Phase space spinor amplitudes for spin 1/2 systems

The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-\half is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-\half magnetic dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo

Tungsten resonance integrals and Doppler coefficients Third quarterly report, Jan. - Mar. 1966

Reactivities, Doppler coefficients, and resonance integrals for tungsten isotope

Using error correction to determine the noise model

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction protocol, and c=0.3+/-0.2 using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.Comment: 10 pages, 3 figures. Added discussion section, improved figure

The remittances behaviour of the second generation in Europe: altruism or self-interest?

Whereas most research on remittances focuses on first-generation migrants, the aim of this paper is to investigate the remitting behaviour of the host country-born children of migrants - the second generation - in various European cities. Some important studies found that migrant transnationalism is not only a phenomenon for the first generation, but also apply to the second and higher generations, through, among other things, family visits, elder care, and remittances. At the same time, the maintenance of a strong ethnic identity in the ‘host’ society does not necessarily mean that second-generation migrants have strong transnational ties to their ‘home’ country. The data used in this paper is from “The Integration of the European Second Generation” (TIES) project. The survey collected information on approximately 6,250 individuals aged 18-35 with at least one migrant parent from Morocco, Turkey or former Yugoslavia, in 15 European cities, regrouped in 8 ‘countries’. For the purpose of this paper, only analyses for Austria (Linz and Vienna); Switzerland (Basle and Zurich); Germany (Berlin and Frankfurt); France (Paris and Strasbourg); the Netherlands (Amsterdam and Rotterdam); Spain (Barcelona and Madrid); and Sweden (Stockholm) will be presented.

Development and analysis of the Software Implemented Fault-Tolerance (SIFT) computer

SIFT (Software Implemented Fault Tolerance) is an experimental, fault-tolerant computer system designed to meet the extreme reliability requirements for safety-critical functions in advanced aircraft. Errors are masked by performing a majority voting operation over the results of identical computations, and faulty processors are removed from service by reassigning computations to the nonfaulty processors. This scheme has been implemented in a special architecture using a set of standard Bendix BDX930 processors, augmented by a special asynchronous-broadcast communication interface that provides direct, processor to processor communication among all processors. Fault isolation is accomplished in hardware; all other fault-tolerance functions, together with scheduling and synchronization are implemented exclusively by executive system software. The system reliability is predicted by a Markov model. Mathematical consistency of the system software with respect to the reliability model has been partially verified, using recently developed tools for machine-aided proof of program correctness

Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems

The evolution of local spin polarization in finite systems involves interference phenomena that give rise to {\bf quantum dynamical echoes }and non-ergodic behavior. We predict the conditions to observe these echoes by exploiting the NMR sequences devised by Zhang et al. [Phys. Rev. Lett. {\bf % 69}, 2149 (1992)], which uses a rare $^{13}$C as {\bf local probe }for a dipolar coupled $^1$H spin system. The non-ideality of this probe when testing mesoscopic systems is carefully analyzed revealing the origin of various striking experimental features.Comment: 4 pages, Revtex, 3 Figures available upon reques

Robust Ising Gates for Practical Quantum Computation

I describe the use of techniques based on composite rotations to combat systematic errors in controlled phase gates, which form the basis of two qubit quantum logic gates. Although developed and described within the context of Nuclear Magnetic Resonanace (NMR) quantum computing these sequences should be applicable to any implementation of quantum computation based on Ising couplings. In combination with existing single qubit gates this provides a universal set of robust quantum logic gates.Comment: 3 Pages RevTex4 including 2 figures. Will submit to PR

Magnetic field sensors using 13-spin cat states

Measurement devices could benefit from entangled correlations to yield a measurement sensitivity approaching the physical Heisenberg limit. Building upon previous magnetometric work using pseudo-entangled spin states in solution-state NMR, we present two conceptual advancements to better prepare and interpret the pseudo-entanglement resource as well as the use of a 13-spin cat state to measure the local magnetic field with a sensitivity beyond the standard quantum limit.Comment: 6 pages, 5 figures; v2: corrected figure 3, expanded conclusion, simplified explanation of equation 2; v3: accepted versio

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules which has been incarcerated in the molecular cage of C$_{60}$ and forms endohedral supramolecular complex H$_2$@C$_{60}$. In this confinement hydrogen acquires new properties. Its translational motion becomes quantized and is correlated with its rotations. We applied infrared spectroscopy to study the dynamics of hydrogen isotopologs H$_2$, D$_2$ and HD incarcerated in C$_{60}$. The translational and rotational modes appear as side bands to the hydrogen vibrational mode in the mid infrared part of the absorption spectrum. Because of the large mass difference of hydrogen and C$_{60}$ and the high symmetry of C$_{60}$ the problem is identical to a problem of a vibrating rotor moving in a three-dimensional spherical potential. The translational motion within the C$_{60}$ cavity breaks the inversion symmetry and induces optical activity of H$_2$. We derive potential, rotational, vibrational and dipole moment parameters from the analysis of the infrared absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H$_2$@C$_{60}$. The same parameters were used to predict H$_2$ energies inside C$_{70}$[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We compare the predicted energies and the low temperature infrared absorption spectra of H$_2$@C$_{70}$.Comment: Updated author lis

Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our method can be extended to a system with an arbitrary density of particles. Keywords: ASEP, Bethe Ansatz, Dynamical Exponent, Spectral Gap