State Property Systems and Orthogonality

The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva–Brussels approach to the foundations of quantum mechanics (Aerts, D. International Journal of Theoretical Physics, 38, 289–358, 1999; Aerts, D. in Quantum Mechanics and the Nature of Reality, Kluwer Academic; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B. International Journal of Theoretical Physics, 38, 359–385, 1999), and the category of state property systems was proven to be equivalent to the category of closure spaces (Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., International Journal of Theoretical Physics, 38, 359–385, 1999; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., The construct of closure spaces as the amnestic modification of the physical theory of state property systems, Applied Categorical Structures, in press). The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the T₀ and T₁ axioms of closure spaces (van Steirteghem, B., International Journal of Theoretical Physics, 39, 955, 2000; van der Voorde, A., International Journal of Theoretical Physics, 39, 947–953, 2000; van der Voorde, A., Separation Axioms in Extension Theory for Closure Spaces and Their Relevance to State Property Systems, Doctoral Thesis, Brussels Free University, 2001), and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components for a general state property system (Aerts, D., van der Voorde, A., and Deses, D., Journal of Electrical Engineering, 52, 18–21, 2001; Aerts, D., van der Voorde, A., and Deses, D. International Journal of Theoretical Physics; Aerts, D. and Deses, D., Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation, and Axiomatics, World Scientific, Singapore, 2002). The concept of orthogonality, very important for quantum axiomatics, had however not yet been introduced within the formal scheme of the state property system. In this paper we introduce orthogonality in an operational way, and define ortho state property systems. Birkhoff's well known biorthogonal construction gives rise to an orthoclosure and we study the relation between this orthoclosure and the operational orthogonality that we introduced.     

Random-Cluster Representation of the Blume–Capel Model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model. Mathematics Subject Classification (2000): 82B20, 60K35.     

On Steady Distributions of Kinetic Models of Conservative Economies

We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat. Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state.     

Intercalation of two-dimensional graphite films on metals by atoms and molecules

An analysis is made of some general laws governing a new physical effect, i.e., the spontaneous penetration of particles (atoms, C₆₀ molecules) adsorbed on a two-dimensional graphite film on a metal (Ir, Re, Pt, Mo,...) to beneath the graphite film (intercalation). It is shown that atoms having low ionization potentials (Cs, K, Na) intercalate a two-dimensional graphite film on iridium at T=300–400K with an efficiency χ≈0.5, accumulating beneath the film to a concentration of up to a monolayer. Atoms having high ionization potentials (Si, Pt, Ni, C, Mo, etc.) intercalate a two-dimensional graphite film on iridium at T≈1000K with an efficiency, χ≈1, forming beneath the film a thick intercalate layer which is strongly bonded chemically to the metal substrate but is probably weakly bonded to the graphite monolayer by van der Waals forces. The presence of a graphite “lid” impeding the escape of atoms from the intercalated state up to record high temperatures T∼2000K leads to superefficient diffusion (with an efficiency close to one) of various atoms (Cs, K) into the bulk of the substrate (Re, Ir). Zh. Tekh. Fiz. 69, 72–75 (September 1999)     

The Tensors of the Averaged Relative Energy–Momentum and Angular Momentum in General Relativity and Some of Their Applications

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper.      

Pulsed electron-beam melting of a copper — steel 316 system: Evolution of the chemical composition,microstructure, and properties

The surface topography, chemical composition, microstructure, nanohardness, and tribological characteristics of a Cu (film, 512 nm)-stainless steel 316 (substrate) system subjected to pulsed melting by a low-energy (20–30 keV), high-current electron beam (2–3 μs, 2–10 J/cm²) were investigated. The film was deposited by sputtering a Cu target in the plasma of a microwave discharge in argon. To prevent local exfoliation of the film due to cratering, the substrate was multiply pre-irradiated with 8–10 J/cm². On single irradiation, the bulk of the film survived, and a diffusion layer containing the film and substrate components was formed at the interface. The thickness of this layer was 120–170 nm irrespective of the energy density. The diffusion layer consisted of subgrains of γ-Fe solid solution and nanosized particles of copper. In the surface layer of thickness 0.5–1 μm, which included the copper film quenched from melt and the diffusion layer, the nanohardness and the wear resistance nonmonotonicly varied with energy density, reaching, respectively, a maximum and a minimum in the range 4.3–6.3 J/cm². As the number of pulsed melting cycles was increased to five in the same energy density range, there occurred mixing of the film-substrate system and a surface layer of thickness ∼2 μm was formed which contained ∼20 at. % copper. Displacement of the excess copper during crystallization resulted in the formation of two-phase nanocrystal interlayers separating the γ-phase grains. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 6–13, December, 2005.     

On Consistency of the Quantum-Like Representation Algorithm

In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H ^b|a and H ^a|b . In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA.     

Monte Carlo Simulation of Hard Hyperspheres in Six,Seven and Eight Dimensions for Low to Moderate Densities

The pair correlation function of hard hyperspheres in six, seven and eight dimensions is obtained from Monte Carlo simulations. The value of the pair correlation function at contact is compared with the results from molecular dynamics calculations and a variety of theoretical approaches. Remarkably good agreement is found with the simple, closed-form equations of Y. Song, E. A. Mason and R. M. Stratt, J. Phys. Chem., 93:6916–6919 (1989). The Monte Carlo results for the equation of state are compared with the theoretical expressions of M. Baus and J. L. Colot, Phys. Rev. A, 36:3912 (1987), M. Luban and J. P. J. Michels, Phys. Rev A, 41:6796 (1990), and high order virial expansions. In addition, in seven dimensions, comparisons are made with the exact PY solution provided by M. Robles, M. L. de Haro and A. Santos, J. Chem. Phys., 120:9113 (2004). Very good agreement was observed between theory and computer simulation in all dimensions.     

Libraries of 2β-(N-substituted piperazino)-5α-androstane-3α, 17β-diols: chemical synthesis and cytotoxic effects on human leukemia HL-60 cells and on normal lymphocytes

Libraries of steroid derivatives with two levels of molecular diversity were prepared to optimize the antiproliferative activity on leukemia HL-60 cells by first varying the amino acid (AA) at R¹ (libraries A, B, C, and D: with 45, 45, 20, and 20 members, respectively) and, subsequently, the capping group at R² (library E: 168 members). The screening of these aminosteroids revealed interesting structure–activity relationships. In library A, the compounds bearing a tetrahydroisoquinolone residue as the first element of diversity showed potent cytotoxicity, principally when isovaleric or cyclohexyl acetic acid was used as a capping group (>40% of cell growth inhibition at 1 μM). In library B, the phenylalanine (Phe) derivatives bearing a cyano group induced a higher growth inhibition than the other Phe derivatives. The screening of library C indicated the increase of hydrophobicity of proline (Pro) seems to preserve the cytotoxic effect achieved by the lead compound. However, the synthesis of structural Pro variants (library D) clearly shows weaker activities when compared to L-Pro building blocks. Finally, by incorporating some of the most active AA of libraries A–D in library E, we observed that the amide coupling functionality gave stronger cytotoxic activity compared to the corresponding sulfonamides or benzylamines. Six of the most active amide derivatives (E-37P, E-41P, E-42P, E-46P, E-48F, and E-12T) were selected and IC₅₀ determined on HL-60 cells as well as on normal human lymphocytes. Among this series of new anticancer agents, good to high selectivity indices (SI = IC₅₀ (lymphocytes)/IC₅₀ (HL-60 cells) = 5 - 55) were obtained.     

Picosecond laser ablation of SiO2 layers on silicon substrates

In this work, we report on laser ablation of thermally grown SiO₂ layers from silicon wafer substrates, employing an 8–9 ps laser, at 1064 (IR), 532 (VIS) and 355 nm (UV) wavelengths. High-intensity short-pulse laser radiation allows direct absorption in materials with bandgaps higher than the photon energy. However, our experiments show that in the intensity range of our laser pulses (peak intensities of <2×10¹² W/cm²) the removal of the SiO₂ layer from silicon wafers does not occur by direct absorption in the SiO₂ layer. Instead, we find that the layer is removed by a “lift off” mechanism, actuated by the melting and vaporisation of the absorbing silicon substrate. Furthermore, we find that exceeding the Si melting threshold is not sufficient to remove the SiO₂ layer. A second threshold exists for breaking of the layer caused by sufficient vapour pressure. For SiO₂ layer ablation, we determine layer thickness dependent minimum fluences of 0.7–1.2 J/cm² for IR, 0.1–0.35 J/cm² for VIS and 0.2–0.4 J/cm² for UV wavelength. After correcting the fluences by the reflected laser power, we show that, in contrast to the melting threshold, the threshold for breaking the layer depends on the SiO₂ thickness.     

Evidence of maximum in the melting curve of hydrogen at megabar pressures

Hydrogen at high pressures of ∼400 GPa might be in a zero-temperature liquid ground state (N. Ashcroft, J. Phys.: Condens. Matter A 12, 129 (2000), E. G. Brovrnan et al., Sov. Phys. JETP 35, 783 (1972)). If metallic hydrogen is liquid, the melting T _melt(P) line should possess a maximum. Here we report on the experimental evaluation of the melting curve of hydrogen in the megabar pressure range. The melting curve of hydrogen has been shown to reach a maximum with T _melt = 1050 ± 60 K at P = 106 GPa and the melting temperature of hydrogen decreases at higher pressures so that T _melt = 880 ± 50 K at P = 146 GPa. The data were acquired with the aid of a laser heating technique where diamond anvils were not deteriorated by the hot hydrogen. Our experimental observations are in agreement with the theoretical prediction of unusual behavior of the melted hydrogen [S. Bonev et al., Nature 481, 669 (2004)]. The article is published in the original.     

Early Universe Quantum Processes in BEC Collapse Experiments

We show that in the collapse of a Bose–Einstein condensate (BEC)⁴certain processes involved and mechanisms at work share a common origin with corresponding quantum field processes in the early universe such as particle creation, structure formation, and spinodal instability. Phenomena associated with the controlled BEC collapse observed in the experiment of Donley et al. (Donley, E., et al. (2001), Nature 412, 295; Claussen, N. (2003), PhD Thesis, University of Colorado; Claussen, N., et al. (2003), Physical Review A 67, 060701(R))(they call it “Bose–Nova,” see also Chin, J., Vogels, J., and Ketterle, W. (2003), Physical Review Letters 90, 160405) such as the appearance of bursts and jets can be explained as a consequence of the squeezing and amplification of quantum fluctuations above the condensate by the dynamics of the condensate. Using the physical insight gained in depicting these cosmological processes, our analysis of the changing amplitude and particle contents of quantum excitations in these BEC dynamics provides excellent quantitative fits with the experimental data on the scaling behavior of the collapse time and the amount of particles emitted in the jets. Because of the coherence properties of BEC and the high degree of control and measurement precision in atomic and optical systems, we see great potential in the design of tabletop experiments for testing out general ideas and specific (quantum field) processes in the early universe, thus opening up the possibility for implementing “laboratory cosmology.” This essay has the same content as v2 of Calzetta and Hu (2002), with a few references updated. For more details, see Calzetta and Hu (2002). ⁴For an excellent introduction to BEC theory, see Pethick and Smith (2002).     

Spectrum of the Metric Operator of a Simple -Symmetric Model

In papers (Krejčiřík D. et al.: J. Phys. A: Math. Gen.: 39(32), 10143–10153 (2006); Krejčiřík D., Tater M.: J. Phys. A: Math. Theor. 41(24), 244 (2008)) a new very simple -symmetric model was introduced and closed formula for the metric operator was found. We use an alternative integral form of this metric operator to study the spectrum of the metric.     

Atomic force microscopy of photochemistry and the Baeyer–Villiger reaction of 4,4′-dimethylbenzophenone in the solid state

Nanostructures are formed by photodimerization of crystalline 4,4^′-dimethylbenzophenone (1) through intermolecular hydrogen abstraction and Baeyer–Villiger reaction of 1 with m-chloroperoxybenzoic acid (MCPBA) (5) in the solid state. Atomic force microscopy (AFM) reveals that the crystal face (001) of 1 during photodimerization exhibits volcanoes, whereas the same face (001) of 1 yields both craters and volcanoes all over the surface from the contact edge of the crystals during the Baeyer–Villiger reaction. All the experimental results are correlated with the bulk crystal structure. Molecular interpretation of the AFM features of 1 is given. Received: 18 April 2000 / Revised version: 26 July 2000; accepted: 27 July 2000 / Published online: 30 November 2000     

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose–Einstein Condensation (BEC) in the Infinite-Range-Hopping Bose–Hubbard model with repulsive on-site particle interaction in the presence of an ergodic random single-site external potential with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. We observe new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at certain fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the suppression of BEC at integer densities observed in Bru and Dorlas (J. Stat. Phys. 113:177–195, 2003) in the absence of a random potential, can disappear as the disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of the density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.     

Sub-nanosecond single-frequency 10-kHz diode-pumped MOPA laser

A single-axial-mode, passively Q-switched (PQS) diode-pumped Nd:YAG laser, generating a diffraction-limited beam train of ≈40–60 μJ, ∼500-ps pulses with adjustable repetition rate in the range 1–10 kHz, was efficiently amplified by a single side-pumped Nd:YVO₄ bounce amplifier. After double-pass amplification, ≈1-MW pulse peak power with 577-ps duration and 545-μJ energy was achieved, still maintaining diffraction-limited beam performance. The average output power was 5.45 W at 10 kHz, corresponding to 13% extraction efficiency. The high brightness of this laser system seems ideal for nonlinear optics and some particular laser processing applications.     

Symmetries on Partially Ordered Abelian Groups

Recently, Foulis (Foulis, D. J. (2003). Compressible groups, Mathematica Slovaca 53, 433–455.) characterized compressions on effect rings, which were introduced as a generalization of unital C*-algebras in the context of ordered abelian groups with order units. In the present paper, we characterize a class of symmetries on effect rings and show their relations to compressions. This characterization leads to a generalization of the notion of orthosymmetric orthoposets (Mayet, R., Pulmannová, S. (1994). Nearly orthosymmetric ortholattices and Hilbert spaces, Foundations of Physics 24, 1425–1437.) to symmetric ordered abelian groups with order units.     

Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point

We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffiths model [Phys. Rev. A 4 (1971) 1071–1077]. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters n, β, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling limits and 18 MDPs for the total spin. These limit results are obtained as (β,K) converges along appropriate sequences (β_n, kn) to points belonging to various subsets of the phase diagram, which include a curve of second-order points and a tricritical point. The forms of the limiting densities in the scaling limits and of the rate functions in the MDPs reflect the influence of one or more sets that lie in neighborhoods of the critical points and the tricritical point. Of all the scaling limits, the structure of those near the tricritical point is by far the most complex, exhibiting new types of critical behavior when observed in a limit-theorem phase diagram in the space of the two parameters that parametrize the scaling limits. American Mathematical Society 2000 Subject Classifications. Primary 60F10, 60F05, Secondary 82B20     

On the Zero Mass Limit of Tagged Particle Diffusion in the 1-d Rayleigh-Gas

We consider the M→0 limit for tagged particle diffusion in a 1-dimensional Rayleigh-gas, studied originaly by Sinai and Soloveichik [Ya. G. Sinai, M. R. Soloveichik, Commun. Math. Phys. 104:423–443 (1986)], and by Szász and Tóth [D. Szász, B. Tóth, Commun. Math. Phys. 104:445–457 (1986)], respectively. In this limit we derive a new type of model for tagged particle diffusion, for which the two central particles, in addition to elastic collisions with the rest of the gas, interact with Calogero-Moser-Sutherland (i.e. inverse quadratic) potential. Computer simulations on this new model reproduce exactly the numerical value of the limiting variance obtained by Boldrighini, Frigio and Tognetti in [C. Boldrighini, S. Frigio, D. Tognetti, J. Stat. Phys. 108:703–712 (2002)]. Dedicated to Domokos Szász on his 65th birthday.     

Exponential Control of Overlap in the Replica Method for <Emphasis Type="Italic">p</Emphasis>-Spin Sherrington-Kirkpatrick Model

In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit for the moments of the partition function Z _N in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap. This work is partially supported by NSF grant.