29 research outputs found
Exceptional Points in Atomic Spectra
We report the existence of exceptional points for the hydrogen atom in
crossed magnetic and electric fields in numerical calculations. The resonances
of the system are investigated and it is shown how exceptional points can be
found by exploiting characteristic properties of the degeneracies, which are
branch point singularities. A possibility for the observation of exceptional
points in an experiment with atoms is proposed.Comment: 4 pages, 4 figures, 1 table, to be published in Physical Review
Letter
Signatures of the classical transition state in atomic quantum spectra
We perform quantum mechanically exact calculations of resonances in the
spectrum of the hydrogen atom in crossed external fields and establish a close
connection between the classical transition state in phase space and features
in the quantum spectrum. By varying the external field strengths, structures
are revealed which are surprisingly similar to the quantized energy levels of
the classical electron motion in the vicinity of the saddle point obtained with
an approximation of the potential. The results give clear evidence for
signatures of the transition state in quantum spectra.Comment: 5 pages, 4 figures, 1 table, one reference was adde
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
Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility
We propose an analysis technique for the exceptional points (EPs) occurring
in the discrete spectrum of open quantum systems (OQS), using a semi-infinite
chain coupled to an endpoint impurity as a prototype. We outline our method to
locate the EPs in OQS, further obtaining an eigenvalue expansion in the
vicinity of the EPs that gives rise to characteristic exponents. We also report
the precise number of EPs occurring in an OQS with a continuum described by a
quadratic dispersion curve. In particular, the number of EPs occurring in a
bare discrete Hamiltonian of dimension is given by ; if this discrete Hamiltonian is then coupled to continuum
(or continua) to form an OQS, the interaction with the continuum generally
produces an enlarged discrete solution space that includes a greater number of
EPs, specifically , in which
is the number of (non-degenerate) continua to which the discrete sector is
attached. Finally, we offer a heuristic quantum phase transition analogy for
the emergence of the resonance (giving rise to irreversibility via exponential
decay) in which the decay width plays the role of the order parameter; the
associated critical exponent is then determined by the above eigenvalue
expansion.Comment: 16 pages, 7 figure
The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
The nonlinear Schroedinger equation is studied for a periodic sequence of
delta-potentials (a delta-comb) or narrow Gaussian potentials. For the
delta-comb the time-independent nonlinear Schroedinger equation can be solved
analytically in terms of Jacobi elliptic functions and thus provides useful
insight into the features of nonlinear stationary states of periodic
potentials. Phenomena well-known from classical chaos are found, such as a
bifurcation of periodic stationary states and a transition to spatial chaos.
The relation of new features of nonlinear Bloch bands, such as looped and
period doubled bands, are analyzed in detail. An analytic expression for the
critical nonlinearity for the emergence of looped bands is derived. The results
for the delta-comb are generalized to a more realistic potential consisting of
a periodic sequence of narrow Gaussian peaks and the dynamical stability of
periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy
Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss
A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results
Saccharosefolgechemie. Teilvorhaben 4a: Herstellung von Tensiden durch reduktive Aminierung von Zuckern Abschlussbericht
SIGLEAvailable from TIB Hannover: F01B1142 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Ernaehrung, Landwirtschaft und Forsten, Bonn (Germany)DEGerman