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     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

A new optical method for measuring the electron-phonon interaction parameter λ〈Ω2〉 using the spectral dependence of the relaxation rate

The spectral dependence of the electron-phonon relaxation rate γ_e−ph(ℏω) in metals is studied in pump-supercontinuum-probe (PSCP) experiments with femtosecond time resolution. Investigation of this spectral dependence, which exhibits a substantial slowing of the relaxation rate γ_e−ph(ℏω) near the Fermi level E _F , using the parametrization γ_e−ph(ℏω)∝λ〈Ω²〉 (ℏω−E _F )² makes it possible to determine directly the electron-phonon interaction parameter λ〈Ω²〉. The parameter λ〈Ω²〉 for YBa₂Cu₃O_7−δ is analyzed using this method. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 329–332 (10 September 1999)     

Random walk with persistence

The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)= _n=0 s ⁿ P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R ²(n), R ⁴(n), and R ⁶(n) are calculated and approximate results forP(R,n) and R ^–1(n) are given.     

Smoothening of a random surface as it results from the edwards-wilkinson kinetic equation

The time evolution of a random surfacez=h(r, t) (r=x, y) formed by a deposition process of the Edwards-Wilkinson type is discussed. The discussion is based on the author’s former derivation of the autocorrelation functionA _h(|r − r′|,t, t′)=〈h(r,t)h(r′,t′)〉 of the height functionh(r,t) under the assumption of a stochastic initial condition [V. Bezák: Acta Physica Univ. Comenianae39 (1998) 135]. Under the assumption of a steady (non-zero) deposition rate, the varianceσ _h ² (t)=〈[h(r,t)]²〉 increases logarithmically in time whilst the correlation lengthl _h(t) of the height functionh(r,t) increases as ∼t ^1/2. Therefore, the ratioσ _h(t)/l _h (t) tends to zero and the surfacez=h(r,t) does always tend towards a smoothened appearance. This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97.     

New phase transition in an easy-axis “triangular” antiferromagnet

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear anti-ferromagnet CsMnI₃ is investigated at T=1.3 K in magnetic fields up to ∼80 kOe and angles between the field and C ₆ axis ϕ≈ 0.5° and ϕ=7°. A new reorientational magnetic phase transition is observed in a field H _c1≈39.0 kOe. The magnetic structure for H>H _c1 is determined. The average Mn²⁺ spins of the magnetic sublattices in the new phase are determined from an analysis of the NMR spectrum to be 〈 S _C 〉=1.63 and 〈S _D 〉=1.72. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 988–993 (25 June 1998)     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Distribution of the conductance of a linear chain of tunnel barriers with fractal disorder

Distributions of the conductance G of a long quantum wire with the fractal distribution of barriers have been obtained in the successive incoherent tunneling regime. The asymptotic behavior (in the limit L → ∞) of moments 〈G ^k (L)〉, average power of the shot noise 〈S(L)〉, and Fano factor agree with the results of the work [C. W. J. Beenakker et al., Phys. Rev. B 79, 024204 (2009)], and the distributions themselves describe well the Monte Carlo simulation results. The equation that has been obtained for the distributions of the resistance and conductance agrees with the recent fractional differential generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the quasi-one-dimensional multichannel disordered semiconductors with a self-similar distribution of scatterers.     

Spectral rigidity and eigenfunction correlations at the Anderson transition

The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if the critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is compressible, in the sense that the variance of the level number in an interval is 〈 (δN)²〉∼χ〈N〉 for 〈N〉≫1. The compressibility, χ=η/2d, is given exactly in terms of the multifractal exponent η =d−D ₂ at the mobility edge in a d-dimensional system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 355–360 (10 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Complex Wavelet Transform of the Bell States

By employing the technique of an integral within an ordered product (IWOP) of operators we recast the complex wavelet transform to a matrix element of the two-mode squeezing-displacing operator U ₂(μ,σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U ₂(μ,σ)|f〉 can be considered as a new kind of spectra for analyzing |f〉, this may have some potential applications in quantum information and calculation. As an example, we numerically calculate wavelet-transform spectrum for the Bell states, which may play a role of distinguishing them one from another.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)     

Typicality of Pure States Randomly Sampled According to the Gaussian Adjusted Projected Measure

Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator ρ of low purity, tr ρ ² ≪1, and yielding the ensemble averaged expectation value tr (ρ A) for any observable A. Assuming that the given statistical ensemble ρ is generated by randomly sampling pure states |ψ〉 according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value 〈ψ|A|ψ〉 is shown to be extremely close to the ensemble average tr (ρ A) for the overwhelming majority of pure states |ψ〉 and any experimentally realistic observable A. In particular, such a ‘typicality’ property holds  whenever the Hilbert space ℋ of the system contains a high dimensional subspace ℋ₊⊂ℋ with the property that all |ψ〉∈ℋ₊ are realized with equal probability and all other |ψ〉∈ℋ are excluded.     

Distribution function for large velocities of a two-dimensional gas under shear flow

The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea _c ^(k) , which behaves for largek asa _c ^(k) ∼k ⁻¹. This divergence is consistent with an algebraic tail of the formf(V) ∼V ^−4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Obtaining Multimode Entangled State Representation by Generalized Radon Transformation of the Wigner Operator

In a preceding paper (Fan and Lv in J. Math. Phys. 50:102108, 2009), the phase-space integration corresponding to the straight line characteristic of two different real parameters λ,τ over the Wigner operator (i.e. the Radon transformation) leads to pure-state density operator |u〉 _{λ,τ  λ,τ} 〈u|, where |u〉 _λ,τ is just the coordinate-momentum intermediate representation. In this work we show that generalized Radon transformation of the Wigner operator yields multimode density operator of continuum variables. This provides us with a new approach for obtaining multimode entangled state representation. The Weyl ordering of the Wigner operator is used in our discussions.     

Polarization of leading Λ hyperons produced by neutrons on target nuclei

The polarization of the leading Λ hyperons produced on carbon and lead target nuclei by 4–10 GeV neutrons in the angle range Θ<8.5° with respect to the beam and with only neutral-particle accompaniment is measured: 〈Π〉=−0.096±0.018 for C and 〈Π〉=− 0.128±0.047 for Pb. The dependence of the polarization on the transverse momentum and the Feynman variable is measured. The normalized invariant cross section as a function of p _⊥ ² is found to be approximated by the function A exp(−Bp _⊥ ² ), where the parameter B is independent of the kind of nucleus (B=8.71±0.09 (GeV/c)⁻² for carbon and B=8.83±0.18 (GeV/c)⁻² for lead). Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 237–240 (25 August 1996)     

Λ and K s 0 production in pC collisions at 10 GeV/c

The experimental data from the 2-m propane bubble chamber have been analyzed for pC → Λ(K _s ⁰ )X reactions at 10 GeV/c. The estimation of experimental inclusive cross sections for Λ and K _s ⁰ production in the p ¹²C collision is equal to σ_Λ = (13.3 ± 1.7) mb and σ _{K s} ⁰ = (4.6 ± 0.6) mb, respectively. The measured 〈Λ〉/〈π⁺〉 ratio from pC reaction is equal to (5.3 ± 0.8) × 10⁻², and it is approximately two times larger than the 〈Λ〉/〈π⁺〉 ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy. The text was submitted by the authors in English.