3,559 research outputs found
On the Thermodynamic Limit of the Lipkin Model
The thermodynamic limit of the Lipkin model is investigated. While the limit
turns out to be rather elusive, the analysis gives strong indications that the
limit yields two analytically dissociated operators, one for the normal and one
for the deformed phase. While the Lipkin Hamiltonian is hermitian and has a
second order phase transition in finite dimensions (finite particle number),
both properties seem to be destroyed in the thermodynamic limit.Comment: 9 pages, 3 figures to appear in JPhys
Resonance scattering and singularities of the scattering function
Recent studies of transport phenomena with complex potentials are explained
by generic square root singularities of spectrum and eigenfunctions of
non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that
such singularities produce a significant effect upon the pole behaviour of the
scattering matrix, and more significantly upon the associated residues. This
mechanism explains why by proper choice of the system parameters the resonance
cross section is increased drastically in one channel and suppressed in the
other channel.Comment: 4 pages, 3 figure
Chirality of wave functions for three coalescing levels
The coalescence of three levels has particular attractive features. Even
though it may be difficult to realise such event in the laboratory (three
additional real parameters must be adjusted), to take up the challenge seems
worthwhile. In the same way as the chiral behaviour of a usual EP can give a
direction on a line, the state vectors in the vicinity of an EP3 provide an
orientation in the plane. The distinction between left and right handedness
depends on the distribution of the widths of the three levels in the vicinity
of the point of coalescence.Comment: Manuscript has been discussed in June 2007 with the experimental
group under Professor Achim Richter at the TU Darmstadt. It has been
presented at the 6th International Workshop on Pseudo Hermitian Hamiltonians,
London, 16-18 July 2007. An expanded version is being prepared for
publication. 3 Figures, 11 page
Chaos in Axially Symmetric Potentials with Octupole Deformation
Classical and quantum mechanical results are reported for the single particle
motion in a harmonic oscillator potential which is characterized by a
quadrupole deformation and an additional octupole deformation. The chaotic
character of the motion is srongly dependent on the quadrupole deformation in
that for a prolate deformation virtually no chaos is discernible while for the
oblate case the motion shows strong chaos when the octupole term is turned on.Comment: 6 pages LaTex plus 4 figures available by contacting the authors
directly, published in PHYS.REV.LETT. 72(1994) 235
Instabilities, nonhermiticity and exceptional points in the cranking model
A cranking harmonic oscillator model, widely used for the physics of fast
rotating nuclei and Bose-Einstein condensates, is re-investigated in the
context of PT-symmetry. The instability points of the model are identified as
exceptional points. It is argued that - even though the Hamiltonian appears
hermitian at first glance - it actually is not hermitian within the region of
instability.Comment: 4 pages, 1 figur
Deformation of Quantum Dots in the Coulomb Blockade Regime
We extend the theory of Coulomb blockade oscillations to quantum dots which
are deformed by the confining potential. We show that shape deformations can
generate sequences of conductance resonances which carry the same internal
wavefunction. This fact may cause strong correlations of neighboring
conductance peaks. We demonstrate the relevance of our results for the
interpretation of recent experiments on semiconductor quantum dots.Comment: 4 pages, Revtex, 4 postscript figure
Shell Structures and Chaos in Deformed Nuclei and Large Metallic Clusters
A reflection-asymmetric deformed oscillator potential is analysed from the
classical and quantum mechanical point of view. The connection between
occurrence of shell structures and classical periodic orbits is studied using
the ''removal of resonances method'' in a classical analysis. In this
approximation, the effective single particle potential becomes separable and
the frequencies of the classical trajectories are easily determined. It turns
out that the winding numbers calculated in this way are in good agreement with
the ones found from the corresponding quantum mechanical spectrum using the
particle number dependence of the fluctuating part of the total energy. When
the octupole term is switched on it is found that prolate shapes are stable
against chaos whereas spherical and oblate cases become chaotic. An attempt is
made to explain this difference in the quantum mechanical context by looking at
the distribution of exceptional points which results from the matrix structure
of the respective Hamiltonians. In a similar way we analyse the modified
Nilsson model and discuss its consequences for nuclei and metallic clusters.Comment: to appear in Physica Scripta., CNLS-94-02, a talk given at the Nobel
sponsored conference SELMA 94 "New Nuclear Phenomena in the Vicinity of
Closed Shell" (Stockholm and Uppsala, 29 Aug.- 3 Sept. 1994
Statistical Fluctuations of Electromagnetic Transition Intensities in pf-Shell Nuclei
We study the fluctuation properties of E2 and M1 transition intensities among
T=0,1 states of A = 60 nuclei in the framework of the interacting shell model,
using a realistic effective interaction for pf-shell nuclei with a Ni56 as a
core. It is found that the B(E2) distributions are well described by the
Gaussian orthogonal ensemble of random matrices (Porter-Thomas distribution)
independently of the isobaric quantum number T_z. However, the statistics of
the B(M1) transitions is sensitive to T_z: T_z=1 nuclei exhibit a Porter-Thomas
distribution, while a significant deviation from the GOE statistics is observed
for self-conjugate nuclei (T_z=0).Comment: 8 pages, latex, 3 figures (ps format
- …