Approach to Equilibrium in a Microscopic Model of Friction

We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field approximation. Letting V₀>0 be the initial velocity of the disk and V_∞>0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the background, we show that, if V_∞−V₀ is positive and sufficiently small, then the disk reaches V_∞ with the power law t^−(d+2), d=1,2,3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions. Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium.     

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V _∞=3.4–4.9 km/s in argon at pressures p _∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar ₂ ⁺ +e→Ar+Ar and ternary recombination Ar⁺+e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures. Zh. Tekh. Fiz. 67, 12–18 (May 1997)     

Adaptive Sub-sampling for Parametric Estimation of Gaussian Diffusions

We consider a Gaussian diffusion X _t (Ornstein-Uhlenbeck process) with drift coefficient γ and diffusion coefficient σ ², and an approximating process Y^e_tY^{\varepsilon}_{t} converging to X _t in L ₂ as ε→0. We study estimators [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} which are asymptotically equivalent to the Maximum likelihood estimators of γ and σ ², respectively. We assume that the estimators are based on the available N=N(ε) observations extracted by sub-sampling only from the approximating process Y^e_tY^{\varepsilon}_{t} with time step Δ=Δ(ε). We characterize all such adaptive sub-sampling schemes for which [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} are consistent and asymptotically efficient estimators of γ and σ ² as ε→0. The favorable adaptive sub-sampling schemes are identified by the conditions ε→0, Δ→0, (Δ/ε)→∞, and NΔ→∞, which implies that we sample from the process Y^e_tY^{\varepsilon}_{t} with a vanishing but coarse time step Δ(ε)≫ε. This study highlights the necessity to sub-sample at adequate rates when the observations are not generated by the underlying stochastic model whose parameters are being estimated. The adequate sub-sampling rates we identify seem to retain their validity in much wider contexts such as the additive triad application we briefly outline.     

Strongly Homotopy Lie Bialgebras and Lie Quasi-bialgebras

Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer–Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann–Schwarzbach. This approach provides a definition of an L _∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L _∞-algebra structure as a particular case of our construction. The formal geometry interpretation leads to a definition of an L _∞ (quasi)bialgebra structure on V as a differential operator Q on V, self-commuting with respect to the big bracket. Finally, we establish an L _∞-version of a Manin (quasi) triple and get a correspondence theorem with L _∞-(quasi)bialgebras. This paper is dedicated to Jean-Louis Loday on the occasion of his 60th birthday with admiration and gratitude.     

A Note on the Koszul Complex in Deformation Quantization

The aim of this short note is to present a proof of the existence of an A _∞-quasi-isomorphism between the A _∞-S(V ^*)-ù(V){\wedge(V)} -bimodule K, introduced in Calaque et al. (Bimodules and branes in deformation quantization, 2009), and the Koszul complex K(V) of S(V ^*), viewed as an A _∞-S(V ^*)-ù(V){\wedge(V)} -bimodule, for V a finite-dimensional (complex or real) vector space.     

The Discrete Spectrum¶of the Perturbed Periodic Schrödinger Operator¶in the Large Coupling Constant Limit

Let A be a periodic Schr?dinger operator and let V ₀≥ 0 be a decaying potential. We study the number of the eigenvalues of the operator A(α) =A−αV ₀ inside a fixed interval (λ₁,λ₂). We obtain an asymptotic formula for as α→∞. Received: 12 September 2000 / Accepted: 22 November 2000     

Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D ₀ in an external potential V, coupled to a quantized radiation field with energy H _f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D ₀+α · A+V +λ H _f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.      

Hydromagnetic surface waves in a moving compressible plasma column

Summary The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when one of the fluids has a relative motion has been studied as a function of the compressibility factors ₁/V ₁, wheres ₁ andV ₁ are the acoustic and Alfvén wave speed in one of the media. Both slow and fast magnetosonic surface waves for each symmetric and asymmetric modes can exist. The nature and existence of these modes depend on the values ofs ₁/V ₁ and ϑ, the angle of wave propagation. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle ϑ. The authors of this paper have agreed to not receive the proofs for correction.     

Dynamics of femtosecond-laser-ablated liquid-aluminum nanoparticles probed by means of spatiotemporally resolved X-ray absorption spectroscopy

We investigated spatiotemporal evolution of expanding ablation plume of aluminum created by a 100-fs, 10¹⁴–10¹⁵-W/cm² laser pulse. For diagnosing dynamic behavior of ablation plume, we employed the spatiotemporally resolved X-ray absorption spectroscopy (XAS) system that consists of a femtosecond-laser-plasma soft X-ray source and a Kirkpatrick–Baez (K–B) microscope. We successfully assigned the ejected particles by analyzing structure of absorption spectra near the L _II,III absorption edge of Al, and we clarified the spatial distribution of Al⁺ ions, Al atoms, and liquid droplets of Al in the plume. We found that the ejected particles strongly depend the irradiated laser intensity. The spatial distribution of atomic density and the expansion velocity of each type of particle were estimated from the spatiotemporal evolution of ablation particles. We also investigated a temperature of the aluminum fine particles in liquid phase during the plume expansion by analyzing the slope of the L _II,III absorption edge in case of 10¹⁴-W/cm² laser irradiation where the nanoparticles are most efficiently produced. The result suggests that the ejected particles travel in a vacuum as a liquid phase with a temperature of about 2500 to 4200 K in the early stage of plume expansion.     

Analytical singlet α s4 QCD contributions into the e+e?-annihilation Adler function and the generalized Crewther relations

The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides (x, y) (or p ², q ²). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α _s ³ corrections to the Gross-Llewellyn Smith sum rule S _GLS of νN deep inelastic scattering and the singlet α _s ³ correction to the e ⁺ e ⁻-annihilation Adler function D _A ^V in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result for S _GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet α _s ⁴ correction to the D _A ^V function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth order corrections to D _A ^V function demonstrates the coincidence of the predicted and obtained ζ₃²-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. Therefore, on the contrary to previous belief, the appearance of ζ₃-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov-Chetykin-Kuhn, that at the 5-loop level the generalized Crewther relation in the channel of vector currents may receive additional singlet contribution, which in this order of perturbation theory is proportional to the first coefficient of the QCD β function.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Beauty-conserving strangeness-changing rare semileptonic decays ofB s meson

The beauty-conserving strangeness-changing decays ofB _s meson are examined. In the charm sector, charm-conserving strangeness changing (Δc = 0, Δs ≠ 0) decays are Cabibbo suppressed and are governed by the CKM elementV _us which is much smaller than the CKM diagonal elementV _cs, so may be of little interest. On the other hand, in theb-sector, beauty-conserving strangeness changing (Δb = 0, Δs ≠ 0) decays are CKM allowed as the CKM matrix elementV _us governing such decays is much larger thanV _bc orV _bu which govern respectively theb →c orb →u transitions. The phase space available, however, is too small for the decays considered here. The numerical estimates for the decay widths of two such modes ofB _s meson are presented.     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

On the High Density Behavior of Hamming Codes with Fixed Minimum Distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n→∞, d→∞, d/n = δ. The problem is relevant for coding theory, and the best available bounds state that the maximum density of the system falls in the interval 1 ≤ ρ V _d ≤ exp (n κ(δ)), being κ(δ) > 0 and V _d the volume of a sphere of radius d. We find a solution of the equations describing the liquid up to an exponentially large value of ρ = ρ V _d , but we show that this solution gives a negative entropy for the liquid phase for ρ >rsimn. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. PACS: 05.20.Jj, 64.70.Pf, 61.20.Gy     

Effect of doping with divalent cationic impurities on relative mobility of edge and screw dislocations in NaCl crystals

In NaCl:Ca and NaCl:Pb crystals, we have investigated the effect of the impurity concentration and temperature on the parameter ξ=l _e /l _s where l _e and l _s are the path lengths traveled by edge and screw dislocations in the stress field of an indenter. The results obtained are explained taking into account additional inhibition of screw dislocations by debris. State Medical University, Moldavian Republic. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–102, May, 1996.     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

S-ordered Expansion of the Intermediate Representation Projector and Its Applications

We first deduce the s-ordered expansion of the Wigner operator. Since Radon transformation of Wigner operator is just the intermediate representation |x〉 _λ,ν projector, we naturally obtain the s-ordered product of |x〉 _λ,νλ,ν〈x|. Accordingly, the completeness relation is still preserved under the s-ordering. Finally, based on it, we obtain the s-ordered expansion of some useful operator in quantum optics, and some new operator identities are revealed accordingly.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Factorization and transverse momentum for two-hadron production in inclusive e + e − annihilation

We study the factorization of processes involving two fragmentation functions in the case of very small transverse momenta. We consider two-hadron production in inclusive e ⁺ e ⁻ annihilation and demonstrate a new simple and illustrative method of factorization for such processes, including leading order α _s corrections. The text was submitted by the authors in English.