3,916 research outputs found
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
Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems
Phase transitions in open quantum systems, which are associated with the
formation of collective states of a large width and of trapped states with
rather small widths, are related to exceptional points of the Hamiltonian.
Exceptional points are the singularities of the spectrum and eigenfunctions,
when they are considered as functions of a coupling parameter. In the present
paper this parameter is the coupling strength to the continuum. It is shown
that the positions of the exceptional points (their accumulation point in the
thermodynamical limit) depend on the particular type and energy dependence of
the coupling to the continuum in the same way as the transition point of the
corresponding phase transition.Comment: 22 pages, 4 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
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
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
Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
A PT-symmetric optically active medium that lases at the threshold gain also
acts as a complete perfect absorber at the laser wavelength. This is because
spectral singularities of PT-symmetric complex potentials are always
accompanied by their time-reversal dual. We investigate the significance of
PT-symmetry for the appearance of these self-dual spectral singularities. In
particular, using a realistic optical system we show that self-dual spectral
singularities can emerge also for non-PT-symmetric configurations. This
signifies the existence of non-PT-symmetric CPA-lasers.Comment: 11 pages, 3 figures, 1 table, accepted for publication in J. Phys.
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