bluuebunny/crossref_metadata_2025 huggingface dataset:
Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras
Authors: Cornwell J. F.
Published: July 2002

The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it is shown that there are two types of irreducible tensor operator, which may be called ‘‘ordinary’’ and ‘‘twisted.’’ The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner–Eckart theorem for both the ordinary and twisted operators. Also included are discussions (within the regular coaction formalisms for compact quantum group algebras) of inner-products, basis functions, projection operators, Clebsch–Gordan coefficients, and two types of tensor product of corepresentations. The formulation of quantum homogeneous spaces for compact quantum group algebras is discussed, and the defining conditions for the irreducible tensor operators associated with such quantum homogeneous spaces and with the unitary irreducible corepresentations of the compact quantum group algebras are then deduced. There are two versions, which correspond to restrictions of the right and left regular coactions. In each case it is again shown that there are ordinary and twisted irreducible tensor operators. Various consequences are deduced, including the corresponding generalizations of the Wigner–Eckart theorem.
The low activity phase of some Dirichlet series
Authors: Contucci Pierluigi , Knauf Andreas
Published: July 2002

We show that a rigorous statistical mechanics description of some Dirichlet series is possible. Using the abstract polymer model language of statistical mechanics and the polymer expansion theory we characterize the low activity phase by the suitable exponential decay of the truncated correlation functions.
Lie algebra cohomology and group structure of gauge theories
Authors: Yang Hyun Seok , Lee Bum-Hoon
Published: July 2002

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator Q° for the Lie algebra cohomology induced by BRST generator Q. We also point out an interesting duality relation—Poincaré duality—with respect to gauge anomalies and Wess–Zumino–Witten topological terms. We consider the consistent embedding of the BRST adjoint generator Q° into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint Nöther charge Q°.
Remarks on the quantization of gauge theories
Authors: Vathsan Radhika
Published: July 2002

The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. It is pointed out that care needs to be exercised in implementing the reduced phase space quantization method properly.
Self-dual solitons in N=2 supersymmetric Chern-Simons gauge theory
Authors: Fuertes Wifredo Garcı́a , Guilarte Juan Mateos
Published: July 2002

The low energy effective theory of planar QED with a non-local four-fermion interaction including Gross–Neveu and Thirring terms is shown to be equivalent to a Chern–Simons–Higgs model of special characteristics. We study the restrictions imposed by self-duality and supersymmetry, finding in both cases a plethora of (some new) topological and non-topological solitons. The non-relativistic limit of our model generalizes the effective Ginzburg–Landau theory for the fractional quantum Hall effect such that our solitons would be the relativistic version of quasi-particle and quasi-hole excitations.
Quantum mechanics in classical dynamics
Authors: Millard Andrew C.
Published: July 2002

Quantum mechanics over an associative ring with a conjugation operation can be recast in a form familiar as a classical dynamical system. The generators of transformations on the classical phase space are the expectation values of anti-self-adjoint operators and are closed under a Poisson bracket that is in direct correspondence with the quantum mechanical commutator. A prescription also exists for determining when a classical flow is equivalent to a quantum mechanical evolution.
Two-dimensional boson and W-symmetry in the quantum Hall effect
Authors: Myung Yun Soo
Published: July 2002

We perform consistently the Gupta–Bleuler–Dirac quantization for a two-dimensional boson with parameter (α) on the circle, the boundary of the circular droplet. For α=1, we obtain the chiral (holomorphic) constraints. Using the representation of Bargmann–Fock space and the Schrödinger picture, we construct the holomorphic wave function. In order to interpret this function, we construct the coherent state representation by using the infinite-dimensional translation (W∞) symmetry for each Fourier (edge) mode. The α=1 chiral wave function explains the neutral edge states for integer quantum Hall effect very well. In the case of α=−1, we obtain a new wave function which may describe the higher modes (radial excitations) of edge states. The charged edge states are described by the |α|≠1 wave function. Finally, the application of our model to the fractional quantum Hall effect is discussed.
The quantized universal enveloping algebras Uq(iso(N)), Uq(e(3,1)) and Uq(e(N)) and the representation theory of Uq(e(3))
Authors: Sachse Sebastian , Weixler Ralf
Published: July 2002

We construct the Hopf algebras of Uq(iso(N)) and Uq(iso(3,1)) as regular functionals on their function algebras, examine the possible *-involutions on these objects, derive the quantized Euclidean algebras Uq(e(N)), and finally give the irreducible representations of Uq(e(3)) depending on two parameters which fix the value of the Casimir operators.
Physical vertex operators in the Ramond sector
Authors: Naito Seichi
Published: July 2002

Introducing physical string coordinate’s modes as well as physical string coordino’s modes, we derive the generating functional of physical vertex operators (GFPVO) of fermionic particles (in superstring), which is just equal to the one already proposed by using superconformal mapping in the Ramond sector. Inversely solving the superconformal mapping problem, we can derive general formulas, which give physical vertex operators of various fermionic particles up to arbitrarily excited mass levels. As an example, we explicitly derive some (Gliozzi–Scherk–Olive-allowed) low-lying physical vertex operators.
Operator formulation of Wigner’s R-matrix theories for the Schrödinger and Dirac equations
Authors: Szmytkowski Radosław
Published: July 2002

The R-matrix theories for the Schrödinger and Dirac equations are formulated in the language of integral operators. In the nonrelativistic theory the central role is played by an integral operator R̂b̂(E) relating function values to normal derivatives on a surface 𝒮 of a closed volume 𝒱, inside which the function satisfies the Schrödinger equation at energy E. In the relativistic theory, the same role is played by two integral operators, R̂b̂(+)(E) and R̂b̂(−)(E), linking on the surface 𝒮 values of upper and lower components of spinor wave functions satisfying in the volume 𝒱 the Dirac equation at energy E. Systematic procedures for constructing the operators R̂b̂(E) and R̂b̂(±)(E), generalizing the methods due to Kapur and Peierls and to Wigner, are presented.
Rest frame system for asymptotically flat space–times
Authors: Moreschi Osvaldo M. , Dain Sergio
Published: July 2002

The notion of center of mass for an isolated system has been previously encoded in the definition of the so-called nice sections. In this article we present a generalization of the proof of existence of solutions to the linearized equation for nice sections, and formalize a local existence proof of nice sections relaxing the radiation condition. We report on the differentiable and non-self-crossing properties of this family of solutions. We also give a proof of the global existence of nice sections.
Moyal–Nahm equations
Authors: Baker L. M. , Fairlie D. B.
Published: July 2002

Various aspects of the Nahm equations in three and seven dimensions are investigated. The residues of the variables at simple poles in the seven-dimensional case form an algebra. A large class of matrix representations of this algebra is constructed. The large N limit of these equations is taken by replacing the commutators by Moyal brackets, and a set of nontrivial solutions in a generalized form of Wigner distribution functions is obtained.
Thermalization of quantum states
Authors: Brody Dorje C. , Hughston Lane P.
Published: July 2002

An exact stochastic model for the thermalization of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterized by an underlying Schrödinger evolution, together with a nonlinear term driving the system toward an asymptotic equilibrium state and a stochastic term reflecting fluctuations. There are two free parameters, one of which can be identified with the heat bath temperature, while the other determines the characteristic time scale for thermalization. Exact expressions are derived for the evolutionary dynamics of the system energy, the system entropy, and the associated density operator.
8D
oscillator and 5D Kepler problem: The case of nontrivial constraints
Authors: Pletyukhov M. V. , Tolkachev E. A.
Published: July 2002

The topologically nontrivial correspondence between the 5D SU(2)-Kepler problem and the 8D singular oscillator is considered. It is shown that both “isospinor” and “isovector” particles on the SU(2) instanton + 1/R background in 5D can be described in terms of an 8D singular oscillator. The energy spectrum is calculated for an arbitrary “isospin” case.
Isolated versus nonisolated periodic orbits in variants of the two-dimensional square and circular billiards
Authors: Robinett R. W.
Published: July 2002

Square and circular infinite wells are among the simplest two-dimensional potentials which can completely solved in both classical and quantum mechanics. Using the methods of periodic orbit theory, we study several variants of these planar billiard systems which admit both singular isolated and continuous classes of nonisolated periodic orbits. (In this context, isolated orbits are defined as those which are not members of a continuous family of paths whose orbits are all of the same length.) Examples include (i) various “folded” versions of the standard infinite wells (i.e., potentials whose geometrical shapes or “footprints” can be obtained by repeated folding of the basic square and circular shapes) and (ii) a square well with an infinite-strength repulsive δ-function “core,” which is a special case of a Sinai billiard. In each variant case considered, new isolated orbits are introduced and their connections to the changes in the quantum mechanical energy spectrum are explored. Finally, we also speculate about the connections between the periodic orbit structure of supersymmetric partner potentials, using the two-dimensional square well and it superpartner potential as a specific example.
Chaotic observables for a free quantum particle
Authors: van Winter Clasine
Published: July 2002

This paper is devoted to the time evolution of observables in the quantum mechanics of a single particle without interaction. It is assumed that wave functions belong to a certain set K2 that is dense in L2. The paper applies to observables represented by positive self-adjoint operators A on L2 with the property that A1/2 maps K2 into L2. Quadratic forms with form domains K2 are used to generate a topology for operators A, defining a topological space X. The space X provides the framework to define sensitive dependence on initial conditions, topological transitivity, and existence of a dense set of periodic points, the three aspects of chaos in Devaney’s definition of chaos for maps on metric spaces. It is shown that every neighborhood of every operator A in X contains operators that establish sensitive dependence on initial conditions, and similarly for the other aspects of chaos. Hence, the time evolution of operators in the Heisenberg picture is chaotic in the sense of this paper.
Analytical solution of the relativistic Coulomb problem with a hard core interaction for a one-dimensional spinless Salpeter equation
Authors: Brau F.
Published: July 2002

In this paper, we construct an analytical solution of the one-dimensional spinless Salpeter equation with a Coulomb potential supplemented by a hard core interaction, which keeps the particle in the x positive region.
On dimension of the global attractor for damped nonlinear wave equations
Authors: Shengfan Zhou
Published: July 2002

In this paper, we obtain a more precise estimate of upper bound of the Hausdorff dimension of the global attractor for damped nonlinear wave equations with the Dirichlet boundary condition. The obtained Hausdorff dimension decreases as the damping grows and is uniformly bounded for large damping, which conforms to physical intuition.
Superintegrability on the two-dimensional hyperboloid. II
Authors: Kalnins E. G. , Miller W. , Hakobyan Ye. M. , Pogosyan G. S.
Published: July 2002

This work is devoted to the investigation of the quantum mechanical systems on the two-dimensional hyperboloid which admits separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C. P. Boyer, E. G. Kalnins, and P. Winternitz [J. Math. Phys. 24, 2022 (1983)], which have not yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.
Null particle solutions in three-dimensional (anti-) de Sitter spaces
Authors: Cai Rong-Gen , Griffiths J. B.
Published: July 2002

We obtain a class of exact solutions representing null particles moving in three-dimensional (anti-) de Sitter spaces by boosting the corresponding static point source solutions given by Deser and Jackiw. In de Sitter space the resulting solution describes two null particles moving on the (circular) cosmological horizon, while in anti-de Sitter space it describes a single null particle propagating from one side of the universe to the other. We also boost the Bañados–Teitelboim–Zanelli black hole solution to the ultrarelativistic limit and obtain the solution for a spinning null particle moving in anti-de Sitter space. We find that the ultrarelativistic geometry of the black hole is exactly the same as that resulting from boosting the Deser–Jackiw solution when the angular momentum of the hole vanishes. A general class of solutions is also obtained which represents several null particles propagating in the Deser–Jackiw background. The differences between the three-dimensional and four-dimensional cases are also discussed.
Positive mass conjecture for five-dimensional Lorentzian manifolds
Authors: Zhang Xiao
Published: July 2002

We extend Witten’s proof on positive mass conjecture to five-dimensional Lorentzian manifolds with a rigorous treatment in mathematics.
Hyperbolic Kac–Moody algebra from intersecting p-branes
Authors: Ivashchuk V. D. , Kim S.-W. , Melnikov V. N.
Published: July 2002

A subclass of a recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological solution to D=11 supergravity related to hyperbolic Kac–Moody algebra F3 (of rank 3). This solution describes the non-Kasner power-law inflation.
On one generalization for the projection matrices method in the S-matrix factorization problem
Authors: Muravyev Dmitry I.
Published: July 2002

A boundary value problem for a 2×2 S-matrix is solved by the method of projection matrices. The S-matrix is assumed to be diagnoalized by orthogonal matrix U(k2)=Ω(k2)/det Ω(k2), where matrix elements of Ω(k2) are polynomials. The equation det Ω(k2)=0 has roots of any order. The example is considered for the roots with order 2.
Nonequilibrium dynamics of infinite particle systems with infinite range interactions
Authors: Bahn Changsoo , Park Yong Moon , Yoo Hyun Jae
Published: July 2002

We discuss the existence and uniqueness of nonequilibrium dynamics of infinitely many particles interacting via superstable pair interactions in one and two dimensions. The interaction is allowed to be of infinite range and singular at the origin. Under suitable regularity conditions on the interaction potential, we show that if the potential decreases polynomially as the distance between interacting two particles increases, then the tempered solution to the system of Hamiltonian equations exists. Moreover, if the potential satisfies further that either it has a subexponential decreasing rate or it is everywhere two-times continuously differentiable, then we show that the tempered solution is unique. The results extend those of Dobrushin and Fritz obtained for finite range interactions.
Generalized Gel’fand–Levitan integral equation for two block Ablowitz–Kaup–Newell–Segur systems
Authors: Corona Gulmaro Corona
Published: July 2002

We derive a generalized Gel’fand–Levitan integral equation for two block Ablowitz–Kaup–Newell–Segur systems. This is possible if we suppose that the matrix coupling coefficients are invertible and come from simple zeroes of the determinant of the diagonal blocks of the scattering matrix.
A conserved current for the field perturbations in the Einstein–Yang–Mills-dilaton–axion theory
Authors: Cartas-Fuentevilla R.
Published: July 2002

Using the self-adjoint character of the operators governing the field perturbations in the Einstein–Yang–Mills-dilaton–axion theory, we demonstrate that a covariantly (both gauge covariant and space–time covariant) conserved current associated with the coupled field perturbations arises, by contrast to other approaches, in a natural way. Our results cover, in particular, the bosonic low-energy limit of the string theory. We discuss how the present results can serve as a starting point for future investigations.
Nonassociative structure of quantum mechanics in curved space–time
Authors: Kerner Edward H.
Published: July 2002

de Sitter space gives a local, osculating (and therefore prototypical) representation of a curved space–time. The de Sitter geodesics allow a description as uniform straight-line motion with respect to a family of preferred frames that are inertial frames interconnected by a projective (fractional-linear) transformation. Use of these frames overcomes the ambiguities of general covariance in stating commutation rules and Hamiltonian structure. But the Hamiltonian for a particle running on a geodesic then necessitates nonassociative elements. The latter are worked out as elements of a Cayley–Dickson algebra of 16 dimensions (doubled octonions, or decahexions), wherein a standard Hilbert space type of format for quantum mechanics is ruled out. A formal Schrödinger wave equation is devised, and exhibits antilinear as well as linear terms in the decahexion components of the wave function. All the same, the Heisenberg laws of motion for a dynamical variable are neatly and unambiguously formulated, giving a full account of the quantum time evolution of the dynamical variable (although the Heisenberg program of diagonalizing the Hamiltonian cannot be executed).
Uniqueness of Gibbs states in one-dimensional antiferromagnetic model with long-range interaction
Authors: Kerimov Azer
Published: July 2002

Uniqueness of Gibbs states in the one-dimensional antiferromagnetic model with very long-range interaction is established.
Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
Authors: Strachan I. A. B.
Published: July 2002

The bi-Hamiltonian structure of certain multicomponent integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax function is that the corresponding bi-Hamiltonian structures are degenerate, i.e., the metric that defines the Hamiltonian structure has a vanishing determinant. Frobenius manifolds provide a natural setting in which to study the bi-Hamiltonian structure of certain classes of hydrodynamic systems. Some ideas on how this structure may be extended to include degenerate bi-Hamiltonian structures, such as those given in the first part of the paper, is given.
Quasi-Hopf superalgebras and elliptic quantum supergroups
Authors: Zhang Yao-Zhong , Gould Mark D.
Published: July 2002

We introduce the quasi-Hopf superalgebras which are Z2-graded versions of Drinfeld’s quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is, the face type Bq,λ(G) and the vertex type Aq,p[sl(n|∧n)] (and Aq,p[gl(n|∧n)]), where 𝒢 is any Kac–Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for Uq[sl(n|∧n) in a nonstandard system of simple roots, all of which are fermionic.
Theory of separability of multi-Hamiltonian chains
Authors: Błaszak Maciej
Published: July 2002

The theory of separability of one-Casimir bi-Hamiltonian chains is extended onto unsplit multi-Casimir bi-Hamiltonian chains. Multi-Casimir extensions of the known one-Casimir chains are constructed.
Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan–Schwinger map
Authors: Daskaloyannis C. , Kanakoglou K. , Tsohantjis I.
Published: July 2002

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well-known Hopf algebraic structure of the Lie algebras, through a realization of Lie algebras using the parabosonic (and parafermionic) extension of the Jordan–Schwinger map. The differences between the Hopf algebraic and the graded Hopf superalgebraic structure on the parabosonic algebra are discussed.
An approach to Mel’nikov theory in celestial mechanics
Authors: Cicogna G. , Santoprete M.
Published: July 2002

Using a completely analytic procedure—based on a suitable extension of a classical method—we discuss an approach to the Poincaré–Mel’nikov theory, which can be conveniently applied also to the case of nonhyperbolic critical points, and even if the critical point is located at the infinity. In this paper, we concentrate our attention on the latter case, and precisely on problems described by Kepler-type potentials in one or two degrees of freedom, in the presence of general time-dependent perturbations. We show that the appearance of chaos (possibly including Arnol’d diffusion) can be proved quite easily and in a direct way, without resorting to singular coordinate transformations, such as the McGehee or blowing-up transformations. Natural examples are provided by the classical Gyldén problem, originally proposed in celestial mechanics, but also of interest in different fields, and by the general three-body problem in classical mechanics.
Multiplicity, invariants and tensor product decompositions of tame representations of U(∞)
Authors: Howe R. Michael , Ton-That Tuong
Published: July 2002

The structure of r-fold tensor products of irreducible tame representations of U(∞)=lim lim → U(n) are described, versions of contragredient representations and invariants are realized, and methods of calculating multiplicities, Clebsch–Gordan, and Racah coefficients are given using invariant theory on Bargmann–Segal–Fock spaces.
Renormalized Hamiltonian for a peptide chain: Digitalizing the protein folding problem
Authors: Fernández Ariel , Colubri Andrés
Published: July 2002

A renormalized Hamiltonian for a flexible peptide chain is derived to generate the long-time limit dynamics compatible with a coarsening of torsional conformation space. The renormalization procedure is tailored taking into account the coarse graining imposed by the backbone torsional constraints due to the local steric hindrance and the local backbone-side-group interactions. Thus, the torsional degrees of freedom for each residue are resolved modulo basins of attraction in its so-called Ramachandran map. This Ramachandran renormalization (RR) procedure is implemented so that the chain is energetically driven to form contact patterns as their respective collective topological constraints are fulfilled within the coarse description. In this way, the torsional dynamics are digitalized and become codified as an evolving pattern in a binary matrix. Each accepted Monte Carlo step in a canonical ensemble simulation is correlated with the real mean first passage time it takes to reach the destination coarse topological state. This real-time correlation enables us to test the RR dynamics by comparison with experimentally probed kinetic bottlenecks along the dominant folding pathway. Such intermediates are scarcely populated at any given time, but they determine the kinetic funnel leading to the active structure. This landscape region is reached through kinetically controlled steps needed to overcome the conformational entropy of the random coil. The results are specialized for the bovine pancreatic trypsin inhibitor, corroborating the validity of our method.
On magnetoresistance of layered conductors
Authors: Peschansky V. G.
Published: July 2002

The dependence of the resistance of a layered conductor with an arbitrary quasi-two-dimensional electron energy spectrum on the magnitude and orientation of a magnetic field relative to the layers is analyzed. It is shown that, when the current flows along the normal to the layers, the resistance of the sample depends significantly on the angle θ between the normal and the strong magnetic field vector; for θ=π/2, the resistance increases linearly with the magnetic field in a wide range of magnetic fields.
The high-frequency conductivity tensor of a two-dimensional electron gas with electron impurity states in a magnetic field
Authors: Gleizer N. V. , Ermolaev A. M.
Published: July 2002

The Lifshits method of local perturbations is used for studying the properties of a two-dimensional electron-impurity system in a quantizing magnetic field perpendicular to the plane of electron motion. The high-frequency conductivity tensor of the system is calculated in the model of independent point impurity atoms, taking into account the impurity states of electrons and spatial dispersion. The dissipative component of the conductivity has narrow resonant peaks at frequencies of electron transitions between the Landau levels and local levels, which are induced by the magnetic field. In zero magnetic field, these peaks merge into one broad peak lying above the threshold frequency for electron transitions from a local level to the energy band. Numerical values of the peak heights are obtained for semiconducting structures with a two-dimensional electron gas.
Point-contact spectroscopy of metallic heterojunctions at high frequencies
Authors: Balkashin O. P.
Published: July 2002

The point-contact spectroscopy is used to study singularities of the electron–phonon spectra of heterojunctions made of different metals Cu–Cu (1 at. % Fe) and Cu–Au. Measurements at high frequencies made it possible to distinguish and identify contributions to the spectrum from the nonequilibrium phonon relaxation.
Pumping of energy into a mesoscopic ring: Exactly solvable model
Authors: Gorelik L. , Kulinich S. , Galperin Yu. , Shekhter R. I. , Jonson M.
Published: July 2002

We consider the energy stored in a one-dimensional ballistic ring with a barrier subjected to a linearly time-dependent magnetic flux. An exact analytical solution for the quantum dynamics of electrons in the ring is found for the case when the electromotive force multiplied by the electron charge, eε, is much smaller than the interlevel spacing, Δ. Electron states exponentially localized in energy space are found for irrational values of the dimensionless ratio A≡Δ/2eε. Relaxation limits the dynamic evolution and the localization does not develop if A is sufficiently close to a rational number. As a result the accumulated energy becomes a regular function of A containing a set of sharp peaks at rational values with small enough denominators (fractional pumping). The shape of the peaks and the distances between them are governed by the interplay between the strength of backscattering and the relaxation rate.
Superconductivity above 250K in Tl1.8Ba2.0Ca2.6Cu3.0O10+δ at high pressure
Authors: Han C. Y. , Lin W. , Wu Y. S. , Yin B. , Tang D. S.
Published: July 2002

The pressure dependence of the superconducting transition temperature Tc (onset) of Tl1.8Ba2.0Ca2.6Cu3.0O10+δ (Tl-2223) has been measured under quasi-hydrostatic pressure (QHP) up to 5.0 GPa. The Tc increases with increasing pressure at a relatively high rate and reaches a maximum at 255.4 K and pressure of about 4.3 GPa. This is the highest Tc yet observed for any high-Tc superconductor. The total change in Tc from ambient condition (Tc=129 K) to the high pressure applied can be greater than 126 K. The Tc above 200 K was replicated several times in our experiments. The site of the maximum of Tc and the value of dTc/dP=1.7 K/GPa (at P=0) agree with previous results obtained by D. Tristan Jover et al. (Physica C 218, 24 (1993)) and J. G. Lin et al. (Physica C 175, 627 (1991)), respectively.
High-temperature superconductivity with d-wave symmetry of the order parameter (Review Article)
Authors: Sergeeva G. G. , Stepanovskiı̆ Yu. P. , Chechkin A. V.
Published: July 2002

It has been established as a result of successful direct experimental studies of the symmetry of the superconducting order parameter that the pairing symmetry in the compounds YBCO, GdBCO, Tl2201, and Bi2212 is of the d-wave type. In this paper, experimental and theoretical results concerning the d-wave superconducting state and the peculiarities of magnetic properties of the d-type superconductor such as pseudogap, charge ordering, and unusual structure of vortex excitations differing from that for s-states are analyzed. Several mechanisms of d-pairing and related microscopic theories are discussed and possible experiments for their verification are proposed.
On the theory of Josephson effect in a diffusive tunnel junction
Authors: Bezuglyi E. V. , Bratus’ E. N. , Galaiko V. P.
Published: July 2002

Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors (with the electron mean free path l smaller than the coherence length ξ0) are studied theoretically in the 1D geometry when the current does not spread in the junction banks. It is shown that the concept of “weak link” with the phase jump Φ∼1 of the order parameter exists only for a low transmissivity of the barrier Γ≪l/ξ0≪1. Otherwise, the presence of the tunnel junction virtually does not affect the distributions of the order parameter modulus and phase. It is found that the Josephson current flowing in the vicinity of the tunnel barrier induces localized states of electron excitations, which are a continuous analog of Andreev’s levels in a ballistic junction. The depth of the corresponding “potential well” is much larger than the separation between an Andreev’s level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic junction in which the Josephson current is transported completely by localized excitations, the contribution to current in a diffusive junction comes from the entire spectral region near the energy gap boundary, where the density of states differs considerably from its unperturbed value. The correction to the Josephson j(Φ) in the second order of the barrier transmissivity, which contains the second harmonic of the phase jump Φ, is calculated and it is found that the true expansion parameter j(Φ) of the perturbation theory for a diffusive junction is not the tunneling probability Γ, but a much larger parameter W=(3ξ0/4l)Γ. This simplifies the conditions for the experimental observation of higher harmonics of j(Φ) in junctions with controllable transmissivity of the barrier.
On the origin of optical conductivity of HTSC in infrared spectral region
Authors: Samovarov V. N.
Published: July 2002

An expression for the frequency dependence of the anomalous component of optical conductivity σMIR(ω) of cuprate superconductors is derived for the entire range of non-Drude intraband excitations 0<ℏω<ℏωg≈1.5–2 eV. The derivation is based on the assumption on finite probability of penetration of an electron (hole) from the hole band to the upper conduction band through the optical gap ℏωg, ensuring the correlated coupling between intraband and interband excitations. It is shown that the available experimental data are in good agreement with the two-component model, taking into account the total contribution of the anomalous component σMIR and the conventional Drude component σD to the conductivity of the metal phase.
Exact instanton solution for quantum tunneling in an uncompensated antiferromagnet
Authors: Ivanov B. A. , Kireev V. E.
Published: July 2002

An exact instanton solution describing macroscopic quantum tunneling for a small antiferromagnetic particle with uncompensated spin and biaxial quadratic anisotropy is constructed. The solution is valid for any relation between anisotropy parameters and relative value of uncompensated spin. The obtained solution is used for calculating the tunneling amplitude taking into account the pre-exponential factor. The amplitude is characterized by a nonanalytic dependence on the ratio of small parameters of the problem, viz., anisotropy in the basal plane and the value of uncompensated spin.
Phase diagram of a strongly anisotropic biaxial ferromagnet and the spectra of coupled magnetoelastic waves
Authors: Mitsaı̆ Yu. N. , Fridman Yu. A. , Kozhemyako O. V.
Published: July 2002

The spectral and thermodynamic properties of a biaxial ferromagnetic crystal are investigated at different temperatures. It is shown that, depending on the direction of the external magnetic field, in the case of a large single-ion anisotropy (much greater than the exchange interaction) there can be both a reorientation phase transition and a transition involving a decrease in the modulus of the magnetization vector. In the first case the elastic and magnetic subsystems actively interact, which leads to the softening of a transverse polarized phonon mode at the point of the orientational phase transition; in the second case the magnon and phonon branches do not interact, and the phase transition takes place through a magnon mode. The phase diagram of a highly anisotropic biaxial ferromagnet is constructed for an arbitrary orientation of the external magnetic field and for arbitrary temperatures.
Reconnection of two vortex rings
Authors: Kida S. , Takaoka M. , Hussain F.
Published: July 2002

The reconnection of two identical viscous vortex rings is investigated numerically. The initial state consists of two rings (of Re≡Γ/ν=578) of a circular cross section placed side by side in a periodic box with their coplanar axes inclined by 30° to the symmetric plane. The subsequent motion is examined by solving the Navier–Stokes equation by a dealiased pseudospectral method in a 643 box. We found two prominent reconnection processes: first, the two vortex rings merge into one by viscous annihilation of opposite vorticity and second, two new rings, which are connected by two ‘‘legs,’’ are created by bridging. The apparent differences with laboratory experiments are discussed.
Molecular-diffusive effects in penetrative convection
Authors: Fernando H. J. S. , Little L. J.
Published: July 2002

An experimental study was performed to investigate the influence of molecular diffusion on turbulent entrainment during penetrative convection. The entrainment coefficient E was determined as a function of the Richardson number Ri and Peclet number Pe. It appears that, in parameter ranges 65<Ri<150 and 103<Pe<104, E is a function of Ri, independent of Pe, which indicates inertial-buoyancy dominated mixing and the unimportance of molecular diffusive effects. At high interfacial stabilities, 30<Ri<300, the entrainment law was found to be given by E∼Ri−1.
Numerical investigation of the flow field behind a shock wave propagating into a carbon–oxygen suspension
Authors: Olim M. , Igra O. , Mond M. , Ben-Dor G.
Published: July 2002

The equations governing the flow field that is developed when a moderately strong shock wave propagates in an oxygen–carbon suspension were developed and solved numerically using the flux-corrected transport technique. A comparison is made between two suspensions. In one suspension the carbon particles are assumed to be inert and in the other, the combustion of the carbon particles is accounted for. In addition, the dependence of the post-shock flow field on the initial loading ratio of the carbon particles was also investigated.
Improved permeability bounds for highly polydisperse materials
Authors: Given James A. , Stell George
Published: July 2002

The influence of polydispersity on the flow of fluid through a medium composed of solid spherical inclusions of many different sizes is studied. Focus is on the case of a medium composed of impenetrable, i.e., nonoverlapping inclusions, which is a good model for flow, e.g., through sand, and also on the case of randomly overlapping inclusions, which provides a well-studied model for flow through porous media. Bounds for the permeability are derived using trial functions of the kind developed by Doi [J. Phys. Soc. Jpn. 40, 507 (1976)] and by Weissberg and Prager [Phys. Fluids 5, 1390 (1962); 13, 2958 (1970)]. It is shown that the bounds for permeability are relatively insensitive to dispersivity of the inclusions or grains composing a material when they are plotted against the proper scaling variable. The porosity is a good scaling variable for materials composed of randomly overlapping inclusions. The mean number of inclusions or grains ρ〈a〉 is shown to be a good scaling variable for permeability bounds on systems of nonoverlapping inclusions. It is shown that the low-density limits of the standard Doi bounds and Weissberg–Prager bounds fail to reproduce the radius-averaged solution of Stokes for flow around a single spherical grain. Also, for extremely disperse media these bounds may become trivial. The improved bounds correct these difficulties.
Application of holography to the measurement of velocity gradients in fluid flows sensitized with photochromic dyes
Authors: Agüí García Juan C. , Hesselink Lambertus
Published: July 2002

A novel joint application of holography and photochromic materials to the experimental measurement of velocity gradients in a fluid flow is presented. A short study of some photochromic materials of interest is presented from the point of view of their applicability to experimental fluid mechanics. This includes a spatiotemporal model for the photoinduced conversion reaction which allows for optimization of the experimental conditions. The forced Rayleigh scattering method for measuring velocity gradients using photochromic materials is then briefly described and applied to the measurement of the velocity gradient in a boundary layer. Spatial resolution of 100 μm and gradient resolution of 3 sec−1 are obtained using these techniques.
Spin-up in a rectangular container
Authors: van Heijst G. J. F. , Davies P. A. , Davis R. G.
Published: July 2002

The spin-up from rest of (i) a homogeneous and (ii) a linearly stratified fluid in a rectangular container has been examined in the laboratory. In the spin-up process leading to the ultimate state of rigid-body rotation, three main stages can be discerned, these being (1) the starting flow, characterized by zero absolute vorticity, (2) flow separation due to cyclonic vorticity generation at the lateral tank walls, and (3) a subsequent organization of the flow into a regular array of alternately cyclonic and anticyclonic cells. During the final stage the flow in these cells gradually decays due to the spin-down/spin-up mechanism provided by the Ekman boundary layer present at the bottom of each cell. Experiments have been performed with free-surface and rigid-lid upper boundary conditions, and the organization of the flow in these cases was observed to be essentially different. In particular, it was noted that the central cell in the free-surface case is always cyclonic. A model for this behavior is advanced, in terms of the tendency of cyclonic vortices to move toward the rotation axis in the free-surface configuration.
Normalization for a turbulent boundary layer with wall suction
Authors: Fulachier L. , Anselmet F. , Benabid T. , Antonia R. A.
Published: July 2002

When a moderate suction rate is applied at the wall of a turbulent boundary layer, the normalized distributions of the Reynolds stresses, temperature variance, and heat fluxes in the inner region are analogous to those obtained without suction, provided the normalization is based on local maxima of the Reynolds shear stress and turbulent heat flux instead of the wall shear stress and the wall heat flux.
Dissipative Korteweg–de Vries description of Marangoni–Bénard oscillatory convection
Authors: Garazo Alfredo N. , Velarde Manuel G.
Published: July 2002

For a horizontal liquid layer open to air and heated either from the air side or the liquid side, threshold values for the onset of oscillatory interfacial instability are provided, as well as the nonlinear evolution equation describing the deformable open surface. The latter equation is the dissipation-modified Korteweg–de Vries evolution equation for solitary excitations in the liquid layer.
The estimated scalar dissipation rate in gas-phase turbulent jets
Authors: Dowling David R.
Published: July 2002

An estimate for the scalar dissipation rate in the turbulent concentration field formed between the nozzle fluid from a round, gas-phase, momentum-driven, turbulent jet and the entrained reservoir fluid is studied. The results are based on the square of the concentration time derivative from high-resolution, single-point measurements made in the self-similar far field of the jet at Reynolds numbers of 5000, 16 000, and 40 000. Results for the temporal behavior, mean value, and statistical properties of the estimated scalar dissipation rate are reported. Peaks in the instantaneous value of the estimated scalar dissipation rate are found to produce a significant, but not dominant, contribution to the average dissipation rate on the jet centerline. The occurrence statistics of these peaks are determined to be other than Poisson distributed. The mean width of the peaks is found to physically correspond to the Taylor scale associated with scalar dissipation, and depend on the inverse square root of the jet Reynolds number. The average estimated scalar dissipation rate is found to be independent of Reynolds number, and self-similar in a manner that is consistent with similarity laws for the turbulent jet. The probability density function (pdf) of the estimated scalar dissipation rate is also found to be self-similar. The compiled distributions, which are based on only one squared field gradient, deviate significantly from lognormality at small values. This result is shown to not preclude the lognormality of the distribution of the true scalar dissipation rate.
On the backreaction of acoustic radiation for distributed two-dimensional vortex structures
Authors: Zeitlin V.
Published: July 2002

Acoustic radiation is calculated by the special hypocycloid-type vortices given by exact solutions of 2-D hydrodynamic equations, the Kirchhoff elliptic vortex being a particular case. Energy and angular momentum balance equations with fluxes due to outgoing waves are used to calculate, in adiabatic approximation, the evolution of parameters governing vorticity distribution. A possible implementation of the same technique to 3-D vortex filaments is briefly discussed.
Wake mechanics for thrust generation in oscillating foils
Authors: Triantafyllou M. S. , Triantafyllou G. S. , Gopalkrishnan R.
Published: July 2002

Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Kármán street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.
Features of nonlinear interactions between a free surface and a shed vortex shear layer
Authors: Tsai Wu-ting , Yue Dick K. P.
Published: July 2002

The nonlinear interaction between a free surface, under gravitational acceleration g, and the vortex shear layer shed by a thin surface-piercing plate, initial submergence h, started abruptly from rest to a constant horizontal velocity U, is studied numerically. The problem is governed by a single parameter, the Froude number Fn = U/√gh. Depending on Fn, three classes of interaction dynamics are identified in the wake of the plate. For subcritical Fn(≲0.7), a plunging breaker forms on the free surface before significant interaction with the vortex sheet occurs. For both transcritical and supercritical Fn, the deformation of the free surface stretches the vortex sheet, and finite-amplitude Kelvin–Helmholtz instabilities arise, which roll up into double-branch spirals. In the transcritical range (Fn∼ 0.7–1.0), the interactions between the free surface and the Kelvin–Helmholtz instabilities remain weak, which allows the latter to roll up continuously into a series of double-branch spirals. For supercritical Fn(≳1.0), the double-branch spiral becomes entrained into the free surface resulting in large surface deformations.
The coupling of interfacial instabilities and the stabilization of two-layer annular flows
Authors: Dijkstra Henk A.
Published: July 2002

In this paper the stability of annular pressure-driven parallel flows of two liquids sandwiching a free cylindrical interface is considered. For small to moderate Reynolds numbers, the interface is susceptible to capillary and interfacial wave instabilities, the latter instability caused by a jump in viscosity at the interface. It is shown that favorable velocity profiles in both liquids may stabilize capillary breakup of the interface and suppress the axisymmetric interfacial wave instability. A long-wave analysis leads to the physical mechanism responsible for stabilization of capillary breakup. This physical mechanism is a generalization of that by which capillary breakup is stabilized by interfacial shear in an annular film of a single liquid. Stabilization of intermediate wavelengths is studied with a mechanical energy analysis, which leads to a description of the energetic processes at work.
The Green’s function for passive scalar diffusion in a homogeneously sheared continuum
Authors: Goddard J. D.
Published: July 2002

The impulsive-source distribution or Green’s function for an unbounded n-dimensional Euclidean space filled by a material medium which undergoes a time-dependent homogeneous deformation and which is characterized by a time-dependent anisotropic diffusion tensor is derived. The special case of time-independent velocity gradients is considered (motions with constant stretch history), in which the anisotropic diffusivity is assumed to arise from the distortion of the otherwise isotropic medium supporting the diffusion process. Explicit reductions are given for steady simple-shearing (viscometric) flows. Also, a brief discussion is given of the relevance to general linear Brownian dynamical systems and the associated Taylor dispersion processes.