States and Structure of von Neumann Algebras

We summarize and deepen recent results on the interplay between properties of states and the structure of von Neumann algebras. We treat Jauch–Piron states and the concept of independence in noncommutative probability theory.     

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k 3) of the annihilation operator of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Entanglement and the factorization-approximation

For a bi-partite quantum system defined in a finite dimensional Hilbert-space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement-operator, which is then shown to represent a non-conserved property for any bi-partite system and any type of interaction. This general relation does not exclude the existence of special initial product states, for which the entanglement remains small over some period of time, despite interactions. For this case we derive an approximation to the full Schr?dinger-equation, which allows the treatment of the composite systems in terms of product states. The induced error is estimated. In this factorization-approximation one subsystem appears as an effective potential for the other. A pertinent example is the Jaynes-Cummings model, which then reduces to the semi-classical rotating wave approximation. Received 8 June 2001     

Kinematically complete final state investigations of molecular photodissociation: two- and three-body decay of laser-prepared H 3 3 s ? 2 A 1 '

We have performed kinematically complete investigations of molecular photodissociation of triatomic hydrogen in a fast beam translational spectrometer recently built in Freiburg. The apparatus allows us to investigate laser-induced dissociation of neutral molecules into two, three, or more neutral products. The fragments are detected in coincidence and their vectorial momenta in the center-of-mass frame are determined. We demonstrate the potential of the method at the fragmentation of the 3 s ² A ₁ ^′ ( N = 1, K = 0) state of triatomic hydrogen. In this state, three-body decay into ground state hydrogen atoms H+H+H, two-body predissociation into H+H ₂ (v , J), and photoemission to the H ₃ ground state surface with subsequent two-body decay are competing channels. In the case of two-body predissociation, we determine the rovibrational population in the H ₂ (v , J) fragment. The vibrational distribution of H ₂ is compared with approximate theoretical predictions. For three-body decay, we measure the six-fold differential photodissociation cross-section. To determine accurate final state distributions, the geometric collection efficiency of the apparatus is calculated by a Monte Carlo simulation, and the raw data are corrected for apparatus efficiency. The final state momentum distribution shows pronounced correlation patterns which are characteristic for the dissociation mechanism. For a three-body decay process with a discrete kinetic energy release we have developed a novel data reduction procedure based on the detection of two fragments. The final state distribution determined by this independent method agrees extremely well with that observed in the triple-coincidence data. In addition, this method allows us to fully explore the phase space of the final state and to determine the branching ratios between the two- and three-body decay processes. Received 29 March 2001     

Quantum structures in traveling-wave spontaneous parametric down-conversion

We analyze theoretically spatial structures appearing in the far diffraction zone of the electromagnetic field emitted in the cavityless parametric down-conversion. We investigate in detail the spatial correlation functions of intensity and demonstrate the existence of strong quantum correlations between the regions of the far field symmetrical with respect to the optical axis. Our simplified model allows us to obtain analytical results for some limiting cases. We demonstrate that in the limit of small diffraction and ideal quantum efficiency of photodetection the noise reduction in the photocurrent difference between symmetrical regions in the far diffraction field becomes complete at zero frequency of photocurrent fluctuations. Received 5 February 2001 and Received in final form 11 April 2001     

Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a and determine their coordinate and their Bargmann representation. The eigenkets of the creation operator are ultrasingular and cannot be considered as a limiting case of normalizable states. Applications of these eigenstates as auxiliary states for purposes of representation of states by path integrals over coherent states are discussed. A completeness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered. Received 9 March 2001 and Received in final form 13 June 2001     

Electronic structures in coupled two quantum dots by 3D-mesh Hartree-Fock-Kohn-Sham calculation

To study the electronic structures of quantum dots in the framework of self-interaction-free including three dimensional effects, we adopt the theory of nonlocal effective potential introduced by Kohn and Sham [#!ks65!#]. For utilizing the advantageous point of the real space (3D) mesh method to solve the original nonlinear and nonlocal Hartree-Fock-Kohn-Sham (HFKS)-equation, we introduce a linearization of the equation in the local form by introducing the local Coulomb potentials which depend on explicitly the two single particle states. In practice, for solving the local form HFKS-equation, we use the Car-Parrinello-like relaxation method and the Coulomb potentials are obtained by solving the Poisson equation under proper boundary conditions. Firstly the observed energy gap between triplet- and singlet-states of N = 4 in DBS [#!tarucha96!#] is discussed to reproduce the addition energies and chemical potentials depending the magnetic field. Next the coupling between two-quantum dots in TBS [#!aht97!#] is studied by adding the square barrier between two dots. The spin-degeneracy [#!aht97!#] measured in gate-voltage depending on magnetic field is well reproduced in the limit of small mismatch. Finally, the electronic states in the ring structure are calculated and discussed how the ring size and magnetic field affect to the structures. Received 30 November 2000     

Electronic structure and magnetism of disordered bcc Fe alloys

We study the electronic structure and magnetic properties of disordered bcc Co_xFe_1-x, Cr_xFe_1-x and Mn_xFe_1-x alloys in their ferromagnetic phases using the Augmented Space Recursion (ASR) technique coupled with the tight-binding linearized muffin tin orbital (TB-LMTO) method. We calculate the density of states and magnetic moment of these alloys to show the variation upon alloying Fe with the other neighbouring 3d transition metals using arguments based on charge transfer, exchange splitting and hybridization effects. Received 10 April 2001 and Received in final form 15 August 2001