81 research outputs found
One-dimensional Bose chemistry: effects of non-integrability
Three-body collisions of ultracold identical Bose atoms under tight
cylindrical confinement are analyzed. A Feshbach resonance in two-body
collisions is described by a two-channel zero-range interaction. Elimination of
the closed channel in the three-body problem reduces the interaction to a
one-channel zero-range one with an energy dependent strength. The related
problem with an energy independent strength (the Lieb-Liniger-McGuire model)
has an exact solution and forbids all chemical processes, such as three-atom
association and diatom dissociation, as well as reflection in atom-diatom
collisions. The resonant case is analyzed by a numerical solution of the
Faddeev-Lovelace equations. The results demonstrate that as the internal
symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and
chemical reactions become allowed and may be observed in experiments.Comment: 5 pages, 4 figure
Quantum Transparency of Barriers for Structure Particles
Penetration of two coupled particles through a repulsive barrier is
considered. A simple mechanism of the appearance of barrier resonances is
demonstrated that makes the barrier anomalously transparent as compared to the
probability of penetration of structureless objects. It is indicated that the
probabilities of tunnelling of two interacting particles from a false vacuum
can be considerably larger than it was assumed earlier.Comment: Revtex, 4 pages, 4 figure
Berry phase in magnetic systems with point perturbations
We study a two-dimensional charged particle interacting with a magnetic
field, in general non-homogeneous, perpendicular to the plane, a confining
potential, and a point interaction. If the latter moves adiabatically along a
loop the state corresponding to an isolated eigenvalue acquires a Berry phase.
We derive an expression for it and evaluate it in several examples such as a
homogeneous field, a magnetic whisker, a particle confined at a ring or in
quantum dots, a parabolic and a zero-range one. We also discuss the behavior of
the lowest Landau level in this setting obtaining an explicit example of the
Wilczek-Zee phase for an infinitely degenerated eigenvalue.Comment: LaTeX, 26 page
On spin evolution in a time-dependent magnetic field: post-adiabatic corrections and geometric phases
We examine both quantum and classical versions of the problem of spin
evolution in a slowly varying magnetic field. Main attention is given to the
first- and second-order adiabatic corrections in the case of in-plane
variations of the magnetic field. While the first-order correction relates to
the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the
second-order correction is shown to be responsible for the next-order geometric
phase and in-plain deflection. A comparison between different approaches,
including the exact (non-adiabatic) geometric phase, is presented.Comment: 10 pages, 1 figure, to appear in Phys. Lett.
Topological spin transport of photons: the optical Magnus Effect and Berry Phase
The paper develops a modified geometrical optics (GO) of smoothly
inhomogeneous isotropic medium, which takes into account two topological
phenomena: Berry phase and the optical Magnus effect. By using the analogy
between a quasi-classical motion of a quantum particle with a spin and GO of an
electromagnetic wave in smoothly inhomogeneous media, we have introduced the
standard gauge potential associated with the degeneracy in the wave momentum
space. This potential corresponds to the Dirac-monopole-like field (Berry
curvature), which causes the topological spin (polarization) transport of
photons. The deviations of waves of right-hand and left-hand helicity occur in
the opposite directions and orthogonally to the principal direction of motion.
This produces a spin current directed across the principal motion. The
situation is similar to the anomalous Hall effect for electrons. In addition, a
simple scheme of the experiment allowing one to observe the topological spin
splitting of photons has been suggested.Comment: 4 pages, 1 figur
Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
Equation for evolution of the four-component Stokes vector in weakly
anisotropic and smoothly inhomogeneous media is derived on the basis of
quasi-isotropic approximation of the geometrical optics method, which provides
consequent asymptotic solution of Maxwell equations. Our equation generalizes
previous results, obtained for the normal propagation of electromagnetic waves
in stratified media. It is valid for curvilinear rays with torsion and is
capable to describe normal modes conversion in the inhomogeneous media.
Remarkably, evolution of the Stokes vector is described by the
Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the
equation for the three-component Stokes vector resembles the Landau-Lifshitz
equation for spin precession in ferromegnetic systems. General theory is
applied for analysis of polarization evolution in a magnetized plasma. We also
emphasize fundamental features of the non-Abelian polarization evolution in
anisotropic inhomogeneous media and illustrate them by simple examples.Comment: 16 pages, 3 figures, to appear in J. Opt. Soc. Am.
New representation of orbital motion with arbitrary angular momenta
A new formulation is presented for a variational calculation of -body
systems on a correlated Gaussian basis with arbitrary angular momenta. The
rotational motion of the system is described with a single spherical harmonic
of the total angular momentum , and thereby needs no explicit coupling of
partial waves between particles. A simple generating function for the
correlated Gaussian is exploited to derive the matrix elements. The formulation
is applied to various Coulomb three-body systems such as , and up to in order to show its usefulness and
versatility. A stochastic selection of the basis functions gives good results
for various angular momentum states.Comment: Revte
Berry Phase of a Resonant State
We derive closed analytical expressions for the complex Berry phase of an
open quantum system in a state which is a superposition of resonant states and
evolves irreversibly due to the spontaneous decay of the metastable states. The
codimension of an accidental degeneracy of resonances and the geometry of the
energy hypersurfaces close to a crossing of resonances differ significantly
from those of bound states. We discuss some of the consequences of these
differences for the geometric phase factors, such as: Instead of a diabolical
point singularity there is a continuous closed line of singularities formally
equivalent to a continuous distribution of `magnetic' charge on a diabolical
circle; different classes of topologically inequivalent non-trivial closed
paths in parameter space, the topological invariant associated to the sum of
the geometric phases, dilations of the wave function due to the imaginary part
of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure
Accidental Degeneracy and Berry Phase of Resonant States
We study the complex geometric phase acquired by the resonant states of an
open quantum system which evolves irreversibly in a slowly time dependent
environment. In analogy with the case of bound states, the Berry phase factors
of resonant states are holonomy group elements of a complex line bundle with
structure group C*. In sharp contrast with bound states, accidental
degeneracies of resonances produce a continuous closed line of singularities
formally equivalent to a continuous distribution of "magnetic" charge on a
"diabolical" circle, in consequence, we find different classes of topologically
inequivalent non-trivial closed paths in parameter space.Comment: 23 pages, 2 Postscript figures, LaTex, to be published in: Group 21:
Symposium on Semigroups and Quantum Irreversibility (Proc. of the XXI Int.
Colloquium on Group Theoretical Methods in Physics
The explanation of unexpected temperature dependence of the muon catalysis in solid deuterium
It is shown that due to the smallness of the inelastic cross-section of the
-atoms scattering in the crystal lattice at sufficiently low temperatures
the -mesomolecules formation from the upper state of the hyperfine
structure starts earlier than the mesoatoms thermolization. It
explains an approximate constancy of the -mesomolecule formation rate in
solid deuterium.Comment: 6 pages, 2 jpeg-figure
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