mad
- …