Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Coherent Optical Spectroscopy Of Molecules And Molecular Beams

This paper presents our recent work on coherent optical spectroscopy of molecules and molecular beams. The theory for these nonlinear optical effects is summarized and related to the measurements in the gas phase and in the condensed phase. Finally, we discuss the importance of these methods, which disentangle the inhomogeneous optical resonances, in understanding nonradiative and optical dephasing processes

How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

Electron and hole states in quantum-dot quantum wells within a spherical 8-band model

In order to study heterostructures composed both of materials with strongly different parameters and of materials with narrow band gaps, we have developed an approach, which combines the spherical 8-band effective-mass Hamiltonian and the Burt's envelope function representation. Using this method, electron and hole states are calculated in CdS/HgS/CdS/H_2O and CdTe/HgTe/CdTe/H_2O quantum-dot quantum-well heterostructures. Radial components of the wave functions of the lowest S and P electron and hole states in typical quantum-dot quantum wells (QDQWs) are presented as a function of radius. The 6-band-hole components of the radial wave functions of an electron in the 8-band model have amplitudes comparable with the amplitude of the corresponding 2-band-electron component. This is a consequence of the coupling between the conduction and valence bands, which gives a strong nonparabolicity of the conduction band. At the same time, the 2-band-electron component of the radial wave functions of a hole in the 8-band model is small compared with the amplitudes of the corresponding 6-band-hole components. It is shown that in the CdS/HgS/CdS/H_2O QDQW holes in the lowest states are strongly localized in the well region (HgS). On the contrary, electrons in this QDQW and both electron and holes in the CdTe/HgTe/CdTe/H_2O QDQW are distributed through the entire dot. The importance of the developed theory for QDQWs is proven by the fact that in contrast to our rigorous 8-band model, there appear spurious states within the commonly used symmetrized 8-band model.Comment: 15 pages, 5 figures, E-mail addresses: [email protected], [email protected]

Advances of orbital gas tungsten arc welding for Brazilian space applications – experimental setup

The present work describes details of the several steps of the technology involved for the orbital Gas Tungsten Arc Welding (GTAW) process of pure commercially titanium tubes. These pieces will be used to connect the several components of the propulsion system of the China-Brazilian Satellite CBERS, and is part of the Brazilian aerospace industry development. The implantation involved the steps of environment control; cut and facing of the base metal; cleaning procedures; piece alignment; choice of the type, geometry and installation of the tungsten electrode; system for the pressure of the purge gas; manual tack welding; choice of the welding parameters; and, finally, the qualification of welding procedures. Three distinct welding programs were studied, using pulsed current with increasing speed, continuous current and pulsed current with decreasing amperage levels. The results showed that the high quality criteria required to the aerospace segment is such that usual welding operations must be carefully designed and executed. The three welding developed programs generated welds free of defects and with adequate morphology, allowing to select the condition that better fits the Brazilian aerospace segment, and to be implanted in the welding of the CBERS Satellite Propulsion System

Financing SME growth in the UK: meeting the challenges after the global financial crisis

In the aftermath of the Global Financial Crisis new forms of SME finance are emerging in the place of traditional banking and equity finance sources. This Special Issue has its origins in a conference organised in June 2014 by the Centre for Enterprise and Economic Development Research (CEEDR) at Middlesex University Business School, where all but the final two papers were presented. The Conference was designed to provide a timely forum for leading academics, practitioners and policy makers to disseminate current research and practitioner knowledge exploring finance gaps and how best to address the financing needs of small high growth potential businesses

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

We study the non-equilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta-correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which fully confirm the predictions of our analytical calculations, namely noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for very low-energy solitons where the noise-induced phonons also make a significant contribution to the soliton diffusion.Comment: Submitted to PRE. Changes made: New simulations with a different method of soliton detection. The results and conclusions are not different from previous version. New appendixes containing information about the system energy and soliton profile

Generation of a Recombinant Gag Virus-Like-Particle Panel for the Evaluation of p24 Antigen Detection by Diagnostic HIV Tests.

BACKGROUND: Detection of HIV-1 p24 antigen permits early identification of primary HIV infection and timely intervention to limit further spread of the infection. Principally, HIV screening should equally detect all viral variants, but reagents for a standardised test evaluation are limited. Therefore, we aimed to create an inexhaustible panel of diverse HIV-1 p24 antigens. METHODS: We generated a panel of 43 recombinantly expressed virus-like particles (VLPs), containing the structural Gag proteins of HIV-1 subtypes A-H and circulating recombinant forms (CRF) CRF01_AE, CRF02_AG, CRF12_BF, CRF20_BG and group O. Eleven 4th generation antigen/antibody tests and five antigen-only tests were evaluated for their ability to detect VLPs diluted in human plasma to p24 concentrations equivalent to 50, 10 and 2 IU/ml of the WHO p24 standard. Three tests were also evaluated for their ability to detect p24 after heat-denaturation for immune-complex disruption, a pre-requisite for ultrasensitive p24 detection. RESULTS: Our VLP panel exhibited an average intra-clade p24 diversity of 6.7%. Among the 4th generation tests, the Abbott Architect and Siemens Enzygnost Integral 4 had the highest sensitivity of 97.7% and 93%, respectively. Alere Determine Combo and BioRad Access were least sensitive with 10.1% and 40.3%, respectively. Antigen-only tests were slightly more sensitive than combination tests. Almost all tests detected the WHO HIV-1 p24 standard at a concentration of 2 IU/ml, but their ability to detect this input for different subtypes varied greatly. Heat-treatment lowered overall detectability of HIV-1 p24 in two of the three tests, but only few VLPs had a more than 3-fold loss in p24 detection. CONCLUSIONS: The HIV-1 Gag subtype panel has a broad diversity and proved useful for a standardised evaluation of the detection limit and breadth of subtype detection of p24 antigen-detecting tests. Several tests exhibited problems, particularly with non-B subtypes

Volatility of Central Europe Exchange Rates: Reaction to Financial Contagion, and Policy Recommendations for European Union Accession

Examines the volatility of the exchange rates in Central Europe. Role of capital account liberalization and financial market integration in exchange rate stability; Remedies employed to financial problems of each countries; Impact of Asian and Russian financial crises on currencies of Central European countries; Recommendations for European Union accession

Characterization of titanium welded joints by the orbital gas tungsten arc welding process for aerospace application

In this work, three welding programs for orbital gas tungsten arc welding (GTAW), previously developed, were used, using pulsed current and increasing speed (#A), constant current (#B) and pulsed current and decreasing current (#C). One of these should be used for the propulsion system of the Satellite CBERS (China – Brazil Earth Resources Satellite). Welded joints using tubes of commercially pure titanium were obtained with these procedures, which were characterized by means of mechanical and metallographic tests. The obtained results showed that the three welding procedures produce welded joints free of defects and with adequate shape. Although small differences on mechanical properties and on microstructure have been observed, the three welding programs attained compatible results with international standards used in the aerospace segment. The welding program #B, due to the reduced heat input used, was considered to obtain slightly advantage over the others