Thermodynamic inequalities for molecular fluids

We consider the application of the classical Gibbs inequality for the Helmholtz free energy to a fluid whose potential energy depends on positions and orientations of the constituent molecules. Properties of the given fluid are related to the properties of a corresponding ‘reference’ fluid whose potential is the unweighted orientational average of the given potential. It is shown that Aˇ-A ₀, where A and A ₀ are the free energies respectively of the given and corresponding reference fluids, and that the high temperature limit of A - A ₀ may be either zero or negative infinite, depending on the nature of the potential. As consequences, it is shown that no general inequality exists relating the entropies of these systems, and that the internal energies U and U ₀ are plausibly expected to satisfy Uˇ-U ₀ at sufficiently high temperature. The case for a general inequality relating U and U ₀ is not decided.     

Resonance method for IR sensing

A highly sensitive method for infrared radiation detection based on thermal resonance in an active bolometer is set forth. An active bolometer is a self-oscillating system consisting of an IR-sensitive cell in a feedback circuit of an adjustable proportional controller. The analysis of an active bolometer autonomous (dark) dynamics reveals that with a generalized gain factor A variation the system evolves from relaxation type towards oscillating and self-oscillating type. When A=A_c, where A_c is a critical value of the generalized gain factor A, the steady state loses stability through self-excited thermal oscillations. The resonance in a system weakly perturbed by IR radiation modulated at self-oscillation frequency q₀[1+exp(iω_ct)] is considered. It is shown that in a small precritical vicinity =(A−A_c)/A_c of the gain factor the amplitude of forced thermal oscillations is proportional to q₀/A_c. The D^* calculation reveals that the detection power of a passive (A=0) bolometer increases with feedback introduction by a factor of 1/||. The detection powers of feasible versions of an active bolometer are compared.     

Rotational band contour analysis in the Ã1A′-[Xtilde]1A′ electronic systems of substituted naphthalenes

The 0₀ ⁰ bands of the à ¹ A′-[Xtilde] ¹ A′ systems of 1-fluoro, 1-hydroxy and 1-aminonaphthalene have been investigated by rotational band contour analysis. The 0₀ ⁰ bands in 1-fluoro and 1-hydroxynaphthalene are 70 per cent type A and 30 per cent type B, and 75 per cent type A and 25 per cent type B hybrids respectively: the electronic transition moment vector has been rotated by about 15° towards the carbon atom C₃ by the F and OH substituents compared to naphthalene (in which, in the Ã-[Xtilde] system, it is along the long in-plane axis). In 1-aminonaphthalene it seems likely that the 0₀ ⁰ band is predominantly type A, but it could not be observed with sufficient intensity to be able to obtain the excited state rotational constants with any certainty.     

First-principles characterisation of the pressure-dependent elastic anisotropy of SnO2 polymorphs

Using DFT calculations, this study investigates the pressure-dependent variations of elastic anisotropy in the following SnO₂ phases: rutile-type (tetragonal; P4₂/mnm), CaCl₂-type (orthorhombic; Pnnm)-, α-PbO₂-type (orthorhombic; Pbcn)- and fluorite-type (cubic; Fm-3m). Experimentally, these polymorphs undergo sequential structural transitions from rutile-type → CaCl₂-type → α-PbO₂-type → fluorite-type with increasing pressure at 11.35, 14.69 and 58.22 GPa, respectively. We estimate the shear anisotropy (A₁ and A₃) on {1?0?0} and {0?0?1} crystallographic planes of the tetragonal phase and (A₁, A₂ and A₃) on {1?0?0}, {0?1?0} and {0?0?1} crystallographic planes of the orthorhombic phases. The rutile-type phase shows strongest shear anisotropy on the {0?0?1} planes (A₂ > 4.8), and the degree of anisotropy increases nonlinearly with pressure. In contrast, the anisotropy is almost absent on the {1?0?0} planes (ie A₁ ~ 1) irrespective of the pressure. The CaCl₂-type phase exhibits similar shear anisotropy behaviour preferentially on {0?0?1} (A₃ > 5), while A₁ and A₂ remain close to 1. The α-PbO₂-type phase shows strikingly different elastic anisotropy characterised by a reversal in anisotropy (A₃ > 1 to < 1) with increasing pressure at a threshold value of 38 GPa. We provide electronic density of states and atomic configuration to account for this pressure-dependent reversal in shear anisotropy. Our study also analyses the directional Young’s moduli for the tetragonal and orthorhombic phases as a function of pressure. Finally, we estimate the band gaps of these four SnO₂ phases as a function of pressure which are in agreement with the previous results.     

ESR studies of Cl2- (VK) centre trapped in irradiated Ca(ClO3)2 . 2H2O single crystals

A Cl₂- centre has been trapped in X or γ-irradiated Ca(ClO₃)₂. 2H₂O single crystals at 298 K, when the irradiated crystals were illuminated with ultra-violet light (360 nm). This centre is formed at the expense of ClO₂ centres in this crystal. This Cl₂ ^- centre is trapped at two magnetically inequivalent sites in the crystal lattice and these sites become equivalent when the static magnetic field is parallel or perpendicular to the b axis. At many orientations this centre reveals ‘super-hyperfine’ interaction with a proton (I = 1/2) of the water of crystallization. The magnetic parameters are close to those observed in alkali chlorides and the E.S.R. spectrum has been fitted to an orthorhombic spin hamiltonian. The principal g values are g_xx = 2·035, g_yy = 2·033 and g_zz = 2·000 and those of the A values are A_xx = 15·0, A_yy = 31·0 and A_zz = 109·0 G. The shfs parameters are A _‖' = 5·0 A _⊥' = 1·0 G. The V_K centre trapped in this lattice is exceptionally stable at room temperature.     

Remarks on a quantum state extension problem

The problem is considered of finding, for a given pair of states on C ^*-algebras A ₁ A ₂ and A ₂ A ₃, a joint extension to A ₁ A ₂ A ₃. The fact that, in contrast to classical probability, such an extension may fail to exist, is related to the fact that different convex decompositions of the same quantum state need not have a common refinement. Improved necessary criteria for extensibility in terms of Bell's inequalities are derived, and are compared to the necessary and sufficient criteria, as well as to entropic bounds in the simplest case.     

On the determination of elliptic differential and finite difference operators in vector bundles overS 1

For an elliptic differential operatorA overS ¹, , withA _k (x) in END(^r) and as a principal angle, the -regularized determinant Det A is computed in terms of the monodromy mapP _A , associated toA and some invariant expressed in terms ofA _n andA _n–1 . A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature ofA whenA is self adjoint and show that the determinant ofA is the limit of a sequence of computable expressions involving determinants of difference approximation ofA.Partially supported by an NSF grant     

Nonexistence of hidden variables in the algebraic approach

Given two unital C*-algebrasA, and their state spacesE _A , E respectively, (A,E _A ) is said to have (, E) as a hidden theory via a linear, positive, unit-preserving map L: A if, for all E _A , L* can be decomposed in E into states with pointwise strictly less dispersion than that of . Conditions onA and L are found that exclude (A,E _A ) from having a hidden theory via L. It is shown in particular that, ifA is simple, then no (, E) can be a hidden theory of (A,E _A ) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra such that (, E) is a hidden theory of (A,E _A ) via a conditional expectation from ontoA.     

亮暗屏蔽光伏孤子在LiNbO3晶体中的大自偏转

用数值方法证实了亮、暗屏蔽光伏孤子在有外加电场的LiNbO₃晶体中都可以发生大自偏转,并验证了这种自偏转现象不但与晶体中受主浓度N_A有关而且还与外加电场E₀有关. 在E₀相同的条件下,N_A越小这种自偏转现象越明显,在N_A相同的条件下,E₀越大自偏转现象越明显. 还发现亮、暗屏蔽光伏孤子的自偏转现象不同：亮屏蔽光伏孤子整体都发生明显偏转,暗屏蔽光伏孤子的偏转只是发生在一侧,其极值位置和另一侧几乎不发生偏转. 关键词： 自偏转 空间孤子 光折变效应     

Kinetic evolutionary behavior of catalysis-select migration

We propose a catalysis-select migration driven evolution model of two-species(A-and B-species) aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K(k;i,j) = Kkij and D species catalysis-select migration rate kernel J(k;i,j) = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0(D0 and C0 are the initial numbers of the monomers of species D and C,respectively).When JD0 KC0 > 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 < 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 > 0 case.     

Sigma-models having supermanifolds as target spaces

We study a topological sigma-model (A-model) in the case when the target space is an (m ₀|m ₁)-dimensional supermanifold. We prove under certain conditions that such a model is equivalent to an A-model having an (m ₀–m ₁)-dimensional manifold as a target space. We use this result to prove that in the case when the target space of A-model is a complete intersection in a toric manifold, this A-model is equivalent to an A-model having a toric supermanifold as a target space.Research supported in part by NSF grant No. DMS-9201366.     

Generalized q-Hermite Polynomials

We consider two operators A and A ⁺ in a Hilbert space of functions on the exponential lattice , where 0<q<1. The operators are formal adjoints of each other and depend on a real parameter . We show how these operators lead to an essentially unique symmetric ground state ψ₀ and that A and A ⁺ are ladder operators for the sequence . The sequence (ψ _n /ψ₀) is shown to be a family of orthogonal polynomials, which we identify as symmetrized q-Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When γ=0 the polynomials are the discrete q-Hermite polynomials of type II, studied in several papers on q-quantum mechanics. Received: 6 December 1999 / Accepted: 21 May 2001     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Spin observables in small-angle elastic → d scattering with an L-type deuteron target at 800 MeV

We have measured spin correlation parameters that describe the elastic scattering of 800 MeV polarized protons from an L-type polarized deuteron target at laboratory angles below 20°. The measured parameters include the correlated analyzing powers A_SL, A_LL and A_NLL and the proton spin-transfer coefficients C_0L,S, C_0L,L, C_SL,N, C_NL,S, C_NL,L and C_LL,N. The results are compared with single-scattering predictions based on different phase-shift solutions for the nucleon-nucleon scattering matrix.     

The spectra and structure of indium iodide: The rotational and vibrational constants of the A0 state

The rotational constants of the A0⁺ state of InI are reported for the first time as B_e = 0.038077 cm⁻¹ and α_e = 0.0002373 cm⁻¹, while T_e = 24402.91 cm⁻¹ for the A0⁺-X0⁺ transition. Accurate vibrational constants for both the A0⁺ and X0⁺ states are computed from the derived band origins.     

Expectation values of unbounded observables

For an unbounded quantum mechanical observableA, the expectation value A _f and the mean square deviation _f A cannot be denned for all (pure) statesf by A _f = (f,Af) and ( _f A)² = (f,A ² f)-(f,Af)², respectively. More general definitions are given here, which are also valid for state mixtures (density matrices). A general uncertainty relation for unbounded observables is derived.     

On the homotopical significance of the type of von Neumann algebra factors

The set of all projections and the set of all unitaries in a von Neumann algebra factorA are studied from the homotopical point of view relative to the operator norm topology.Two projectionsE andF can be deformed continuously to each other if and only ifEF and 1–E1–F where denotes the equivalence of projections inA in the sense of von Neumann. In other words, the relative dimension and co-dimension are a complete homotopical invariants of projections inA and label pathwise connected components of the set of projections.The first homotopy group ₁(U(A)) of unitaries inA is shown to be 0 forA of infinite type. For typeII ₁ and typeI _n factors, ₁(U(A)) are isomorphic to additive groups of realsR and integersZ, respectively, in which the first homotopy group ₁(F U(A)) of the center ofU(A) is imbedded asZ andnZ, respectively.     

Three classes of space-time with a uniformly accelerating and nonrotating gravitational source

Three classes of Petrov type-D nonrotating empty spaces, which we denote asA ₊ ^* ,A ₋ ^* , anda ₀ ^* , can be seen to represent, respectively, a gravitational field of a uniformly accelerating source which moves with velocity slower, faster than, or equal to that of light. The first two classes of space-time,A ₊ ^* andA ₋ ^* , approach to the last one,a ₀ ^* , as the acceleration becomes greater and greater. The inertial frame in a flat space-time, relative to which a faster-thanlight particle moving along a spacelike geodesic behaves as an ordinary particle, is given and discussed. The behaviors of Killing horizons in the classes,A ₊ ^* andA ₋ ^* are investigated. Comparisons are made between the analysis by Farhoosh and Zimmerman and ours. Our identification of the acceleration parameter seems to be more appropriate than that by the above authors.     

Rotational band contour analysis in the à 1 A′-[Xtilde] 1 A′ electronic systems of substituted naphthalenes

The 0₀ ⁰ bands of the à ¹ A′-[Xtilde] ¹ A′ electronic systems of 2-fluoro, 2-hydroxy- and 2-aminonaphthalene have been identified and then rotationally analysed by the method of rotational band contour analysis. The effect of 2-substitution on the direction of the electronic transition moment vector in naphthalene is found to be drastic: the vector is oriented by about 70–80° (anti-clockwise in figure 1) by the substituent. However, the orientation is almost unaffected by the nature of the substituent.

The 0₀ ⁰ bands are all type A, B hybrids but predominantly type B. Significant differences in the 0₀ ⁰ band rotational contours in the three molecules are reflected in the different values of ΔA, ΔB and ΔC found from the contour analyses. An attempt to interpret the changes of rotational constants in terms of changes in geometry from the ground to the excited state suggest very strongly that the geometry change of the naphthalene rings in all the molecules is similar to that in naphthalene itself but that the carbon-substituent bonds contract in the excited state. The contraction increases from F to OH to NH₂ and is probably quantitatively similar to that suggested previously for the corresponding monosubstituted benzenes.     

Instantons in aU(1) lattice gauge theory: A Coulomb dipole gas

We study the decompositionA=A _I +A _SW of aU(1) lattice gauge field into instanton and spin wave parts. The action also decomposes,A=A _I +A _SW +R. HereA _I is a Coulomb dipole gas,A _SW is a zero mass free field, andR is a higher order remainder. We studyA _I in detail, ford4, in the dilute gas case (which corresponds to the low temperature limit of the gauge field theory). We establish the leading behavior of the free energy:f ^–d a. Here is the lattice spacing,a is a geometrical constant and is an activity defined in terms of a small number of instanton configurations. Our methods suggest the absence of screening in the dilute dipole gas,d4, in contrast to Debye screening for the dilute monopole gas.Supported in part by the National Science Foundation under Grant PHY 76-17191Supported in part by the National Science Foundation under Grant PHY 75-21212