Abelian faces of state spaces ofC*-algebras

LetF be a closed face of the weak* compact convex state space of a unitalC*-algebraA. The class ofF-abelian states, introduced earlier by the author, is studied further. It is shown (without any restriction onA orF) thatF is a Choquet simplex if and only if every state inF isF-abelian, and that it is sufficient for this that every pure state inF isF-abelian. As a corollary, it is deduced that an arbitraryC*-dynamical system (A, G, ) isG-abelian if and only if every ergodic state is weakly clustering. Nevertheless the set of allF-abelian (or evenG-abelian) states is not necessarily weak* compact.     

A comprehensive,time-resolved SANS investigation of temperature-change-induced sponge-to-lamellar and lamellar-to-sponge phase transformations in comparison with <Superscript>2</Superscript>H -NMR results

Time-resolved small-angle neutron scattering (TR-SANS) was employed to observe temperature-induced phase transitions from the sponge (L ₃ to the lamellar ( L _α phase, and vice versa, in the water-oil (n -decane)-non-ionic surfactant ( C₁₂E₅ system using both bulk and film contrast. Samples of different bilayer volume fractions φ and solvent viscosities η were investigated applying various amplitudes of temperature jump ΔT . The findings of a previous ²H -NMR study could be confirmed, where the lamellar phase formation was determined to occur through a nucleation and growth process, while it was concluded that the L ₃ -phase develops in a mechanistically different and more rapid manner involving uncorrelated passage formation. Likewise, the kinetic trends of the nucleation and growth transition (decreased transition time with increase of φ and ΔT were witnessed once again. Additionally, NMR and SANS data that demonstrate a strong dependency of that process on solvent viscosity η are presented. Contrariwise, it is made evident via both SANS and NMR results that the L _α -to-L ₃ transition time is independent (within experimental sensitivity) of the varied parameters (φ , ΔT , η . Unusual scattering evolution in one experiment, originating from a highly ordered lamellar phase, intriguingly hints that a major rate determining factor is the disruption of long-range order. Furthermore, the bulk contrast investigations give insight into structure peak shifts/development during the transitions, while the film contrast experiments prove the bilayer thickness to be constant throughout the phase transitions and show that there is no evidence for a change in the short-range order of the bilayer structure. The latter was considered possible, due to the different topology of the L ₃ and L _α phases. Lastly, an unexpected yet consistent appearance of anisotropic scattering is detected in the L ₃ -to- L _α transitions.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s ₀), where B is a Boolean algebra and s ₀ is a state on B.     

Statistical estimates of the influence of the source divergence angle on the characteristics of acoustic radiation transmitted through the atmosphere

The method of statistical simulation (Monte Carlo) is used for the first time to study the influence of the angular source divergence on the characteristics of transmitted acoustic radiation with allowance for the multiple scattering contribution. Results of calculations for a point source of unit power with divergence angles φ = 5, 10, 15, 20, and 25° at frequencies F = 1, 2, 3, and 4 kHz are presented for the outer scale of turbulence L ₀ = 10, 15, 20, 40, 60, and 80 m. It is established that for F = 2 kHz the multiple scattering contribution to the transmitted radiation intensity increases with the outer scale of turbulence from ∼10% (for L ₀ = 10 m) to 90% (for L ₀ = 60 m); for L ₀ = 80 m, the transmitted radiation intensity is virtually completely determined by the contribution of multiple scattering. When the width of the source directivity pattern (2φ) increases from 10 to 50°, the intensity of transmitted acoustic radiation decreases by 96%. Based on the results of statistical simulation, analytical dependences of the transmitted radiation intensity on the sound source divergence angle are suggested for typical sodar frequencies.     

Investigation of final-stage sintering of various microsize structures prepared by micro powder injection molding

Micro powder injection molding (μPIM) has been developed as a potential technique for mass production of microcomponents in microsystems due to its shaping complexity at low cost, in which sintering is a crucial step to dictate the final properties of the microcomponents. In this paper, final-stage sintering behavior of 316L stainless steel microsize structures prepared by μPIM, φ100 μm and φ60 μm, respectively, was studied. The effect of size reduction in the regime of micrometers on the density of various microsize structures was investigated. Sintering kinetics of the microsize structures of φ100 μm and φ60 μm were studied based on particle level sintering models. It is found that the microsize structures of φ60 μm had higher density than the microsize structures of φ100 μm given the same sintering condition. The results indicate that size reduction in the regime of micrometers facilitated densification of microsize structures. The grain growth mechanism of microsize structures varied with size. Whereas the grain growth of the microsize structures of φ100 μm is governed by surface-diffusion-controlled pore drag, the grain growth of the microsize structures of φ60 μm is controlled by boundary diffusion. During densification, the microsize structures, φ100 μm and φ60 μm, are both controlled by lattice diffusion. The corresponding activation energies are reported in the paper.     

OZI rule violation in p¯p annihilation into φππ by two step processes

The φπ⁺π⁻ production in pˉp annihilation at rest is strongly enhanced by a two step mechanism with intermediate KˉKππ states. The relative yield of the φ production due to the resonant final state interaction decreases with increasing total energy of the pˉp system. Received: 4 August 1997     

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function f, the correlation function C=〈δfδf〉, the retarded and advanced density response functions χ ^R,A =δf/δφ to an external potential φ, and the associated memory functions Σ ^R,A,C . The basis of the theory is an effective action functional Ω of external potentials φ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density f and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques (involving Legendre transform and vertex functions) are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations that automatically imply the conservation laws of mass, momentum and energy. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green’s functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach used in the kinetic theory of fluids in thermal equilibrium. For non-equilibrium fluids, popular closures of the BBGKY hierarchy (e.g. Landau, Boltzmann, Lenard-Balescu-Guernsey) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.     

Weighted Bergman Kernels and Quantization}

Let Ω be a bounded pseudoconvex domain in C ^N , φ, ψ two positive functions on Ω such that − log ψ, − log φ are plurisubharmonic, and z∈Ω a point at which − log φ is smooth and strictly plurisubharmonic. We show that as k→∞, the Bergman kernels with respect to the weights φ ^{k ψ} have an asymptotic expansion

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3 ≤ d < 4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T ≥ 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value φ = 1/(d − 1) to the new one φ = 1/2(d − 1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent φ = 1/2(d − 1) in the quantum tricritical region.     

Formulation and picture of quantum phase

Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e ^iφ≡cosφ+i sinφ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ = π/2, the correlative quantum phase is a unitary pure imaginary number e ^iπ/2≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schr?dinger equation and can completely describe a photon’s behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.     

Production of φ mesons in near-threshold πN and NN reactions

We analyze the production of φ mesons in πN and NN reactions in the near-threshold region, using throughout the conventional “non-strange” dynamics based on such processes which are allowed by the non-ideal ω-φ mixing. We show that the occurrence of the direct φNN interaction may show up in different unpolarized and polarization observables in πN→Nφ reactions. We find a strong non-trivial difference between observables in the reactions pp→ppφ and pn→pnφ caused by the different role of the spin singlet and triplet states in the entrance channel. A series of predictions for the experimental study of this effect is presented. Received: 27 January 2000     

The nature of binding in the ground state of the scandium dimer

For the study of the nature of binding in the Sc₂ dimer, the ground state, X⁵Σ _u ^–, was calculated by the valence multireference configuration interaction method with single and double excitations plus Davidson correction, MRCISD (+Q), at the complete basis set (CBS) limit. The employment of the C_2v symmetry group, allowed us to obtain the Sc atoms in different states at the dissociation limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc₂ dissociates on one Sc in the ground state and the other in the second excited quartet state, ⁴F _u . The spectroscopic parameters of the ground potential curve, obtained at the valence MRCISD (+Q)/CBS level, are: R _e  = 5.20 bohr, D _e  = 50.37 kcal/mol, and ω _e  = 234.5 cm^-1. The obtained value for the harmonic frequency agrees very well with the experimental one, ω _e  = 239.9 cm^-1. The dissociation energy with reference to the dissociation on two Sc in the ground states was estimated as D _e  = 9.98 kcal/mol. In contrast with many other studied transition-metal dimers, which are attributed to the van der Waals bonded molecules, the Sc₂ dimer is stabilized by the covalent bonding on the hybrid atomic orbitals.     

Theoretical study of incoherent φ photoproduction on a deuteron target

We study the photoproduction of φ mesons in deuteron, paying attention to the modification of the cross-section from bound protons to the free ones. For this purpose we take into account Fermi motion in single scattering and rescattering of φ to account for φ absorption on a second nucleon as well as the rescattering of the proton on the neutron. We find that the contribution of the double scattering for φ is much smaller than the typical cross-section of γp → φp in free space, which implies a very small screening of the φ production in deuteron. The contribution from the proton rescattering, on the other hand, is found to be not negligible compared to the cross-section of γp → φp in free space, and leads to a moderate reduction of the φ photoproduction cross-section on a deuteron at forward angles if the LEPS set-up is taken into account. The Fermi motion allows contribution of the single scattering in regions forbidden by phase-space in the free case. In particular, we find that for momentum transfer squared close to the maximum value, the Fermi motion changes drastically the shape of dσ/dt, to the point that the ratio of this cross-section to the free one becomes very sensitive to the precise value of t chosen, or the size of the bin used in an experimental analysis. Hence, this particular region of t does not seem to be the most indicated to find effects of a possible φ absorption in the deuteron. This reaction is studied theoretically as a function of t and the results are contrasted with recent experiments at LEPS and Jefferson Lab. The effect of the experimental angular cuts at LEPS is also discussed, providing guidelines for future experimental analyses of the reaction.     

Dissipative tunneling in nanosystems

A quantum dynamical problem has been analytically solved for a two-level system where localized states L ₀ and R ₀ are strongly coupled with reservoirs of local oscillations {L _n } and {R _n }. It is additionally assumed that the spectra of reservoirs are equidistant and the coupling constants are the same. It has been shown that the evolution of states L ₀ and R ₀ in recurrence cycles depends on three independent factors, which characterize exchange with the two-level system, exchange of L ₀ with {L _n } (R ₀ with {R _n }) and the phonon-induced decay of {L _n } and {R _n }. In addition to coherent oscillations with the frequency of the two-level system, Δ, and dissipative tunneling with a rate Δ²/πC ² (where C is the matrix element of the coupling of L ₀ and R ₀ with L _n and R _n ), a new regime appears where L-R transitions are induced by the partial recovery of the populations of L ₀ and R ₀ in each recurrence cycle due to synchronous transitions from reservoirs. These transitions induce repeating changes in the populations of the states of the two-level system (Loschmidt echo). The number and width of the echo components increase with the cycle number. Evolution becomes irregular because of the mixing of the contributions from pulses of the neighboring cycles, when the cycle number k exceeds the critical value k _c = π² C ². Unlike the populations, their cycle-average values remain regular at k ≫ k _c. When Δ ≪ πC ², the cycle-average populations oscillate with a frequency of ΔΩ/πC ² irrespective of mixing. The frequency of oscillations of the populations of the states {L _n } and {R _n } is approximately nΩ(Δ/2πC ²)², where Ω is the spacing between the neighboring levels of the reservoir and nΩ is the difference between the energies of the states L ₀ and L _n . The appearance of the mentioned low-frequency oscillations is due to the formation of collective states of the two-level system that are “dressed” by the reservoir. The predicted oscillations can be detected by femtosecond spectroscopy methods.     

Cosmological Spacetimes Balanced by a Weyl Geometric Scale Covariant Scalar Field

A Weyl geometric approach to cosmology is explored, with a scalar field φ of (scale) weight −1 as crucial ingredient besides classical matter. Its relation to Jordan-Brans-Dicke theory is analyzed; overlap and differences are discussed. The energy-stress tensor of the basic state of the scalar field consists of a vacuum-like term Λg _{μ ν} with Λ depending on the Weylian scale connection and, indirectly, on matter density. For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the energy-stress tensor of the φ-field can keep space-time geometries in equilibrium. A short glance at observational data, in particular supernovae Ia (Riess et al. in Astrophys. J. 659:98ff, 2007), shows encouraging empirical properties of these models.     

On (3,3)-Homogeneous Greechie Orthomodular Posets

We describe (3,3)-homogeneous orthomodular posets for some cardinality of their sets of atoms. We examine a state space and a set of two-valued states of such logics. Particular homogeneous OMPs with exactly k pure states (k = 1,...,7, 10,11) have been constructed.     

Asymmetric Diffusion and the Energy Gap Above¶the 111 Ground State of the Quantum XXZ Model

We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the axis, the Goldstone theorem implies that the spectral gap above such ground states must tend to zero as L→∞. In [3] it was proved that, by perturbing in a sub-cylinder with basis of linear size R≪L the interface ground state, it is possible to construct excited states whose energy gap shrinks as R ^-2. Here we prove that, uniformly in the height of the cylinder and in the location of the interface, the energy gap above the interface ground state is bounded from above and below by const.L ^-2. We prove the result by first mapping the problem into an asymmetric simple exclusion process on ℤ³ and then by adapting to the latter the recursive analysis to estimate from below the spectral gap of the associated Markov generator developed in [7]. Along the way we improve some bounds on the equivalence of ensembles already discussed in [3] and we establish an upper bound on the density of states close to the bottom of the spectrum. Received: 9 August 2001 / Accepted: 29 October 2001     

Spectral theory in quantum logics

If one supposes a quantum logicL to be a -orthocomplete, orthomodular partially ordered set admitting a set of -orthoadditive functions (called states) fromL to the unit intervals [0, 1] such that these states distinguish the ordering and orthocomplement onL, then the observables onL are identified withL-valued measures defined on the Borel subsets of the real line. In this structure (and without the aid of Hilbert space formalism) the author shows that (1) the spectrum of an observable can be completely characterised by studying the observable (A–)^–1, and (2) corresponding to every observableA there is a spectral resolution uniquely determined byA and uniquely determiningA.     

CORAL: QSPR models for solubility of [C60] and [C70] fullerene derivatives

Quantitative structure–property relationships (QSPRs) between the molecular structure of [C₆₀] and [C₇₀] fullerene derivatives and their solubility in chlorobenzene (mg/mL) have been established by means of CORAL (CORrelations And Logic) freeware. The CORAL models are based on representation of the molecular structure by simplified molecular input line entry system (SMILES). Three random splits into the training and the external validation sets have been examined. The ranges of statistical characteristics of these models are as follows: n = 18, r ² = 0.748–0.815, s = 15.1 –17.5 (mg/mL), F = 47–71 (training set); n = 9, r ² = 0.806–0.936, s = 12.5–17.5 (mg/mL), F = 29–103 (validation set).