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

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

Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

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

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