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

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

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

A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.Comment: 15 pages (Latex), 3 epsi figures, to appear in PhysRev B, 55 Nr. 20 (1997

Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules

Mechanisms of whispering-gallery (WG) modes coupling in microdisk photonic molecules (PMs) with slight and significant size mismatch are numerically investigated. The results reveal two different scenarios of modes interaction depending on the degree of this mismatch and offer new insight into how PM parameters can be tuned to control and modify WG-modes wavelengths and Q-factors. From a practical point of view, these findings offer a way to fabricate PM microlaser structures that exhibit low thresholds and directional emission, and at the same time are more tolerant to fabrication errors than previously explored coupled-cavity structures composed of identical microresonators.Comment: 3 pages with 5 figures (to appear in Opt. Lett. 2007

Orbital Magnetism in Small Quantum Dots with Closed Shells

It is found that various kind of shell structure which occurs at specific values of the magnetic field leads to the disappearance of the orbital magnetization for particular magic numbers of small quantum dots with an electron number $A < 30$.Comment: 4 pages, latex file, four figures as postscript files, to appear at JETP Letters, December 199

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

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

Observation of extremely slow hole spin relaxation in self-assembled quantum dots

We report the measurement of extremely slow hole spin relaxation dynamics in small ensembles of self-assembled InGaAs quantum dots. Individual spin orientated holes are optically created in the lowest orbital state of each dot and read out after a defined storage time using spin memory devices. The resulting luminescence signal exhibits a pronounced polarization memory effect that vanishes for long storage times. The hole spin relaxation dynamics are measured as a function of external magnetic field and lattice temperature. We show that hole spin relaxation can occur over remarkably long timescales in strongly confined quantum dots (up to ~270 us), as predicted by recent theory. Our findings are supported by calculations that reproduce both the observed magnetic field and temperature dependencies. The results suggest that hole spin relaxation in strongly confined quantum dots is due to spin orbit mediated phonon scattering between Zeeman levels, in marked contrast to higher dimensional nanostructures where it is limited by valence band mixing.Comment: Published by Physical Review