Bianchi Type I Viscous Universe with Variable G and Λ

Exact solutions for an anisotropic Bianchi type I model with bulk viscosity and variable G and are obtained. We have found some solutions that correspond to our earlier work for the isotropic one. Unlike Kalligas et al., an inflationary solution with a variable energy density has been found where the anisotropy energy decreases exponentially with time. There is a period of hyper-inflation during which the energy density remains constant.     

Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.     

Evaluation of the density matrix for an ensemble of anharmonic oscillators by a path integral approach

Considering the Feynman path integral representation for the configuration-space density matrix for an ensemble of anharmonic oscillators, we determine the stationary paths near which the integrand remains stationary. By taking the path integral to be saturated by contributions from the neighborhood of the path which maximizes the integrand we evaluate the density matrix explicitly in analytic form. This seems to be the first such evaluation of a path integral for a system not describable by a quadratic Hamiltonian. We also comment briefly on the question of analyticity with respect to the perturbation parameter.     

Letter: The Energy Density of the Quaternionic Field as Dark Energy in the Universe

In this article we describe a model of the universe consisting of a mixture of the ordinary matter and a so-called cosmic quaternionic field. The basic idea here consists in an attempt to interpret as the energy density of the quaternionic field whose source is any form of energy including the proper energy density of this field. We set the energy density of this field to and show that the ratio of ordinary dark matter energy density assigned to is constant during the cosmic evolution. We investigate the interaction of the quaternionic field with the ordinary dark matter and show that this field exerts a force on the moving dark matter which might possible create the dark matter in the early universe. Such determined fulfils the requirements asked from the dark energy. In this model of the universe, the cosmological constant, the fine-tuning and the age problems might be solved. Finally, we sketch the evolution of the universe with the cosmic quaternionic field and show that the energy density of the cosmic quaternionic field might be a possible candidate for the dark energy.     

On the instanton-induced portion of the nucleon strangeness II: the MIT model beyond the linearized approximation

If instantons are introduced into the MIT bag model in such a way that the bag radii are allowed to vary, the MIT bag interior can accommodate an instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the non-perturbative QCD vacuum). The instanton contribution to the baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model radii (which is associated with the increase of the instanton density) is very favorable from the standpoint of nuclear physics. Received: 7 February 2003 / Revised version: 1 April 2003 / Published online: 23 May 2003 RID="a" ID="a" e-mail: klabucar@phy.hr RID="b" ID="b" e-mail: kkumer@phy.hr RID="c" ID="c" e-mail: dmekter@rudjer.irb.hr RID="d" ID="d" e-mail: bp@phy.hr. Present address: Faculty of Civil Engineering, University of Rijeka, HR-51000 Rijeka, Croatia     

Imaging of electron potential landscapes on Au(111)

The Hohenberg-Kohn theorem states that the ground state electron density completely determines the external potential acting on an electron system. Inspired by this fundamental theorem, we developed a novel approach to map directly the electron potential in surface systems: linear response theory applied to the total electron density as measured with scanning tunneling microscopy determines the external potential. Potential imaging is demonstrated for the s-p derived surface state on Au(111), where the "herringbone" reconstruction induces a periodic potential modulation, the details of which are revealed by our technique.     

On Selection Criteria for the Tuning Parameter in Robust Divergence

Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.     

Dipolar bosons in a planar array of one-dimensional tubes

We investigate bosonic atoms or molecules interacting via dipolar interactions in a planar array of one-dimensional tubes. We consider the situation in which the dipoles are oriented perpendicular to the tubes by an external field. We find various quantum phases reaching from a "sliding Luttinger liquid" phase to a two-dimensional charge density wave ordered phase. Two different kinds of charge density wave order occur: a stripe phase in which the bosons in different tubes are aligned and a checkerboard phase. We further point out how to distinguish the occurring phases experimentally.     

A ring of instantons inducing a monopole loop

We consider the superposition of infinitely many instantons on a circle in . The construction yields a self-dual solution of the Yang-Mills equations with action density concentrated on the ring. We show that this configuration is reducible in which case magnetic charge can be defined in a gauge invariant way. Indeed, we find a unit charge monopole (worldline) on the ring. This is an analytic example of the correlation between monopoles and action/topological density, however with infinite action. We show that both the Maximal Abelian Gauge and the Laplacian Abelian Gauge detect the monopole, while the Polyakov gauge does not. We discuss the implications of this configuration.     

Variable flip angle imaging and fat suppression in combined gradient and spin-echo (GREASE) techniques

Conventional "proton density" and "T2-weighted" spin-echo images are susceptible to motion induced artifact, which is exacerbated by lipid signals. Gradient moment nulling can reduce motion artifact but lengthens the minimum TE, degrading the "proton density" contrast. We designed a pulse sequence capable of optimizing proton density and T2-weighted contrast while suppressing lipid signals and motion induced artifacts. Proton density weighting was obtained by rapid readout gradient reversal immediately after the excitation RF pulse, within a conventional spin-echo sequence. By analyzing the behavior of the macroscopic magnetization and optimizing excitation flip angle, we suppressed T1 contribution to the image, thereby enhancing proton density and T2-weighted contrast with a two- to four-fold reduction of repetition time. This permitted an increased number of averages to be used, reducing motion induced artifacts. Fat suppression in the presence of motion was investigated in two groups of 8 volunteers each by (i) modified Dixon technique, (ii) selective excitation, and (iii) hybrid of both. Elimination of fat signal by the first technique was relatively uniform across the field of view, but it did not fully suppress the ghosts originating from fat motion. Selective excitation, while sensitive to the main field inhomogeneity, largely eliminated the ghosts (0.21 +/- 0.05 vs. 0.29 +/- 0.06, p less than 0.01). The hybrid of both techniques combined with bandwidth optimization, however, showed the best results (0.17 +/- 0.04, p less than 0.001). Variable flip-angle imaging allows optimization of image contrast which, along with averaging and effective fat suppression, significantly improves gradient- and spin-echo imaging, particularly in the presence of motion.     

Overview of edge electrostatic turbulence experiments on TCV

Experiments on edge turbulence in the TCV tokamak have been performed for the first time at the beginning of 2003. This paper presents an overview of some of the results obtained, concentrating in particular on two areas: universality of density fluctuations and the dynamical coupling between radial turbulent-driven fluxes and parallel flows.Plasma fluctuations in the edge of the TCV tokamak have been found to exhibit statistical properties which are universal across a broad range of discharge conditions. Analysis of the time series of density fluctuations in the entire scrape-off layer (SOL) region from just inside the magnetic separatrix to the plasma-wall interface, yields a probability distribution function (PDF) of density which conforms closely to a Gamma distribution. In the wall vicinity, the density fluctuations exhibit clear evidence of self-similarity and are characterised by a PDF with universal shape and with a standard deviation proportional to the mean density. It is also found that radial particle-flux fluctuations scale solely with the mean density. Such findings indicate that it may be possible to improve the prediction of transport in the critical plasma-wall interaction region of future large-scale tokamaks.Recent experiments on JET [C. Hidalgo et al.: Phys. Rev. Lett. 91 (2003) 065001] have investigated a possible link between turbulent transport and the parallel flows. Similar experiments have been performed on TCV for a variety of plasma conditions and flow magnitudes. Although correlations have been found as seen on JET, especially in the wall vicinity, it appears that the magnitude of the coupling is insufficient to drive any significant flow.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

A semiclassical interpretation of wave mechanics

The single-particle wave function =Re^iS/h has been interpreted classically: At a given point the particle momentum is S, and the relative particle density in an ensemble is R ² . It is first proposed to modify this interpretation by assuming that physical variables undergo rapid fluctuations, so that S is the average of the momentum over a short time interval. However, it appears that this is not enough. It seems necessary to assume that the density also fluctuates. The fluctuations are taken to be random and to satisfy conditions required for agreement with quantum mechanics. In some cases the fluctuating density may take on instantaneous negative values. One gets agreement with quantum mechanics for the spin correlations of two particles in a singlet state. This comes about because of the correlations between the fluctuations of the variables of the two particles, the effect of which is equivalent to an action at a distance. The relation to Bell's inequality is discussed.     

On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations

Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results, we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow efficient numerical calculations with an arbitrarily high accuracy as demonstrated with an implementation in Python publicly available on GitLab. Finally, we discuss the (in)validity of Gaussian approximations of the information density.     

No-broadcasting theorem and its classical counterpart

Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.     

Kinetic energy of an inhomogeneous electron gas

It is well known that the kinetic energy of a system of N noninteracting particles in an external field V(r) in the nondegenerate ground state is a universal functional of the particle density (r) [1]. However, the explicit form of this functional is defined only for a certain class of functions (r). In particular, in the case of an almost constant or a slowly varying density we obtain the wellknown Thomas-Fermi-Weizsäcker-Kirzhnits functional [1, 2]. In [3] the kinetic energy functional of an electron in an atom is obtained in the WKB approximation. The kinetic energy of electrons with quantum numbers n andl is represented as the sum of two terms. The first term is written in the form of the density of the electrons with the given quantum numbers times some orthogonalized pseudopotential, which takes into account the orthogonality of their wave functions with respect to the core (its form is discussed below). The second term is the intrinsic kinetic energy of the electrons. The introduction of an orthogonalized pseudopotential is very convenient for the calculation of atomic properties [4, 5]. It is therefore of great interest to extend the results of [3] to the case of an electron gas in a metal and to obtain an expression for its orthogonalized crystalline pseudopotential. The solution of these problems is the aim of the present paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 117–120, July, 1977.     

表面等离子激元非线性表面增强拉曼散射效应

本文采用热蒸发法制备得到纳米Ag颗粒作为增强拉曼衬底, 利用入射光子与纳米颗粒表面价电子的相互作用机理, 激发出高能表面等离子激元, 其表面等离子形成的高能"热点"起到表面增强拉曼散射效果. 通过比较不同入射光强下的拉曼峰强, 指出纳米Ag颗粒的增强拉曼散射效果可以实现低探测光强下的高散射强度, 即纳米Ag颗粒的表面等离子激元具有非线性的表面增强拉曼散射效果, 可降低对样品的光、热损伤, 以利于拓展拉曼散射光谱的应用范围. 同时比较不同纳米Ag颗粒衬底的表面增强拉曼散射效果表明, 采用的热蒸发工艺具有较大的工艺域度, 具有较强的工艺兼容性.     

Observations of density fluctuations in an elongated Bose gas: ideal gas and quasicondensate regimes

We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.     

A Real Quaternion Spherical Ensemble of Random Matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form Y=A ^?1 B, where A and B are independent N×N matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue joint probability density function and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices β=1,2,4. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure Y=A ^?1 B, where A and B are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.     

Nothing moves a surface: vacancy mediated surface diffusion

We report scanning tunneling microscopy observations, which imply that all atoms in a Cu(001) surface move frequently, even at room temperature. Using a low density of embedded indium "tracer" atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultralow density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.