Two-point correlation function in systems with van der Waals type interaction

The behavior of the bulk two-point correlation function G(;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r ^{- (d + σ)}, with 2 < d < 4, 2 < σ < 4 and d + σ≤6. It is shown that G(;T| d ) decays as r ^{- (d - 2)} for 1 ≪r≪ξ, exponentially for ξ≪r≪r ^*, where r ^* = (σ - 2)ξlnξ, and again in a power law as r ^{- (d + σ)} for r≫r ^*. The analytical form of the leading-order scaling function of G(;T| d ) in any of these regimes is derived. Received 28 May 2001     

Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature

We study a class of continuous time Markov processes, which describes ± 1 spin flip dynamics on the hypercubic latticeℤ ^d , d≥ 2, with initial spin configurations chosen according to the Bernoulli product measure with density p of spins + 1. During the evolution the spin at each site flips at rate c= 0, or 0 < α≤ 1, or 1, depending on whether, respectively, a majority of spins of nearest neighbors to this site exists and agrees with the value of the spin at the given site, or does not exist (there is a tie), or exists and disagrees with the value of the spin at the given site. These dynamics correspond to various stochastic Ising models at 0 temperature, for the Hamiltonian with uniform ferromagnetic interaction between nearest neighbors. In case α= 1, the dynamics is also a threshold voter model. We show that if p is sufficiently close to 1, then the system fixates in the sense that for almost every realization of the initial configuration and dynamical evolution, each site flips only finitely many times, reaching eventually the state + 1. Moreover, we show that in this case the probability q(t) that a given spin is in state − 1 at time t satisfies the bound: for arbitrary ɛ > 0, q(t) ≤ exp(−t ^{(1/ d ) −ɛ}), for large t. In d= 2 we obtain the complementary bound: for arbitrary ɛ > 0, q(t) ≥ exp(−t ^{(1/2) +ɛ}), for large t. Received: 12 July 2001 / Accepted: 1 February 2002     

Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds

 We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice ℤ ^d . Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean- field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on ℤ ^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q≥3, the r-component cubic models with r≥4 and the O(N)-nematic liquid-crystal models with N≥3. Received: 22 July 2002 / Accepted: 12 January 2003 Published online: 5 May 2003 RID="⋆" ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted without charge. Communicated by J. Z.Imbrie     

The μCF Experiments at PSI – A Conclusive Review

During 25 years pioneering μCF experiments were performed at PSI. After initial study of the Wolfenstein–Gershtein effect in H/D, an intense research program on dμd fusion led to the early discovery of resonant dμd formation at low temperature and to the first direct observation of μd spin flip. With the Gatchina ionisation chamber absolute precisions of ∼1% on the determination of dμd formation and spin flip rates were recently obtained in good agreement with the theory. In a very large effort the highly resonant dμt fusion cycle was investigated. Record cycle rates up to 2×10⁸ s⁻¹ and yields up to 124 fusions per muon were measured. By slope analysis and by direct observation, effective sticking ω _s = (0.505 ± 0.029)% is the final PSI result. Clear experimental evidence of large epithermal resonances in D/T and H/D/T mixtures was found. This revised version was published online in August 2006 with corrections to the Cover Date.     

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Properties of Sr- and Sb-doped PZT–Portland cement composites

Lead zirconate titanate (PZT) ceramic-cement-based composites have increasingly been recognized as an attractive new composite material for use as a sensor in structural applications. In this work, PZT was doped with Sr and Sb (PSZT) to give it greater dielectric constant (ε _r) and higher piezoelectric coefficient (d ₃₃) values than normal PZT and is the first time that it is mixed with normal Portland cement to produce a 0–3 connectivity PSZT–Portland cement composite using PSZT contents of 50% and 70% by volume. Scanning electron micrographs show PSZT ceramic particles closely surrounded by the hydrated cement matrix where a dense microstructure can be observed in the interfacial zone. Both the ε _r and d ₃₃ values were found to increase with PSZT content and the values are amongst the highest so far for these types of composites, where the ε _r and d ₃₃ values reached 590 and 48 pC/N, respectively.     

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.     

Dielectric, ferroelectric and piezoelectric properties of 0-3 barium titanate–Portland cement composites

In this work, barium titanate (BT) and cement composites of 0-3 connectivity were produced with BT concentrations of 30%, 50% and 70% by volume using the mixing and pressing method. The dielectric constant (ε _r ) and the dielectric loss (tan δ) at room temperature and at various frequencies (0.1–20 kHz) of the ferroelectric BT-Portland cement composites with different BT concentrations were investigated. The results show that the dielectric constant of BT-PC composites was found to increase as BT concentration increases, and that the highest value for ε _r —of 436—was obtained for a BT concentration of 70%. In addition, the dielectric loss tangent decreased with increasing BT concentration. Moreover, several mathematical models were used; the experimental values of the dielectric constants are closest to those calculated from the cube model. The 0-3 cement-based piezoelectric composites show typical ferroelectric hysteresis loops at room temperature. The instantaneous remnant polarization (P _ir ), at an applied external electrical field (E ₀) of 20 kV/cm (90 Hz) of 70% barium titanate composite, was found to have a value ≈3.42 μC/cm². Furthermore, the piezoelectric coefficient (d ₃₃) was also found to increase as BT concentration increases, as expected. The highest value for d ₃₃ was 16 pC/N for 70% BT composite.     

Van der Waals attraction between cylinders,rods or fibers

In a first step, we calculate the van der Waals energy between two cylinders by pairwise integration of unscreenedr ⁻⁶ interactions between any two molecules. It turns out proportional tod ^−3/2 at small separations and proportional tod ⁻⁵ at large separationsd of the cylinders. In a second step, we use an integration method for multiplet interactions, which relates the latter to screening and represents the van der Waals energy by macroscopic reaction fields. We expand these reaction fields in terms of modified Bessel functions. The van der Waals energy evolves from a sum over the numberl of field reflections, from a frequency integral over the dielectric constants involved, and from a wave number integral over the radii and the separation of the cylinders. The lowest order term verifies the results found by integration of pair interactions, yet replaces the unscreened polarizabilities of the atoms by the screened dielectric constants of the media. The higher order reflection termsl≧2 likewise turn out to be proportional tod ^−3/2 at small separationsd, but decrease in weight more rapidly than 1/l ³. Their contribution at large separation is proportional tod ^−(4l+1). From a comparison of our results with those obtained for spheres and half-spaces, we conclude that retardation entails ad ^−5/2 and ad ⁻⁶ law at small and large separations, respectively. This suggestion is confirmed by preliminary calculations based on the Helmholtz equation.     

Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr ²,ν=4πpr ^{2 2} andw=(4π/3)(ρ+ε)r ² whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ > ε but singular for 2ρ ≤ ε.     

On Almost Randomizing Channels with a Short Kraus Decomposition

For large d, we study quantum channels on C ^d obtained by selecting randomly N independent Kraus operators according to a probability measure μ on the unitary group . When μ is the Haar measure, we show that for , such a channel is ε-randomizing with high probability, which means that it maps every state within distance ε/d (in operator norm) of the maximally mixed state. This slightly improves on a result by Hayden, Leung, Shor and Winter by optimizing their discretization argument. Moreover, for general μ, we obtain an ε-randomizing channel provided . For d = 2 ^k (k qubits), this includes Kraus operators obtained by tensoring k random Pauli matrices. This leads to more efficient constructions of almost randomizing channels. The proof uses recent results on empirical processes in Banach spaces.     

Low-energy electron spectrum in copper oxides in the multiband p-d model

An exact diagonalization of the Hamiltonian in the p-d model of a CuO₆ cluster was used to obtain dependences on the model parameters of the lowest-energy two-hole terms: the energy difference between the 2p orbitals of planar and apical oxygen Δ(apex)=ε(2p)−ε[2p(apex)], the crystal field parameter , and the ratio of the distances between the copper atom and the apical and planar oxygen atoms d(apex)/d(pl). In the limit of large d(apex)/d(pl) and Δ_d, our model is equivalent to the three-band p-d model and, in this case, large singlet-triplet splitting Δε⩾1 eV is also observed. As the parameters decrease, a singlet-triplet crossover is observed. Two mechanisms are identified for stabilization of the triplet term ³ B _1g (0) as the ground state. It is shown that for realistic values of the parameters, reduction of the p-d model to the three-band model is limited by the low energies of the current excitations because of the presence of the lower excited ³ B _1g and ¹ A _1g cluster states. Intercluster hopping causes strong mixing of singlet and triplet states far from the G point. The results of the calculations are compared with data obtained by angle-resolved photoelectron emission in Sr₂CuO₂Cl₂. Fiz. Tverd. Tela (St. Petersburg) 40, 184–190 (February 1998)     

Confinement of massless particles: Photon

Confinement of massless particles in a suitably chosen dielectric medium is considered. Light waves of selected frequencies are shown to be confined in a medium with dielectric constantε(r)=a/r−b ². A wave theoretical analysis gives equispaced frequency spectrum for the confined light, the radial dependence of its electric wave vector resembling that of hydrogen atom wave functions. In the large frequency limit an eikonal approximation of the problem gives elliptic orbits for the confined rays. Higher frequency orbits are shown to be closer to the centre of the medium than the lower frequency ones.     

Iron based carbon nanocomposites for electromagnetic wave absorber with wide bandwidth in GHz range

The electromagnetic wave absorption properties of resin compacts containing 40 vol. % composite powders of α-Fe/C(a), and Fe₃C/C(a) were characterized in a frequency range of 0.05–26.5 GHz, according to a conventional reflection/transmission technique. The real part (ε_r ^′) and the imaginary part (ε_r ^′′) of relative permittivity were constantly low in the 2–14 GHz (ε_r ^′= ∼12.4 and ε_r ^′′= ∼0.6) for α-Fe/C(a) resin composites, and in the 1–26.5 GHz (ε_r ^′= ∼9.6 and ε_r ^′′= ∼0.8) for Fe₃C/C(a) ones. The imaginary part (μ_r ^′′) of relative permeability exhibited wide peaks in the 1–9 GHz range for α-Fe/C(a), and in the 2–26.5 GHz range for Fe₃C/C(a) owing to their different magnetocrystalline anisotropy field values. Consequently, the resin compacts with 40 vol. % α-Fe/C(a), and Fe₃C/C(a) powders provided good electromagnetic wave absorption performances (reflection loss <-20 dB) in ranges of 4.3–8.2 GHz, and 9–26.5 GHz over absorber thicknesses of 1.8–3.3 mm, and 1.0–2.4 mm, respectively. PACS 76.50.+g; 61.46.+w; 75.50.Bb; 75.30.Gw; 75.20.En     

Dynamic generation of entangling wave packets in XY spin system with decaying long-range couplings

The dynamic generation of spin entanglement between two distant sites in a XY model with 1/r ² decay long-range couplings was studied. Due to the linear dispersion relation ε(k)∼|k| of magnons in such a model, a well-located spin state can be dynamically split into two moving entangled local wave packets without changing their shapes. Interestingly, when such two wave packets meet at the diametrically opposite site after the fast period τ = Nπ/J, the initial well-located state is completely recurrent. Numerical calculation was performed to confirm the analytical result even if the ring system of sizes N up to several thousands is considered. The truncation approximation for the coupling strengths was also studied. Numerical simulation shows that the above conclusions still hold even if the range of the coupling strength is truncated to a relatively short scale compared with the size of the spin system. Supported by the National Natural Science Foundation of China (Grant Nos. 90203018, 10474104 and 60433050) and the National Fundamental Research Program of China (Grant Nos. 2001CB309310 and 2005CB724508)     

Hitting Time and Dimension in Axiom A Systems, Generic Interval Exchanges and an Application to Birkoff Sums

In this note we prove that for equilibrium states of axiom A systems having positive dimension the time τ _B (x) needed for a typical point x to enter for the first time in a typical ball B with radius r behaves for small r as τ _B (x)∼ r ^−d where d is the local dimension of the invariant measure at the center of the ball. A similar relation is proved for a full measure set of interval exchanges. Some applications to Birkoff averages of unbounded (and not L ¹) functions are shown.     

Spinodal Decomposition¶for the Cahn–Hilliard–Cook Equation

This paper gives theoretical results on spinodal decomposition for the stochastic Cahn–Hilliard–Cook equation, which is a Cahn–Hilliard equation perturbed by additive stochastic noise. We prove that most realizations of the solution which start at a homogeneous state in the spinodal interval exhibit phase separation, leading to the formation of complex patterns of a characteristic size. In more detail, our results can be summarized as follows. The Cahn–Hilliard–Cook equation depends on a small positive parameter ε which models atomic scale interaction length. We quantify the behavior of solutions as ε→ 0. Specifically, we show that for the solution starting at a homogeneous state the probability of staying near a finite-dimensional subspace ?_ε is high as long as the solution stays within distance r _ε=O(ε ^R ) of the homogeneous state. The subspace ?_ε is an affine space corresponding to the highly unstable directions for the linearized deterministic equation. The exponent R depends on both the strength and the regularity of the noise. Received: 2 May 2000 / Accepted: 8 July 2001     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Quantum statistical monte carlo methods and applications to spin systems

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem⁽¹⁾ thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures. Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985.     

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.