Some current problems in perovskite nano-ferroelectrics and multiferroics: kinetically-limited systems of finite lateral size

We describe some unsolved problems of current interest; these involve quantum critical points in ferroelectrics and problems which are not amenable to the usual density functional theory, nor to classical Landau free energy approaches (they are kinetically limited), nor even to the Landau–Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter) because they are dominated by finite aperiodic boundary conditions.     

Sum rules and the landau theory of fermi liquids

The Landau theory predicts spectral weight functions for density and spin-density fluctuations which in the long-wavelength, low-frequency limit should be equal to the true spectral weight functions of a system of interacting fermions. This correspondence plus well-known frequency sum rules provides a means to examine the Landau quasiparticle interaction parameters. Two inequalities are derived:F ₁ G ₁ and another relating the first three spin-symmetric Landau coefficients to the radial distribution function and the two-particle potential. We find that the third-moment sum rule is not entirely exhausted by Landau-accountable excitations, and therefore it is the highest order sum rule which can still probe the theory. A third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction. We do not examine this result in detail, but merely conjecture that it may indicate a basic weakness in the Landau theory of spin-density fluctuations.     

Critical Velocities in Two-Component Superfluid Bose Gases

On the ground of the Landau criterion we study the behavior of critical velocities in a superfluid two-component Bose gas. It is found that under motion of the components with different velocities the velocity of each component should not be lower than a minimum phase velocity of elementary excitations (s ₋). The Landau criterion yields a relation between the critical velocities of the components (v _c1, v _c2). The velocity of one or even both components may exceed s ₋. The maximum value of the critical velocity of a given component can be reached when the other component does not move. The approach is generalized for a two-component condensate confined in a cylindrical harmonic potential.      

Boundary Conditions at the Bulk–Aerogel Interface of Superfluid 3He-B

We study the interface between bulk and aerogel impregnated with ³ He-B. The magnetic susceptibility at the interface determines a boundary condition for the texture, which can be parameterized by the orbital vector L. We use Ginzburg–Landau theory to calculate the boundary condition assuming homogeneous aerogel and a sharp interface. Recent NMR measurements give reason to conjecture that L tends to be parallel to interface. Our numerical calculations confirm this conjecture in the Ginzburg–Landau (GL) regime. However, the orienting energy is one order of magnitude smaller than at a solid wall, and therefore can easily be overshadowed by a nearby wall.     

Macroscopic Elastic Studies of Orientational Ordering in Single-Crystal Fullerites

Abstract

We give an overview on dynamic mechanic experiments in single-crystal fullerites C₆₀ and C₇₀. Elastic properties and thermal expansion in the vicinity of ordering phase transitions were studied. Landau theory and simple microscopic models are used to describe the experimental results.

     

Nonanalytic properties and normal current of superfluid3He-A atT=0 K

The nonanalytic behavior of³He-A atT=0 K is discussed. The textual free energy due to order-parameter spatial variation is studied inq space. It is shown that the gradient expansion does not hold atT=0 K, because the free energy involvesq ² lnq. The logarithmic terms are estimated in leading order. It is also shown that even in a uniform texture, normal current along thel vector exists atT=0 K. This comes from the fact that the Landau criterion of superfluidity is partly violated in³He-A.     

Particle number fluctuations in an ideal Bose gas

Abstract

We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.     

The damping of helicon waves in a tipped magnetic field

The damping of helicon waves in indium was measured under nonlocal conditions with a variable angle between the wave vectorq and the magnetic field. In contrast to the predictions of the free-electron theory, the damping was not a monotonic function of the angle and exhibits considerable structure, which is attributed to minima in the Landau damping for certain orientations of the magnetic field. Minima in the damping are to be expected for such field directions as give rise to cyclotron orbits having a substantial number of electron states with orbital velocities perpendicular toq. In simple situations the critical orientations of the magnetic field may be deduced from a given Fermi surface by a geometrical construction. The construction has been extended to indium, and the tipping angles found are in reasonable agreement with the experiment.Based on a thesis to be submitted to the Senate of the Technion, Israel Institute of Technology, in partial fulfillment of the requirements for D.Sc. degree.     

Domain nucleation in thermomagnetic memory systems near the Curie point

The approximation of Landau second-order phase transitions for ferromagnetics near the Curie point is used for a numerical determination of the two-dimensional microstructure which forms the basis of a data-storage domain. This structure and its lower level of the spectrum of small oscillations are strongly delocalized. Depending on the recording regimes, this may be responsible for the severe irregularity of the domain wall shape sometimes observed or the formation of ring domains. Pis’ma Zh. Tekh. Fiz. 24, 13–17 (August 26, 1998)     

Possible Mechanism of a New Type of Three-Dimensional Quantized Hall Effect in Layered Semiconductors Bi2−xSnxTe3

We have found a new type of three-dimensional quantized Hall effect (QHE) in layered semiconductors Bi₂–xSn_xTe₃ (x0.0125) single crystals. The Hall resistivity is not expressed in a universal relation applicable for a conventional QHE and depends appreciably on the doped Sn concentration x. The flat Hall plateaus are visible at higher Landau levels but are rather suppressed at lower regions. The calculated Landau levels of the upper valence band (UVB) with the best-fit band parameters are in excellent agreement with the experiments, including spin splitting. For Bi₂–xSn_xTe₃, the Sn-originated impurity band (IB) has resonant nature and enhances the density of states at the Fermi level of UVB. The charge transfer occurs between the quantized UVB and the resonant IB or the lower valence band (LVB) for Bi₂–xSn_xTe₃ or Bi₂Te₃, respectively, and the Landau levels are enhanced appreciably. We have revealed that the quasi-localized states are formed in quantized three-dimensional density of state spectra. We have proposed a possible model for the present QHE, which is a modification of Mani's model, where the quasi-localized state is formed at the disorder-originated tail of each Landau level. In the quasi-localized regime, the IB or LVB are responsible for the carrier reservoir to regulate the Hall resistivity.     

Superconductivity from Repulsion: Ginzburg–Landau Phenomenology of Cuprates

We develop Ginzburg–Landau approach to the problem of superconducting pairing with large momentum under screened Coulomb repulsion (η_K-pairing). Two-component order parameter arising in this scheme can be associated with charge and orbital current degrees of freedom of the relative motion of η_K-pair corresponding to superconducting and orbital antiferromagnetic ordered states, respectively. All basic features of the phase diagram of cuprate superconductors result directly from the η_K-pairing concept. PACS numbers: 74.20.-z, 74.20.De, 74.72.-h.     

Experimental study of organic zero-gap conductor α-(BEDT-TTF)2I3

Abstract

A zero-gap state with a Dirac cone type energy dispersion was discovered in the organic conductor α-(BEDT-TTF)₂I₃ under high hydrostatic pressures. This is the first two-dimensional (2D) zero-gap state discovered in bulk crystals with a layered structure. In contrast to the case of graphene, the Dirac cone in this system is highly anisotropic. The present system, therefore, provides a new type of massless Dirac fermion system with anisotropic Fermi velocity. This system exhibits remarkable transport phenomena characteristic to electrons on the Dirac cone type energy structure. The carrier density, written as n∝T², is a characteristic feature of the 2D zero-gap structure. On the other hand, the resistivity per layer (sheet resistance R_S) is given as R_S=h/e² and is independent of temperature. The effect of a magnetic field on samples in the zero-gap system was examined. The difference between zero-gap conductors and conventional conductors is the appearance of a Landau level called the zero mode at the contact points when a magnetic field is applied normal to the conductive layer. Zero-mode Landau carriers give rise to strong negative out-of-plane magnetoresistance.     

A family of second‐order boundary dampers for finite element analysis of two and three‐dimensional problems in transient exterior acoustics

Numerical modelling of exterior acoustics problems involving infinite medium requires truncation of the medium at a finite distance from the obstacle or the structure and use of non‐reflecting boundary condition at this truncation surface to simulate the asymptotic behaviour of radiated waves at far field. In the context of the finite element method, Bayliss–Gunzburger–Turkel (BGT) boundary conditions are well suited since they are local in both space and time. These conditions involve ‘damper’ operators of various orders, which work on acoustic pressure p and they have been used in time harmonic problems widely and in transient problems in a limited way. Alternative forms of second‐order BGT operators, which work on ṗ (time derivative of p) had been suggested in an earlier paper for 3D problems but they were neither implemented nor validated. This paper presents detailed formulations of these second‐order dampers both for 2D and 3D problems, implements them in a finite element code and validates them using appropriate example problems. The developed code is capable of handling exterior acoustics problems involving both Dirichlet and Neumann boundary conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of Impurities on Supersolid Condensate: A Ginzburg–Landau Approach

Basing our arguments on a wavefunction that contains both positional and superfluid order, we propose a Ginzburg–Landau functional for a supersolid with the two order parameters necessary to describe such a phase: density n _B (r) and supersolid order parameter ψ _V . We argue that adding lighter. ³He atoms to a ⁴He supersolid produces attractive regions for vacancies, leading to patches of higher T _c. On the other hand, the supersolid stiffness decreases in this granular state with increased ³He disorder. Both effects are linear in ³He concentration.     

On the Local Stability of the Quadrupole Vortex in Superfluid 3He-B

Studies with a constrained Ginzburg–Landau approach have suggested that the Quadrupole core vortex in ³ He-B should be a saddle point of the free energy (G. E. Volovik and M. M. Salomaa, JETP Lett. 45 , 56 (1987)). We have carried out a careful numerical analysis in the framework of the quasiclassical theory with the conclusion that the core in fact is a local minimum. No constrains were imposed on the phase space. The Quadrupole vortex can be a contender for the second vortex in the Manchester group experiment (Bevan et al., JLTP (1987)).     

Formation of NbSe2 Nanotubes by Electron Irradiation

Abstract

In this work, we report the production of NbSe₂, (niobium diselenide) nanotubes by high doses of electron irradiation. The apparatus used for irradiation was a 2 MeV Van de Graaff accelerator, while the irradiation conditions were the following: voltage 1.3 MeV, current 5μA, dose rate 25 kGy/min, and total dosage 1000 kGy. Samples were analyzed with a high-resolution transmission electron microscope. The main characteristics observed were huge and very well defined nanotubes of several nm long and few nm wide, which are presumably hollow, although they are capped at one end. At this level of irradiation, we were able to find neither onion-like structure nor nanoparticles through out other areas, as it is usual in similar hexagonal structures of the dichalcogenide family.     

Panoramic photographs as nineteenth century book illustrations

Abstract

The earliest panoramic photograph exposed on a single plate is attributed to Friedrich von Martens, a German, who resided in France in the 1840s. The 4.7 x 15 inch curved daguerreotype was produced in a camera equipped with a lens which pivoted over an angle of about 150°.¹ Some dealers in ‘philosophical instruments’ included in their offers of cameras, from the mid 1840s through the 1850s, ‘Traversing’ cameras.² These they described as providing panoramic views, about 3" x 10", on a curved plate. However, neither the original von Martens, nor any of the ‘Traversing’ cameras, are known to have survived.     

Introduction

Abstract

In this first issue we begin the serialization of twelve articles under the general heading of Early Photography in Eastern Europe. Together they will form a compendium of information and comment not now available from any other source. The fame of Nicefor N'eps and Luijs ?aks Dagers may have travelled to Latvia and beyond, but the West has remained largely uninformed of photographic achievements in the East. International gatherings of the kind that bring scientists and engineers into regular communion are still a great rarity among photographic historians who, more often than not, have tended to view their task in nationalistic terms. No doubt this outlook stems from the fact that photography itself did much to raise national consciousness in many lands. The East was not short of photographic heroes but, on the whole, they remained local heroes (pace Joseph Petzval; pace Count Esterházy}, not unsung, but rarely more than folksung. Language problems may have contributed to this state of affairs, as did the bitter wars and struggles against unacceptable regin1es, which run like a grinding refrain through all accounts of the past century. Again and again, the work of talented photographers was destroyed, sometimes accidentally, often with savage deliberation.     

Analysis-of-Marginal-Tail-Means (ATM): A Robust Method for Discrete Black-Box Optimization

Abstract

We present a new method, called analysis-of-marginal-tail-means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications in many real-world engineering problems (e.g., manufacturing optimization, product design, and molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this by combining both rank- and model-based optimization, via the use of marginal tail means. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions from data, then finding a good compromise which best exploits additive structure. ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network.