2,553 research outputs found
The physics of exceptional points
A short resume is given about the nature of exceptional points (EPs) followed
by discussions about their ubiquitous occurrence in a great variety of physical
problems. EPs feature in classical as well as in quantum mechanical problems.
They are associated with symmetry breaking for -symmetric
Hamiltonians, where a great number of experiments have been performed in
particular in optics, and to an increasing extent in atomic and molecular
physics. EPs are involved in quantum phase transition and quantum chaos, they
produce dramatic effects in multichannel scattering, specific time dependence
and more. In nuclear physics they are associated with instabilities and
continuum problems. Being spectral singularities they also affect approximation
schemes.Comment: 13 pages, 2 figure
Exceptional Points of Non-hermitian Operators
Exceptional points associated with non-hermitian operators, i.e. operators
being non-hermitian for real parameter values, are investigated. The specific
characteristics of the eigenfunctions at the exceptional point are worked out.
Within the domain of real parameters the exceptional points are the points
where eigenvalues switch from real to complex values. These and other results
are exemplified by a classical problem leading to exceptional points of a
non-hermitian matrix.Comment: 8 pages, Latex, four figures, submitted to EPJ
Phases of Wave Functions and Level Repulsion
Avoided level crossings are associated with exceptional points which are the
singularities of the spectrum and eigenfunctions, when they are considered as
functions of a coupling parameter. It is shown that the wave function of {\it
one} state changes sign but not the other, if the exceptional point is
encircled in the complex plane. An experimental setup is suggested where this
peculiar phase change could be observed.Comment: 4 pages Latex, 2 figures encapsulated postscripts (*.epsi) submitted
to The European Physical Journal
Quantum Chaos, Degeneracies and Exceptional Points
It is argued that, if a regular Hamiltonian is perturbed by a term that
produces chaos, the onset of chaos is shifted towards larger values of the
perturbation parameter if the unperturbed spectrum is degenerate and the
lifting of the degeneracy is of second order in this parameter. The argument is
based on the behaviour of the exceptional points of the full problem.Comment: RevTeX with 4 figs. available from the authors; to appear in
Phys.Rev.
Fano-Feshbach resonances in two-channel scattering around exceptional points
It is well known that in open quantum systems resonances can coalesce at an
exceptional point, where both the energies {\em and} the wave functions
coincide. In contrast to the usual behaviour of the scattering amplitude at one
resonance, the coalescence of two resonances invokes a pole of second order in
the Green's function, in addition to the usual first order pole. We show that
the interference due to the two pole terms of different order gives rise to
patterns in the scattering cross section which closely resemble Fano-Feshbach
resonances. We demonstrate this by extending previous work on the analogy of
Fano-Feshbach resonances to classical resonances in a system of two driven
coupled damped harmonic oscillators.Comment: 8 pages, 5 figures, submitted to J. Phys.
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
Time Reversal and Exceptional Points
Eigenvectors of decaying quantum systems are studied at exceptional points of
the Hamiltonian. Special attention is paid to the properties of the system
under time reversal symmetry breaking. At the exceptional point the chiral
character of the system -- found for time reversal symmetry -- generically
persists. It is, however, no longer circular but rather elliptic.Comment: submitted for publicatio
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