Theta-point exponent for polymer chain in random media

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent _p ⁰ of polymer chains remains unchanged for small disorder concentration (p>p _c ). At the percolation thresholdp=p _c , using a Flory-type approximation, we conjecture that _pc ⁰ =5/(d _B +7), whered _B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p _c shifts to a dimensiond _c >3. We also propose that the-point varies practically linearly withp for 1>pp _c .     

Statistical mechanics of polymer networks of any topology

The statistical mechanics is considered of any polymer network with a prescribed topology, in dimensiond, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made toO(²), whered=4–, of the basic critical dimensions _L associated with anyL-leg vertex (L1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent _G of any networkG toO(²), includingL-leg star polymers. The infinite sets of contact critical exponents between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents ₀, ₁, ₂ calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimensiond=4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constitutingL-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents _L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled.     

Critical exponents of Manhattan Hamiltonian walks in two dimensions,from Potts andO(n) models

We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq ^1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model in the low-temperature phase withn =q ^1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < T_c), corresponding to a conformal theory with central chargeC = –2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .     

Quantum Tori, Mirror Symmetry and Deformation Theory

We suggest to compactify the universal covering of the moduli space of complex structures by noncommutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of Abelian varieties, this approach gives quantum tori as a noncommutative boundary of the moduli space. Relations to mirror symmetry, modular forms and deformation theory are discussed.     

q-Deformation of the Double Complex Ernst Equation

From a known three-dimensional representation of the double quantum algebra su _q ((J)), a nonlinear q-deformed Ernst equation system is obtained. By using a gauge covariant form, the deformation effects are found to generate a torsion in the field and to form a gauge field with source.     

Pionic degrees of freedom in atomic nuclei and quasielastic knockout of pions by high-energy electrons

The microscopic mechanism of the identical bands in odd-odd nucleus ¹⁹⁴Tl and its neighbor odd-A nuclei ^193,195Tl is investigated using the particle-number-conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. It is found that the blocking effect of the high-j intruder orbital plays an important role in the variation of moments of inertia (J⁽¹⁾ and J⁽²⁾) with rotational frequency for the superdeformed bands and identical bands. The variation of the occupation probability of each cranked orbital and the contributions to moment of inertia from each cranked orbital are presented.     

Quantum particle-like configurations of the electromagnetic field

We construct explicitly three-dimensional localized solutions of the free Maxwell's equations with a phase expi(k x - t) which move like relativistic particles. The total field energyE of the moving lump is proportional to the frequency and its momentumP is proportional to the wave vectork, withE ² =P ² +M ². Further, if the angular momentum is different from zero, thenE =. These solutions thus model the wave-particle duality of quantum particles.     

Block spin approach to φ 3 4 field theory

A block spin approach to the Euclidean ⁴ field theory in three dimensions is proposed by using the three-dimensional version of Gawedzki and Kupiainen's block spin transformation method. The lattice ₃ ⁴ model recovers the rotation invariance in the continuum limit, when the coupling constant is small.     

Hollow nanoparticles of <Emphasis Type="Italic">β</Emphasis>-iron oxide synthesized by chemical vapor condensation

Hollow nanoparticles of -Fe₂O₃ were synthesized by chemical vapor condensation (CVC). A structural study revealed that the nanoparticles, 10–20 nm in diameter, consisted of hollow structures with several shells 3–5 nm in thickness. TEM observation indicated that the shells of the -Fe₂O₃ nanoparticles consist of several grain structures having different crystal orientations. This feature of the crystallinity enables us to infer the formation mechanism of the hollow structure of the -Fe₂O₃ nanoparticles during CVC process.     

Near-Field Induced FIR Josephson-Detection by c-Axis-Oriented YBa2Cu3O7-δ-Films

A novel approach to intrinsic Josephson-detection of far infrared radiation is reported utilizing near-zone field effects at electric contacts on c-axis oriented YBa₂Cu₃O_7- films. While only a bolometric signal was observed focusing the radiation far off the contacts on c-axis normal films, irradiating the edge of contacts yielded an almost wavelength independent fast signal showing the characteristic intensity dependence of Josephson-detection. The signal is attributed to a c-axis parallel component of the electric radiation field being generated in the near-zone field of diffraction at the metallic contact structures.     

The spherical limit forn-vector correlations

We investigate then limit of then-vector model single-spin and pairspin correlation functions. In this limit we show that the correlation functions become those of the corresponding spherical model.     

Intrinsical Randomness of Kolmogorov ℤd-Actions on a Lebesgue Space

We introduce a concept of an intrinsically weak and strong randomness of a ^d -action on a Lebesgue space and we show that Kolmogorov ^d -actions are intrinsically weak random, and Bernoulli ^d -actions are intrinsically strong random.     

Integrability and PT-Symmetry of N-Body Systems with Spin-Coupling δ-Interactions

We study the PT-symmetric boundary conditions for "spin"-related -interactions and the corresponding integrability for both bosonic and fermionic many-body systems. The spectra and bound states are discussed in detail for 1/2-spin particle systems.     

Photophysical Behavior of β-Carboline-3-Carboxylic Acid N-Methylamide

The solvent and temperature effect of fluorescence and phosphorescence and its polarization characteristics for -carboline-3-carboxylic acid N-methylamide were studied. From the results obtained it is concluded that the first excited singlet state changes from the * type in a polar solvent (EPA) to the n* type in a nonpolar solvent (MC) and that the lowest singlet excited states (* type and n* type) interact by vibronic coupling. In the nonpolar solvent (MC) the lowest singlet excited states are very close in energy and consequently the vibronic coupling is stronger. It has been found that the 0–0 band of the phosphorescence emission in EPA is polarized out of plane, using the excitations corresponding to absorptions into the first and second excited * singlet states. This fact and the order of lifetime measured indicate an emitting triplet that is *. The origin of this polarization is very likely mixing as a result of spin–orbit coupling. However, the vibrational structures and changing polarization outside the 0–0 band indicate that second-order effects involving spin–orbit coupling and vibronic interactions are important and the mixing scheme appears to be and . The proximity effect can qualitatively explain the absence of phosphorescence and the stronger vibronic interaction between the n* and the * states of -carboline-3-carboxylic acid .N-methylamide in a hydrocarbon solvent (MC).     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation—an -machine—is the minimal one consistent with accurate prediction. We establish several results on -machine optimality and uniqueness and on how -machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from -machines to those from ergodic and information theories.     

Collective structures of the <Superscript>131</Superscript>Cs nucleus

The collective structures of ¹³¹Cs have been investigated by in-beam -ray spectroscopic techniques following the ¹²⁴Sn (^11B , 4n) reaction at a beam energy E_lab = 57MeV. The previously established rotational bands, built on g_7/2, d_5/2 and the unique-parity h_11/2 orbitals, have been extended and evolve into new bands involving rotationally aligned (h_11/2)² and (h_11/2)² quasiparticles. In addition, a new multiquasiparticle band based on the g_7/2 g_7/2 h_11/2 configuration has also been observed. Theoretical interpretations for the assigned configurations are discussed in the framework of Total Routhian Surface (TRS) and Tilted Axis Cranking (TAC) model calculations. TAC model calculations predict a decrease in the B(M1) values with increasing rotational frequency for the g_7/2/d_5/2 (h_11/2)² and h_11/2 (h_11/2)² bands, thus indicating a magnetic rotation character for these bands.