arXiv subjects

Günter Wunner

Publications and source records attributed to Günter Wunner.

96 records · Page 6Linked to original sources

arXiv2008

Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction

The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscillating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses.

quant-ph↗

arXiv2007

Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction

The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1/r-interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, non-symmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.

nlin.CD↗

arXiv2007

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.

nlin.CD↗

arXiv2006

hbar expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

We extend a theory of first order hbar corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_{4v}-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the hbar expansion method.

nlin.CD↗

arXiv1997

The Hydrogen Atom in Combined Electric and Magnetic Fields with Arbitrary Mutual Orientations

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields. Resonance energies and oscillator strengths are obtained by exact diagonalization of the Hamiltonian in a complete basis set, even far above the ionization threshold. At high excitation energies around the Stark saddle point the eigenenergies exhibit strong level repulsions when the angle between the fields is varied. The large avoided crossings occur between states with the same approximately conserved principal quantum number, n, and this intramanifold mixing of states cannot be explained, not even qualitatively, by conventional perturbation theory. However, it is well reproduced by an extended perturbation theory which takes into account all couplings between the angular momentum and Runge-Lenz vector. The large avoided crossings are interpreted as a quantum manifestation of classical intramanifold chaos. This interpretation is supported by both classical Poincaré surfaces of section, which reveal a mixed regular-chaotic intramanifold dynamics, and the statistical analysis of nearest-neighbor-spacing

quant-ph↗

arXiv1995

PHOTON SPLITTING IN STRONGLY MAGNETIZED COSMIC OBJECTS -- REVISITED

We reassess the importance of photon splitting to spectral formation in cosmic X-ray and $γ$-ray sources with magnetic fields of several $10^{12}$ gauss. Our analysis is based on the recent numerically accurate evaluation of the full relativistic expression for photon splitting at neutron star magnetic field strengths (Mentzel et al. 1994). Using these results we demonstrate that Adler's (1971) widely used approximation formula for photon splitting underestimates the correct splitting rate by {\em several} orders of magnitude, at these magnetic field strengths. Even down at X-ray energies of a few tens of keV magnetic photon splitting is found to be an efficient photon conversion process, producing mean free paths as short as several tens of centimeters for fields on the order of $5 \times 10^{12}$ gauss. We conclude that previous analyses of the contributions of magnetic photon splitting to spectral formation based on Adler's approximation formula are physically unreliable, and, in particular, that photon splitting must be included in realistic modelings of spectra of both strongly magnetized cosmic X-ray and $γ$-ray sources.

astro-ph↗