Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

Generation of macroscopic superposition states with small nonlinearity

We suggest a scheme to generate a macroscopic superposition state (Schrodinger cat state) of a free-propagating optical field using a beam splitter, homodyne measurement, and a very small Kerr nonlinear effect. Our scheme makes it possible to reduce considerably the required nonlinear effect to generate an optical cat state using simple and efficient optical elements.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.

Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

The design of planar gradient coils. Part ll: A weighted superposition method

In this work a superposition technique for designing gradient coils for the purpose of magnetic resonance imaging is outlined, which uses an optimized weight function superimposed upon an initial winding similar to that obtained from the target field method to generate the final wire winding. This work builds on the preliminary work performed in Part I on designing planar insertable gradient coils for high resolution imaging. The proposed superposition method for designing gradient coils results in coil patterns with relatively low inductances and the gradient coils can be used as inserts into existing magnetic resonance imaging hardware. The new scheme has the capacity to obtain images faster with more detail due to the deliver of greater magnetic held gradients. The proposed method for designing gradient coils is compared with a variant of the state-of-the-art target field method for planar gradient coils designs, and it is shown that the weighted superposition approach outperforms the well-known the classical method.

Beyond the sphere of the English facial approximation literature: Ramifications of German papers on western method concepts

In the English literature, facial approximation methods have been commonly classified into three types: Russian, American, or Combination. These categorizations are based on the protocols used, for example, whether methods use average soft-tissue depths (American methods) or require face muscle construction (Russian methods). However, literature searches outside the usual realm of English publications reveal key papers that demonstrate that the Russian category above has been founded on distorted views. In reality, Russian methods are based on limited face muscle construction, with heavy reliance on modified average soft-tissue depths. A closer inspection of the American method also reveals inconsistencies with the recognized classification scheme. This investigation thus demonstrates that all major methods of facial approximation depend on both face anatomy and average soft-tissue depths, rendering common method classification schemes redundant. The best way forward appears to be for practitioners to describe the methods they use (including the weight each one gives to average soft-tissue depths and deep face tissue construction) without placing them in any categorical classificatory group or giving them an ambiguous name. The state of this situation may need to be reviewed in the future in light of new research results and paradigms.

Assessing facial approximation accuracy: How do resemblance ratings of disparate faces compare to recognition tests?

In the past, the accuracy of facial approximations has been assessed by resemblance ratings (i.e., the comparison of a facial approximation directly to a target individual) and recognition tests (e.g., the comparison of a facial approximation to a photo array of faces including foils and a target individual). Recently, several research studies have indicated that recognition tests hold major strengths in contrast to resemblance ratings. However, resemblance ratings remain popularly employed and/or are given weighting when judging facial approximations, thus indicating that no consensus has been reached. This study aims to further investigate the matter by comparing the results of resemblance ratings and recognition tests for two facial approximations which clearly differed in their morphological appearance. One facial approximation was constructed by an experienced practitioner privy to the appearance of the target individual (practitioner had direct access to an antemortem frontal photograph during face construction), while the other facial approximation was constructed by a novice under blind conditions. Both facial approximations, whilst clearly morphologically different, were given similar resemblance scores even though recognition test results produced vastly different results. One facial approximation was correctly recognized almost without exception while the other was not correctly recognized above chance rates. These results suggest that resemblance ratings are insensitive measures of the accuracy of facial approximations and lend further weight to the use of recognition tests in facial approximation assessment. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Chemical and structural disorder in eumelanins: A possible explanation for broadband absorbance

We report the results of an experimental and theoretical study of the electronic and structural properties of a key eumelanin precursor-5,6,-dihydroxyindole-2-carboxylic acid ( DHICA) - and its dimeric forms. We have used optical spectroscopy to follow the oxidative polymerization of DHICA to eumelanin and observe red shifting and broadening of the absorption spectrum as the reaction proceeds. First principles density functional theory calculations indicate that DHICA oligomers ( possible reaction products of oxidative polymerization) have the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital red-shifted gaps with respect to the monomer. Furthermore, different bonding configurations ( leading to oligomers with different structures) produce a range of gaps. These experimental and theoretical results lend support to the chemical disorder model where the broadband monotonic absorption characteristic of all melanins is a consequence of the superposition of a large number of nonhomogeneously broadened Gaussian transitions associated with each of the components of a melanin ensemble. These results suggest that the traditional model of eumelanin as an amorphous organic semiconductor is not required to explain its optical properties and should be thoroughly reexamined. These results have significant implications for our understanding of the physics, chemistry, and biological function of these important biological macromolecules. Indeed, one may speculate that the robust functionality of melanins in vitro is a direct consequence of its heterogeneity, i.e., chemical disorder is a "low cost" natural resource in these systems

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Transfer of nonclassical properties from a microscopic superposition to macroscopic thermal states in the high temperature limit

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.

Observing a coherent superposition of an atom and a molecule

We demonstrate that it is possible, in principle, to perform a Ramsey-type interference experiment to exhibit a coherent superposition of a single atom and a diatomic molecule. This gedanken experiment, based on the techniques of Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the commonly accepted superselection rule that forbids coherent superpositions of eigenstates of differing atom number. A Bose-Einstein condensate plays the role of a reference frame that allows for coherent operations analogous to Ramsey pulses. We also investigate an analogous gedanken experiment to exhibit a coherent superposition of a single boson and a fermion, violating the commonly accepted superselection rule forbidding coherent superpositions of states of differing particle statistics. In this case, the reference frame is realized by a multimode state of many fermions. This latter case reproduces all of the relevant features of Ramsey interferometry, including Ramsey fringes over many repetitions of the experiment. However, the apparent inability of this proposed experiment to produce well-defined relative phases between two distinct systems each described by a coherent superposition of a boson and a fermion demonstrates that there are additional, outstanding requirements to fully lift the univalence superselection rule.