Thermal Entanglement of the Two-Qubit Heisenberg Spin Chain Coupled to a Single-Mode Cavity Field

Thermal entanglement of a two-qubit Heisenberg spin chain coupled to a single-mode cavity field is investigated. It is found that (1) thermal entanglement without the rotating-wave approximation (RWA) is explicitly smaller than that obtained with the RWA, which means that the counter-rotating terms have a large impact on thermal entanglement, therefore they cannot be neglected; (2) the case (ω≪Ω) is more beneficial for enhancing thermal entanglement than the resonance case (ω=Ω), the near-resonant case (ω≈Ω) and the case (ω≫Ω); (3) for thermal entanglement, there is a competition process between the exchange coupling J (the direct-coupling between the two two-level atoms) and the coupling constant g (which deduces the indirect effect between the two two-level atoms); the critical value of g increases with the spin coupling strength J.     

Generalized Two-Mode Squeezed States and Some Nonclassical Characteristics

A class of generalized two-mode squeezed states |φ〉 is presented, which are generated from the generalized two-mode squeezing operator U(γ,λ) acting on the two-mode coherent state |α ₁,α ₂〉. We first investigate some mathematical properties of U(γ,λ) including the squeezing transformation under U(γ,λ), ket-bra integral form in the coordinate representation, normally ordered form. Then we evaluate some nonclassical characteristics of the state |φ〉 such as higher-order squeezing behavior, entanglement analysis and analytical expression of the Wigner function.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Reflectance fluctuations in an absorbing random waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an N-mode disordered waveguide with weak absorption g per mean free path. Two distinct regimes are identified. The regime γ N ²≫1 shows universal fluctuations. With increasing length L of the waveguide, the variance of the reflectance changes from the value 2/15N ², characteristic for universal conductance fluctuations in disordered wires, to another value 1/8N ², characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value 1/3N to 1/4N. In the regime γ N ²≫1, the large-L distribution of the reflectance R becomes very wide and asymmetric, P(R)∝(1−R)⁻² for R≪1−γN. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 289–293 (25 August 1996) Published in English in the original Russian journal. Edited by J. R. Anderson.     

Coherent inelastic processes on nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. For taking into account the influence of the nucleus matter, the optical model, based on the conception of the refraction index, is used. Analytical formulas for the effective cross section σ _coh (a → b) are obtained, taking into account that, at ultrarelativistic energies, the main contribution into σ _coh (a → b) is provided by very small transferred momenta in the vicinity of the minimal longitudinal momentum transferred to the nucleus. It is shown that the cross section σ _coh (a → b) may be expressed through the “forward” amplitudes of inelastic scattering f _a+N+b+N (0) and elastic scattering f _a+N+a+N(0), f _b+N+b+N(0) on a separate nucleon, and it depends on the ratios L _a /R and L _b /R (L _a and L _b are the mean lengths of the free path in the nucleus matter for the particles a and b, respectively, and R is the nucleus radius). In particular, when L _a /R ≫ 1, but L _b /R ≪ 1 (or L _a /R ≪ 1, but L _b /R ≫ 1), σ _coh (a → b) is equal to the ratio of the “forward” cross sections of inelastic scattering a + N → b + N and elastic scattering of the particle b (or a) on a nucleon, multiplied by the cross section of scattering on the “black” nucleus πR ². When both conditions L _a /R ≫ 1 and L _b /R ≫ 1 are satisfied, σ _coh (a → b) is proportional to the factor R ⁴/k ², where k is the initial energy of particle a in the laboratory frame. The text was submitted by the authors in English.     

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

Multi-Hamiltonian structure of kdv hierarchy by Drienfeld-Sokolov formalism

Conserved quantities and the multi-Hamiltonian structure for the integrable coupled kdv system which is associated with the isospectral flow [(∑ _i=0 ^N−1 ε _i λ ⁱ )∂² + ∑ _i=0 ^N−l V ₁λ ⁱ ]φ=λ ^N φ are deduced by the Drienfeld-Sokolov formalism.     

Model for laser-induced thermal degradation and ablation of polymers

Ablation of organic polymers is described on the basis of photothermal bond breaking within the bulk material. Here, we assume a first-order chemical reaction, which can be described by an Arrhenius law. Ablation starts when the density of broken bonds at the surface reaches a certain critical value. In order to understand the ablation behavior near the threshold fluence, φ_th, non-stationary regimes must be considered. The present treatment reveals several qualitative differences with respect to models that treat ablation as a surface process: (i) Ablation starts sharply with a front velocity that has its maximum value just after the onset. (ii) The transition to the quasi-stationary ablation regime is faster. (iii) Near threshold, the ablated depth h has a square-root dependence on laser fluence, i.e., h∝(φ-φ_th)^1/2. The ablation velocity is very high even near φ_th. (iv) With φ≈φ_th ablation starts well after the laser pulse. (v) The depletion of species is responsible for the Arrhenius tail observed with fluences φ≤φ_th. (vi) Residual modification of material has maximum near the threshold. (vii) Stationary regimes of ablation demonstrate change of effective activation energy with laser intensity. The model calculations are applied to Polyimide (Kapton^TM H). Here, differences in single-pulse ablated depth determined from mass loss and profilometry should be about 10 nm. Received: 16 February 1999 / Accepted: 18 February 1999 / Published online: 28 April 1999     

Conditions for XUV amplification considering recombination in clusters

3 cm^-l for a wavelength of λ_R≈200 Å in a time ≲1 ps can be expected. The measurable gain G_real depends on the cluster density N_cl. For N_cl≈10¹⁶ cm^-3 we expect G_real≳20 cm^-1. Received: 30 October 1997     

Heavy quark currents in ultra-high energy neutrino interactions

We discuss heavy quark contributions to the neutrino-nucleon total cross section at very high energies, well above the real top production threshold. The top-bottom weak current is found to generate strong left-right asymmetry of neutrino-nucleon interactions. We separate contributions of different helicity states and make use of the κ-factorization to derive simple and practically useful formulas for the left-handed (F _L ) and right-handed (F _R ) components of the conventional structure function 2xF ₃ = F _L − F _R in terms of the integrated gluon density. We show that F _L ≫ F _R and, consequently, xF ₃ ≈ F _T , where F _T is the transverse structure function. The conventional structure function F ₂ = F _S + F _T at Q ² ≪ m _t ² appears to be dominated by its scalar (also known as longitudinal) component F _S and the hierarchy F _S ≫ F _L ≫ F _R arises naturally. We evaluate the total neutrino-nucleon cross section at ultra-high energies within the color dipole BFKL-formalism.     

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     

Cluster ion emission from LiF induced by MeV N<Superscript>q+</Superscript> projectiles and <Superscript>252</Superscript>Cf fission fragments

Ion cluster desorption yields from LiF were measured at PUC-Rio with ≈0.1 MeV/u N ^q+ (q = 2,4,5,6) ion beams by means of a time-of-fight (TOF) mass spectrometer. A ²⁵²Cf source mounted in the irradiation chamber allows immediate comparison of cluster emissions induced by ≈65 MeV fission fragments (FF). Emission of (LiF) _n Li⁺ clusters are observed for both the N beams and the ²⁵²Cf fission fragments. The observed cluster size n varies from 1 to 6 for N ^q+ projectiles and from 1 to ≈40 for the ²⁵²Cf-FF. The size dependence of the Y(n) distributions suggests two cluster formation regimes: (i) recombination process in the outgoing gas phase after impact and (ii) emission of pre-formed clusters from the periphery of the impact site. The corresponding distribution of ejected negative cluster ions (LiF) _n F⁻ closely resembles that of the positive secondary (LiF) _n Li⁺ ions. The desorption yields of positive ions scale as Y(n) ∼ q ⁵. A calculation with the CASP code shows that this corresponds to a cubic scaling ∼S _e ³ with the electronic stopping power S _e , as predicted by collective shock wave models for sputtering and models involving multiple excitons (Frenkel pair sputtering). We discuss possible interpretations of the functional dependence of the evolution of the cluster emission yield Y(n) with cluster size n, fitted by a number of statistical distributions.     

Conserved Noise Restricted Curvature Model

A restricted curvature model with conservation of total number of particles is introduced. The surface width W of the model grows as t ^β at the beginning with β≈0.25 and becomes saturated at L ^α for t≫L ^z with α≈1.5, where L is the system size. The conservation law leads to a new universality class following sixth-order linear equation with conservative noise. The relation between our model and the equation is discussed.     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Scale-dependent elastic response of closed phospholipid bilayers to transmembrane molecular pumping activity: a key for exo-endocytosis physiological process

Summary The question is asked on the physiological role of the universal molecular biological function activity of lipid transmembrane translocation in living-cell membranes. The elastic response of closed bilayers to phospholipid translocation is theoretically found to be scale dependent, leading to vesiculation for plasma membrane characteristic-size bilayers (R _m≈10 μm), and to dilation strain for endocytic-vesicles characteristic-size bilayers (R _m≈0.1 μm). Both vesiculation and dilation effects are experimentally proved. On the basis of this scaledependent behaviour, it is argued that transmembrane pumping activity could control both the vesiculation and the fusion processin vivo, namely the exo-endocytic cellular-membrane traffic process itself. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

On Wilson’s theory of confinement

According to recent results, the Gell-Mann-Low function β(g) of four-dimensional φ⁴ theory is nonalternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means the possibility of constructing a continuous theory with finite interaction at large distances. This conclusion is in visible contradiction to the lattice results indicating triviality of φ⁴ theory. This contradiction is resolved by a special character of renormalizability in φ⁴ theory: to obtain the continuous renormalized theory, there is no need to eliminate a lattice from the bare theory. In fact, such kind of renormalizability is not accidental and can be understood in the framework of Wilson’s many-parameter renormalization group. Application of these ideas to QCD shows that Wilson’s theory of confinement is not purely illustrative, but has a direct relation to a real situation. As a result, the problem of analytical proof of confinement and a mass gap can be considered solved, at least on the physical level of rigor.     

Paramagnetic relaxation of Er in an Er single crystal

The paramagnetic relaxation of Er in an Er single crystal was measured atT≫T _N and compared to the relaxation of Er ions in a polycrystalline Pb host. The results indicate an enhancement of at most 50% of the f-conduction electron exchange interaction in Er, as expected for highly ionic f-orbitals. The ratio of the quadrupole moments of the¹⁵⁴ Er(I ^π=11⁻) and the¹⁵⁵ Er(I ^π=13/2⁺) isomers was measured to be 1.18(3) indicating onset of nuclear deformation at N=87. Deceased May, 1986