From Convolutionless Generalized Master to Pauli Master Equations

Previously we have proved that time integrals of memory functions (i.e. markovian transfer rates from Pauli Master Equations — PME) in Time-Convolution Generalized Master Equations (TC-GME) for probabilities of finding a state of an asymmetric system interacting with a bath with a continuous spectrum are exactly zeroprovided that no approximation was involved. This is irrespective of the usual finite-pertubational-order correspondence with the Golden Rule transition rates. Here, attention is turned to an alternative way to derive the rigorous PME from the Time-Convolutionless Generalized Master Equations (TCL-GME). Arguments are given that the long-time limit of coefficients in TCL-GME for the above probabilities is, under the same assumption and presuming that this limit exists, equal to zero.The author should like to acknowledge a support of grants GAUK-292 of the Grant Agency of Charles University and GAR-2428 of the Czech Grant Agency.     

Atomic and electronic structures of GaAs (001) surface

The atomic and electronic structures of α, β, β₂, and ζ reconstructions for the Ga-terminated GaAs (001)-(4×2) surface are investigated in the framework of the pseudopotential approach. Total, surface, and local densities of electron states, electron-energy spectra, and relative surface energies of the structures under consideration are calculated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 44–52, October, 2006.     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

A Class of Weakly Self-Avoiding Walks

We define a class of weakly self-avoiding walks on the integers by conditioning a simple random walk of length n to have a p-fold self-intersection local time smaller than n ^β , where 1<β<(p+1)/2. We show that the conditioned paths grow of order n ^α , where α=(p−β)/(p−1), and also prove a coarse large deviation principle for the order of growth.     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

Three-photon absorption coefficients in ZnSe/ZnS0.18Se0.82 strained-layer superlattices

Summary We provide the first experimental determination of three-photon absorption (ThPA) coefficients α⁽³⁾ in a quasi-bidimensional structure. The measurements of α⁽³⁾ have been performed on a sample of a ZnSe/ZnS_0.18Se_0.82 strainedlayer superlattice at fixed excitation energies corresponding to the exciton resonances near the direct band gap. The evidence of the ThPA process in such energy range points out the huge enhancement of exciton non-linearities in quantum-confined systems.     

The anisotropy of fluorescence in ring units III: Tangential versus radial dipole arrangement

The time dependence of the anisotropy of fluorescence can indicate the coherent exciton transfer regime in molecular rings. We are comparing time development of this quantity after an impulsive excitation obtained for the ring models of bacterial antenna complexes with tangential and radial optical transition dipole moments arrangement as in nonameric LH2 and octameric LH4 units. We use non-correlated static Gaussian disorder in the local exciton energies. We take into account simultaneously dynamic disorder using a Markovian treatment of the interaction with the bath. We show that the influence of dynamic disorder on difference of the anisotropy of fluorescence is more important then the influence of static disorder in consequence of different band width.     

紫细菌B800缺失LH2能量传递模型的构建及性质

构建B800缺失LH2对于阐明光合作用中光能传递的分子机制与捕光复合体组装机制具有重要意义。采用吸收光谱、荧光光谱、分子筛层析、超滤和SDS-PAGE等方法研究了紫细菌两个典型种外周捕光复合体 (LH2) 约800 nm特征光谱 (B800) 细菌叶绿素 (BChl) 缺失能量传递模型的构建方法及性质。结果表明：在pH 8.0 Tris-HCl(10 mmol·L-1) 缓冲液中,0.08% SDS能够使来自Rhodobacter azotoformans的LH2 B800 BChl特异性解离,解离体系中加入10%(φ) 甲醇,通过超滤脱除游离BChl,构建了B800缺失LH2,但该缺失模型不够稳定。在pH 1.9缓冲液中,来自Rhodopseudomonas palustris的LH2 B800 BChl能够特异性解离,通过层析得到两个组分。一个组分的B800 BChl不能通过层析脱除,能够重新自组装成LH2。另一个组分为B800缺失LH2,该缺失模型稳定。两种LH2均存在2类以上B800 BChl结合位点,并得到了两类Rhodopseudomonas palustris B800 BChl解离的LH2,但未发现类似紫色硫细菌中的B800吸收光谱劈裂现象。B800缺失LH2均未呈现约800 nm特征荧光光谱。采用两种方法构建了两个物种B800缺失LH2能量传递模型。利用BChl与缺失B800 LH2结合能力不同的特性,将Rhodopseudomonas palustris中的LH2分成两个类型,实现了异质性亚基LH2的分离。     

Entanglement and Mixedness of Locally Cloned Non-Maximal W-State

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W-state or W-type state |X〉=α|001〉₁₂₃+β|010〉₁₂₃+γ|100〉₁₂₃,α ²+β ²+γ ²=1 shared by three distant partners. Also we have considered the case β=γ, to obtain a range for α ², for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixedness of inseparable states with their amount of inseparability, for that range of α ².     

Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit

We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal modes are excited, and perform a very accurate systematic study of the equilibrium time as a function of the number N of particles, the specific energy ε, and the parameters α and β. While at any fixed N the equilibrium time is found to be a stretched exponential in 1/ε, in the thermodynamic limit, i.e. for N→∞ at fixed ε, we observe a crossover to a power law. Concerning the (usually disregarded) dependence of T _eq on α and β, we find it is nontrivial, and propose and test a general law. A central role is played by the comparison of the FPU models with the Toda model.     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Local Energy Statistics in Spin Glasses

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E _N < β _c N, where β _c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies. Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from Physics and Biology” and by the European Science Foundation in the Programme RDSES.     

Chaos and Monte Carlo Approximations of the Flip-Annihilation process

The flip-annihilation process is a random particle process with one-dimensional local interaction in discrete time, initially presented by one of us, namely Toom in 2004. Its components are enumerated by integer numbers and every component has two states, “minus” and “plus”. At every time step two transformations occur. The first one, called “flip”, independently turns every minus into plus with probability β. The second one, called “annihilation”, acts thus: whenever a plus is a left neighbor of a minus, both disappear with probability α independently from other components. What is interesting about this process is that it is ergodic for β>α/2 and non-ergodic for β<α ²/250. It is natural to conjecture that there is some transition curve, which we call the true curve and denote by , which separates the areas of ergodicity and non-ergodicity of this process from each other. The estimates, mentioned above, albeit rigorous, leave a large gap between them and the present article’s purpose is to obtain some closer, albeit non-rigorous, approximations of the true curve. We do it in two ways, one of which is a chaos approximation and the other is a Monte Carlo simulation. Thus we obtain two curves, which are much closer to each other than the rigorous estimations. Also we fill in, albeit only numerically, another shortcoming of the rigorous estimation β<α ²/250, namely that it leaves us uncertain whether the true curve has a zero or positive slope at the point α=β=0. Both approximate curves have a positive slope at α=0, as we hoped.     

Excitons in monoclinic zinc diphosphide. Longitudinal exciton and the mixed mode

Exciton absorption spectra in high-quality β-ZnP₂ single crystals have been investigated at T=1.7 K for various directions of the wave vector and various polarization states of the radiation. It has been unambiguously established that the additional high-energy A series, which in some works has been called a D series and ascribed to ZnP₂ crystals, of so-called “rhombic” symmetry,^1,8,10,11 is an intrinsic exciton of the β-ZnP₂ series. A mixed mode has been detected for the first time, and the energy of the longitudinal exciton has been determined. The selection rules for the exciton transitions have been analyzed by a group-theoretical approach, and the symmetry of the nS states of the single exciton has been established on the basis of the experimental data — Γ ₂ ⁻ (z). Fiz. Tverd. Tela (St. Petersburg) 41, 193–202 (February 1999)     

Absorption spectrum and excitons in thin films of the solid electrolyte RbCu4Cl3I2

We have investigated the absorption spectrum of thin films of the superionic conductor RbCu₄Cl₃I₂ synthesized on NaCl crystalline substrates. It is shown that the electron and exciton excitations in the energy interval 3–6 eV are associated with optical transitions in the CuHal sublattice, and the edge of the fundamental band is controlled by optical transitions in the Cu(II)Hal sublattice. It is found that the large band gap of this compound (E _g =3.86 eV) in comparison with those of CuCl and CuI is a result of the small number of Cu ions in the second coordination sphere. The temperature dependence of the spectral position and half-width of the low-temperature exciton band reveals features associated with the phase transitions γ→β (T _c1=170 K) and β→α (T _c2=220 K) and with disordering of the cation sublattice attendant to the transition to the superionic state. Fiz. Tverd. Tela (St. Petersburg) 40, 1022–1026 (June 1998)     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

On the mechanism of phase transformation in Ag2Se

A differential thermal analysis ΔT _y (T) in vacuum has been performed, and the temperature gradient ΔT _x (T) along the Ag₂Se sample during the transition α → β has been studied. It has been shown that the transitions α → α′ and β′ → β are displacive transitions and that the transition α′ → β′ is a reconstructive transition. It has been found that the temperature gradient along the sample during the transition α′ → β′ passes through a deep minimum due to a strong increase in the specific heat capacity.     

Measurements of K-shell ionization cross sections of35Br,37Rb,39Y using low energy protons

K-shell ionization cross section measurements are reported for₃₅Br,₃₇Rb and₃₉Y targets caused by protons over 300–400 keV energy range in 20 keV increment. The K-shell ionization cross sections (σ _k ^l ) at different energies were deduced from the K_α and K_β X-ray production cross sections which were obtained from X-ray yields of the K_α and K_β transitions. The experimental values are compared with the calculated values of ECPSSR theory and empirical reference cross sections. The resultant K-shell ionization cross sections are found to be in reasonable agreement with the ECPSSR theory. The K_α/K_β intensity ratios are also presented and compared with other experimental values and also with the theoretical one-hole values given by Scofield.     

Dynamic-mechanical and nuclear magnetic resonance study of relaxation processes in ultra-high molecular weight polyethylene fibres

The relaxation processes (α, β, and γ) in UHMW PE fibres drawn to different draw ratios λ have been studied by dynamic-mechanical and nuclear magnetic resonance methods. The temperature dependences of tensile loss moduli E″ and spin-lattice relaxation times T ₁ have been analyzed assuming distribution of correlation times τ according to the Davidson—Cole function. The activation energies E _a and parameters ε characterizing widths of distribution, and asymptotic value τ ₀ for correlation times have been determined from experimental data for low-temperature γ-process and for high-temperature α-process. A weak β-process has been found by dynamic-mechanical method and quantitative analysis was made only for fibres with λ = 9. The temperature dependences of second moment M ₂ of the broad-line NMR spectra have been analyzed according to the Gutowsky—Pake formula, which includes only a single correlation time τ _c without distribution. In this case the activation energies E _a and values of τ ₀ have been determined.     

The Hume-Rothery rules and phase stabilities in noble metal alloys

Results from martensitic transformations are used to evaluate stabilities of the equilibrium phases in the Hume-Rothery electron compounds based on Cu, Ag and Au, and to give arguments why the electron concentration plays such an important role in the selection of the crystal structures. It is shown that the vibrational entropy difference observed for the martensitic transformation from ordered bcc to the close packed martensite and its e/a dependence can also account for the entropy difference ΔS ^α/β between the equilibrium α and β at high temperatures, and can be made largely responsible for the composition dependence of the (α+β) two phase field. The enthalpy of mixing can be decomposed into a small term which depends on the average periodic lattice, which is different in α and β but which is nearly the same in all alloys studied, and a contribution which is due to the difference in the properties of the atoms and which can be expressed by pair interchange energies. This contribution depends strongly on the specific alloy system, but is independent of structure, which is compatible with a pair interchange energy depending only on pair distance but not on structure, as suggested by simple pseudopotential theory. The same pair interchange energies account also for long range order and the critical ordering temperature. The evaluation for several alloy systems shows a surprisingly good agreement within this picture, and permits to understand better why the electron concentration plays such an important role also for other structures, although the energy contribution of the conduction electrons is only a small part of the total enthalpy of formation of any of the equilibrium structures.