bluuebunny/crossref_metadata_2025 huggingface dataset:
On spherically symmetric perfect fluid solutions
Authors: Hajj-Boutros J.
Published: July 2002

Many exact solutions for the spherically symmetric perfect fluid distribution of matter with shear, acceleration, and expansion are obtained. One of them is expressed in terms of Painlevé’s third transcendent.
On the τ-functions of A(2)2
Authors: Post G.
Published: July 2002

A general construction of partial differential equations satisfied by the components of τ-functions is given by considering the tensor products of modules. This procedure is applied to the A(2)2- modules L(Λ0) and L(Λ1), leading to the Kaup equation and Sawada–Kotera equation, respectively. Although L(Λ0) and L(Λ1) are of different level, one can consider L(Λ0)⊗L(Λ1), leading to so-called modified equations. This last construction is new, and leads to a different choice of y, the variable that generates the equations.
Spectral function methods for nonlinear diffusion equations
Authors: Delic G.
Published: July 2002

Two spectral function methods are developed for linear and nonlinear diffusion equations in one dimension where the nonlinearity is in the inhomogeneous term and occurs as a power of the solution. In the single spectral function method polynomial spectral functions in the spatial variable are introduced. The spectral resolution of the diffusion equation in the Hilbert space spanned by these functions yields a system of ordinary differential equations which is then integrated in discrete steps of the time variable. The double spectral method introduces polynomial spectral functions in both space and time variables and thereby eliminates the need for time integration through application of an iterative algorithm. Both methods are compared against analytical solutions for the linear cases and against the numerical solutions for the nonlinear cases. The second spectral function method was found to be more efficient than the first by a factor of 6 in the case of nonlinear problems.
The analytical wavefunctions of the SU(3) limit in the interacting boson model
Authors: Long Gui Lu , Sun Hong Zhou
Published: July 2002

The Su(3) limit intrinsic states in the interacting boson model (IBM) are given by the group theoretical method. A method to calculate the physical states from the intrinsic states is given. Using this method, the physical states of the SU(3) limit ground state band are given completely. Some preliminary results are also obtained for beta and gamma band states. The wavefunctions obtained are expressed in terms of the five building blocks of the IBM wave functions belonging to Sun, Zhang, and Feng. In the SU(3) limit it is found that the building block T+d, which represents three d bosons coupled to zero angular momentum, appears even in the ground state band wavefunctions. The wavefunctions have very interesting physical implications.
On the Cauchy problem for Yang–Mills equations with external current
Authors: Świerczyński Z.
Published: July 2002

The Cauchy problem for Yang–Mills equations with the external current in (3+1)-dimensional space-time is considered. The formulation in which only the spatial part of the current four-vector is given is studied. The global existence theorem is proved.
Irreducible tensor description. I. A classical gas
Authors: Banach Zbigniew , Piekarski Slawomir
Published: July 2002

A classical, moderately rarefied, simple, monatomic gas is considered, and it is supposed that its behavior is governed by Boltzmann’s equation. Then, after a brief review of the fundamental properties of the symmetric traceless tensors, the irreducible equations of transfer for the relative symmetric traceless moments of the one-point distribution function f are systematically derived and related to those of Johnston. Subsequently, Grad’s expansion of the distribution function in terms of reducible three-dimensional Hermite ‘‘polynomials,’’ which does not fit in together and with the equations of transfer just mentioned, is rigorously transformed into its irreducible counterpart fashioned by mathematical apparatus such as one-dimensional Laguerre polynomials and Ikenberry’s tensorial harmonics. Finally, some useful conversion formulas between the relative symmetric traceless moments and the tensorial Laguerre–Ikenberry expansion coefficients of f are deduced and the irreducible variant of Grad’s moment truncation procedure is discussed. The conclusions that have so far been reached concerning Grad’s method are quite specific in that they apply to one-dimensional (classical or quasiparticle) gases. In many cases of interest, the treatment of certain aspects of the kinetic theory of ‘‘actual’’ gases requires, as a prerequisite, a comprehensive discussion of some complicated tensorial problems. In this work the so-called irreducible tensor description of three-dimensional gaseous systems is exploited, and this subject is developed only insofar as it relates to Grad’s moment procedure and to those universal questions which have already been formulated in previous papers. [Z. Banach, J. Stat. Phys. 48, 813 (1987); Arch. Mech. (to be published); Physica A 129, 95 (1984); 145, 105 (1987).]
The complete classification of generalized homogeneous symplectic manifolds
Authors: Grigore D. R. , Popp O. T.
Published: July 2002

The classification scheme for homogeneous symplectic manifolds is completed and generalized including the case when the symmetries are symplectic only up to a factor and the group is nonconnected. This improved classification also describes the possible coverings in terms of classes of some discrete subgroups. As an application, the possibility of mixed symplectic and antisymplectic symmetries is studied for some physical groups: rotations in three dimensions, the Poincaré group and the Galilei group (including inversions). Some new possibilities (with compactified energy), not appearing previously in the literature, have been found even for the connected Galilei group.
A Clifford algebra quantization of Dirac’s electron positron field
Authors: Cho H. T. , Diek Adel , Kantowski R.
Published: July 2002

The quantum field theory of free Dirac particles (four-component massive spin- 1/2 particles) is ‘‘derived’’ by a Segal quantization procedure. First, details are given on how the spinor space of Dirac is actually a minimal left ideal of the Clifford algebra associated with a Lorentz inner product space (+,−,−,−), and how the homogeneous group actions break the natural two-component quaternion structure to give familiar four-component complex spinors. Second, Wigner’s procedure for constructing unitary representations of the Poincaré group is used to construct the appropriately induced infinite-dimensional representation of the inhomogeneous group starting from the above four-dimensional nonunitary representation. Third, and finally, Segal’s procedure for quantizing classical Fermion fields is adapted to this infinite-dimensional Hilbert space to obtain the Clifford algebra of annihilation–creation operators for spin- 1/2 particles. The familiar Fock space appears as a minimal left ideal in this second Clifford algebra.
Two explicit solutions in a reducible relativistic system
Authors: Carbonaro P.
Published: July 2002

By reconsidering the linear equation which describes in the hodograph plane the motion of a relativistic fluid, a significant difference with respect to the analogous equation obtained in the classical fluid dynamic theory is found; while the latter satisfies a condition which greatly simplifies the determination of the Riemann function (required for the integration), the former does not fulfill in general a similar condition except when adopting specific pressure laws. Implications and properties of the relativistic system in these extreme cases are discussed.
Harmonic analysis of directing fields
Authors: Coleman Robert Alan , Korte Herbert
Published: July 2002

The structure of a directing field is determined by the projective structure of space-time and by various tensor (force) fields. Given a sufficient variety of such directing fields, which can be measured directly given only the ability to track material bodies with respect to an arbitrary coordinate system, it is shown how the projective and tensor fields involved can be determined (and hence measured). This method employs the technique of harmonic analysis on the forward unit hyperboloid. For the important and physically relevant case of an electromagnetic directing field, the projective structure and the electromagnetic field tensor can be determined using only one class of charged monopoles characterized by a given charge-to-mass ratio. The method also provides a new empirical criterion for determining whether or not a directing field is geodesic.
Magnetic monopoles without string in the Kähler–Clifford algebra bundle: A geometrical interpretation
Authors: Maia Adolfo , Recami Erasmo , Rodrigues Waldyr A. , Rosa Marcio A. F.
Published: July 2002

In substitution for Dirac monopoles with string (and for topological monopoles), ‘‘monopoles without string’’ have recently been introduced on the basis of a generalized potential, the sum of a vector A, and a pseudovector γ5 B potential. By making recourse to the Clifford bundle 𝒞(τM,g) [(TxM,g)=R1,3; 𝒞(TxM,g)=R1,3], which just allows adding together for each x∈M tensors of different ranks, in a previous paper a Lagrangian and Hamiltonian formalism was constructed for interacting monopoles and charges that can be regarded as satisfactory from various points of view. In the present article, after having ‘‘completed’’ the formalism, a purely geometrical interpretation of it is put forth within the Kähler–Clifford bundle 𝒦(τ*M,ĝ) of differential forms, essential ingredients being a generalized curvature and the Hodge decomposition theorem. Thus the way is paved for the extension of our ‘‘monopoles without string’’ to non-Abelian gauge groups. The analogy with supersymmetric theories is apparent.
Graph theory and a special class of symplectic transformations: The generalized Jacobi variables
Authors: Lim Chjan C.
Published: July 2002

The well-known Jacobi variables in celestial mechanics are generalized to other Hamiltonian systems which include vortex dynamics. A combinatorial algorithm for constructing the generalized Jacobi variables is given; for any binary tree T(N) with N leave, there is a 2N×2N real symplectic matrix MT (T(N),Γ) which completely defines a linear canonical transformation to these relative variables. This algorithm yields a direct proof of the symplectic property for all the generalized Jacobi variables. An application to vortex dynamics is outlined here.
Polyakov string in variable dimensions
Authors: Short K. M.
Published: July 2002

A nonperturbative approach to Polyakov string theory in variable dimensions will be developed. The result leads to a reinterpretation of the critical dimension and an effective compactification of the theory. At each stage the variable dimension theory is based on Gaussian measures, so a discussion of Gaussian measures in linear topological vector spaces is included, detailing the sets of measure zero that arise when the inner product is degenerate. The dimension can be taken to ∞ and the limiting sum exists. The limit represents a correction to [Det Δ]−1/2, which arises as a naive limit. The analysis involves an interplay between zero modes and sets of measure zero with respect to the Gaussian measures. Target space isometries require the factoring out of equivalent configurations from the path integral, which necessitates a discussion of functional Haar measures. The inclusion of source terms is considered.
New geometric formulation of string theory
Authors: Short Kevin M.
Published: July 2002

A new formulation of string theory that is applicable to curved target spaces will be developed. The observables in the new formulation represent the deformations of the image surface. The path integral is ‘‘gauge fixed,’’ but it retains a global gauge invariance. A measure for the embedding integration is developed which encodes a new geometric regularization procedure. The formulation can be applied to target spaces of any dimension. A new interpretation is given to the critical dimension concept, which leads to the ‘‘dynamics of dimension,’’ whereby mass terms or interactions dynamically appear in the theory. Calculations are presented for the genus zero and genus 1 surfaces. At no point is a cosmological term added to the action, and no conformal anomaly is present. There is some discussion of the connection with general relativity. Certain mathematical aspects arise and are included in the Appendices.
Wake-free waves in one and three dimensions
Authors: Bombelli L. , Couch W. E. , Torrence R. J.
Published: July 2002

A recent paper by Gottlieb [J. Math. Phys. 29, 2434 (1988)] provides examples of acoustic wave equations, in various dimensions, that have nontrivial families of solutions that are progressing waves of order 1, and relates this to whether or not these equations satisfy Huygens’ principle. A statement made in that paper related to Huygens’ principle in one space dimension is clarified, and it is shown in this connection that, in general, the relationship between the possession of progressing wave solutions and the satisfaction of Huygens’ principle is more complex than the situation described by Gottlieb. In addition, the attractive properties of progressing waves of order 1 are retained by progressing waves of any finite order, and we use this to generalize in several ways Gottlieb’s results on ‘‘wake-free’’ solutions of the acoustic equation in three dimensions.
Two finite-dimensional completely integrable Hamiltonian systems associated with the solutions of the MKDV hierarchy
Authors: Gu Zhuquan
Published: July 2002

In this paper the equations of the MKDV hierarchy and their Lax pairs are obtained from zero curvature equations. Using trace formulas of the spectral problem and the Lax pairs, two finite-dimensional completely integrable systems are found. The solving equations of the MKDV hierarchy are transformed into the solving Hamiltonian canonical equations.
Dynkin-like diagrams and representations of the strange superalgebra P(n)
Authors: Frappat L. , Sciarrino A. , Sorba P.
Published: July 2002

Using an extension P̃(n) of the noncontragredient superalgebra P(n), on which a nondegenerate Killing form can be constructed, simple root systems (SRSs) are introduced. To each SRS is associated a Dynkin-like diagram. Then the maximal regular sub-(super)algebras are obtained. Moreover, a procedure to construct highest weight irreducible representations of P(n) is presented.
Vacuum energy for 3+1 dimensional space-time with compact hyperbolic spatial part
Authors: Bytsenko Andrei A. , Cognola Guido , Vanzo Luciano
Published: July 2002

The vacuum energy for a massless scalar field defined on a hyperbolic manifold H3/Γ is evaluated using zeta-function and heat kernel regularization techniques and Selberg trace formula for cocompact group Γ. A negative contribution to the vacuum energy associated with trivial line bundle related to character χ=1 is found.
The Casimir theorem and the inversion problem in electrodynamics at first quantized level
Authors: Bosco B. , Ricci P. , Sacchi M. T.
Published: July 2002

The inversion problem in electrodynamics is analyzed for a nonlocalized source. The model used is the generalized Schrödinger current from continuum to continuum states. The general expressions of the electric and magnetic multipoles in terms of the infinite transitions from which they are generated and the contribution of each transition are derived. It is shown, for a particular example, that the scattering wave functions of a given transition are determined in terms of the electric and magnetic multipole amplitudes to which the transition gives rise. It can be shown (but the proof is not given in this paper) that similar results are valid for every transition and are, therefore, quite general. It is also shown that the couple of wave functions corresponding to each transition satisfies a Schrödinger equation with an energy dependent potential which is completely determined by the same multipole amplitudes. In this way, the most clear connection between scattering and electromagnetic phenomena is displayed.
Quantum transformation theory in fermion Fock space
Authors: Zhang Yong-de , Tang Zhong
Published: July 2002

In this article a general linear quantum transformation U for the following fermion system with n modes, (b′+,b̃′)=U(b+,b̃)U−1=(b+,b̃)(B̃, A, C̃D), is studied. All above transformations in Fock space are proved to form a ray representation of a group which is isomorphic with O(2n,C). The explicit expressions of operator U in terms of the normal ordered product and non-normal ordered product are obtained. A series of auxiliary identities are given. It has been mentioned that the results are applicable to the case of fermion fields with interaction.
Spectral analysis and stability properties of a relativistic deformation of the harmonic oscillator
Authors: Caliceti E. , Cherubini A. M.
Published: July 2002

The spectral properties are established and the stability of the eigenvalues under the singular perturbation representing the relativistic corrections are proven for a family of ordinary differential operators describing a relativistic deformation of the quantum harmonic oscillator.
Quantum and semiclassical representations over Lagrangian submanifolds in su(2)*, so(4)*, and su(1,1)*
Authors: Karasev Mikhail , Kozlov Mikhail
Published: July 2002

Irreducible representations of three simplest Lie algebras are realized over Lagrangian submanifolds Λ (over closed curves, tori, and spheres) in coadjoint orbits. The intertwining operator is constructed which enables to pass from an abstract representation to a ‘‘Λ representation.’’ The integral kernel of the intertwining operator involves special ‘‘Λ-coherent states.’’ The simple integral formulas are obtained for exact and semiclassical eigenvectors and for solutions of the Cauchy problem over Lie algebras, mentioned in the title. The Hamiltonians considered are nonanalytic in general.
Supersymmetry and the Atiyah–Singer index theorem. I. Peierls brackets, Green’s functions, and a proof of the index theorem via Gaussian superdeterminants
Authors: Mostafazadeh Ali
Published: July 2002

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green’s function and functional integral methods provide a direct derivation of the index as a single universal superdeterminant.
Quantum chaos: An entropy approach
Authors: Sl/omczyński Wojciech , Życzkowski Karol
Published: July 2002

A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov–Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ‘‘Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.’’ John Milton, Paradise Lost, Book II
Canonical coherent states for the relativistic harmonic oscillator
Authors: Aldaya V. , Guerrero J.
Published: July 2002

In this paper there are constructed manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given SL(2,R) representation, once a change of variables z∈C→zD∈ unit disk is performed. Also introduced are higher-order, relativistic creation and annihilation operators, â,â°, with canonical commutation relation [â, â°]=1 rather than the covariant one [ẑ, ẑ°]≊ energy and naturally associated with the SL(2,R) group. The canonical (relativistic) coherent states are then defined as eigenstates of â. Finally, a canonical, minimal representation is constructed in configuration space by means of eigenstates of a canonical position operator.
Markov diffusions in comoving coordinates and stochastic quantization of the free relativistic spinless particle
Authors: Morato Laura M. , Viola Lorenza
Published: July 2002

We revisit the classical approach of comoving coordinates in relativistic hydrodynamics and we give a constructive proof for their global existence under suitable conditions, which is proper for stochastic quantization. We show that it is possible to assign stochastic kinematics for the free relativistic spinless particle as a Markov diffusion globally defined on M 4. Then introducing dynamics by means of a stochastic variational principle with Einstein’s action, we are lead to positive-energy solutions of the Klein–Gordon equation. The procedure exhibits relativistic covariance properties.
Moduli-space structure of knots with intersections
Authors: Grot Norbert , Rovelli Carlo
Published: July 2002

It is well known that knots are countable in ordinary knot theory. Recently, knots with intersections have raised a certain interest, and have been found to have physical applications. We point out that such knots—equivalence classes of loops in R3 under diffeomorphisms—are not countable; rather, they exhibit a moduli-space structure. We characterize these spaces of moduli and study their dimension. We derive a lower bound (which we conjecture being actually attained) on the dimension of the (nondegenerate components) moduli spaces, as a function of the valence of the intersection.
Free quantum fields on the Poincaré group
Authors: Toller M.
Published: July 2002

A class of free quantum fields defined on the Poincaré group is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski space–time and they are ‘‘elementary’’ in the sense that they describe particles that transform according to irreducible unitary representations of the symmetry group, given by the product of the Poincaré group and of the group SL(2,C) considered as an internal symmetry group. Some of these fields describe particles with positive mass and arbitrary spin and particles with zero mass and arbitrary helicity or with an infinite helicity spectrum. In each case the allowed SL(2,C) internal quantum numbers are specified. The properties of local commutativity and the limit in which one recovers the usual field theories in Minkowski space–time are discussed. By means of a superposition of elementary fields, one obtains an example of a field that presents a broken symmetry with respect to the group Sp(4,R) that survives in the short-distance limit. Finally, the interaction with an accelerated external source is studied and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a finite critical value.
The Stückelberg–Kibble model as an example of quantized symplectic reduction
Authors: Wiedemann U. A. , Landsman N. P.
Published: July 2002

Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory to the Stückelberg–Kibble model. We explicitly construct the physical state space ℋphys, which carries a massive representation of the Poincaré group. The longitudinal one-particle component arises from a particular Bogoliubov transformation of the five (unphysical) degrees of freedom one has started with. Our discussion exhibits the particular features of the proposed constrained quantization theory in great clarity.
Supertraces on the algebras of observables of the rational Calogero model with harmonic potential
Authors: Konstein S. E. , Vasiliev M. A.
Published: July 2002

We define a complete set of supertraces on the algebra SHN(ν), the algebra of observables of the N-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of N=1 and N=2 to arbitrary N. It is shown that SHN(ν) admits q(N) independent supertraces, where q(N) is a number of partitions of N into a sum of odd positive integers, so that q(N)≳1 for N≥3. Some consequences of the existence of several independent supertraces of SHN(ν) are discussed, such as the existence of ideals in associated W∞-type Lie superalgebras.
The nonsimultaneous nature of the Schwarzschild R=0 singularity
Authors: Hellaby Charles
Published: July 2002

The relationship between the two well-behaved coordinate systems of Lemaître–Tolman–Novikov, and Kruskal–Szekeres–Penrose indicates that the Schwarzschild R=0 singularity is intrinsically nonsimultaneous. It follows that the simultaneous synchronous coordinates of Wald and Yip do not exist on the complete Schwarzschild manifold. In the process, the coordinate transformations between the Schwarzschild exterior model in its various common coordinate systems and the vacuum Lemaître–Tolman model (which includes Novikov coordinates and the closed Kantowski–Sachs model) is derived. It is also shown that, contrary to statements in the literature, the closed Kantowski–Sachs model is well-behaved limit of the Lemaître–Tolman model.
Examples of separating coordinates for the Klein–Gordon equation in 2+1-dimensional flat space–time
Authors: Hinterleitner F.
Published: July 2002

We consider the domains of those pseudo-orthogonal coordinate systems in flat 2+1-dimensional space–time which allow for the separation of the Klein–Gordon equation by a product ansatz and which were characterized by Kalnins and Miller in connection with the symmetry group of the wave equation. The horizons of these domains which were constructed as enveloping surfaces of the common tangent null planes of the coordinate surfaces turn out to be ruled surfaces, generated by the totality of tangents of a null curve. This paper is a report on a longer one containing the horizons and domains of the full number of 87 separating coordinate systems.
Preliminary classification of q
t=f(q,q
x,q
xx,q
xxx)
Authors: Satır Ahmet
Published: July 2002

The preliminary classification of qt=f(q,qx,qxx,qxxx) is given. The results are compared with Fokas’s symmetry and Mikhailov–Shabat–Sokolov formal symmetry approaches.
Gauge invariant perturbations of black holes. I. Schwarzschild space–time
Authors: Fernandes Joe F. Q. , Lun Anthony W. C.
Published: July 2002

We cast the perturbed Bianchi identities, in the Schwarzschild background, into a form involving only tetrad and coordinate gauge invariant Newman–Penrose field quantities. These quantities, which arise naturally in our approach, are gauge invariant quantities of spin-weight ±2, ±1, and 0. Some of the integrability conditions for the Bianchi identities then provide a system of six gauge invariant perturbation wave equations for the spin-weighted quantities. These wave equations are, respectively, the (spin-weight ±2) Bardeen–Press equations, two new (spin-weight ±1) gravitational wave equations, and two (spin-weight 0) Regge–Wheeler equations. Other integrability conditions provide the transformation identities that relate the field quantities to each other, and hence relate the various perturbation wave equations to one another. In particular, this method provides an alternative derivation of the transformations between the Bardeen–Press and Regge–Wheeler equations. The integrability conditions also allow us to relate the Bardeen–Press quantities of opposite spin-weight, and we investigate how this relationship compares with the Teukolsky–Starobinsky identities. Finally, we give a derivation of the gauge invariant Zerilli equation, and show how it is related to the fundamental equations mentioned above.
Natural renormalization
Authors: Schnetz Oliver
Published: July 2002

A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration constants differential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by application to the toy example of a free massive bosonic theory. Then we apply the scheme to the φ4-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed and the beta-function and the anomalous dimension are calculated up to fourth and fifth order, respectively.
Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model
Authors: Zirnbauer Martin R.
Published: July 2002

An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N=1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov’s σ model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supersymmetric version of Pruisken’s nonlinear σ model with couplings σxx=N/4 and σxy=N/2 at the symmetric point. It follows that the model for N=2, which describes a spin degenerate Landau level and the random flux problem, is noncritical. On the basis of symmetry considerations and inspection of the Hamiltonian limit, a modified network model is formulated, which still lies in the quantum Hall universality class. The prospects for deformation to a Yang–Baxter integrable vertex model are briefly discussed.
Colored noise and a characteristic level crossing problem
Authors: Kłosek M. M. , Hagan P. S.
Published: July 2002

In this paper we discuss the activation of a dynamical system of one spatial variable forced by an external Gaussian stationary colored noise. The model is an analog of the Smoluchowski equation when external fluctuations are present. We assume that the underlying deterministic dynamics are derived from a potential forming a well. We enlarge the state space by including the noise variable, and then use half-range expansion techniques, singular perturbations, and matched asymptotics to solve the boundary value problem for the steady-state probability density function, in the asymptotic limit of small correlation time and over the entire regime of noise strength. We find a uniformly valid expression for the activation rate to the top of the potential barrier (a characteristic point for the unforced dynamical system). We show the important effects of the boundary behavior of the process on its activation rate. If the intensity of the noise is small compared to the autocorrelation of the noise, then the effective activation energy is modified by the noise autocorrelation. We consider an example of the activation process in a double well potential, and compare our uniformly valid results with results reported in the literature.
Nonlinear constraints and soliton solutions of 1+2-dimensional three-wave equation
Authors: Zhou Zixiang
Published: July 2002

Using the nonlinear constraint method, the explicit expressions of localized solitons of the 1+2-dimensional three-wave equation are obtained. After the lth Darboux transformation, each component of the solution has, at most, l2 peaks when the parameters for each single Darboax transformation are large enough. This gives a corresponding asymptotic property for the DSI equation, although all the peaks of each component move in the same velocity here.
Clebsch–Gordan coefficients in the asymptotic limit
Authors: de Guise Hubert , Rowe David J.
Published: July 2002

We investigate the graded structure of the tensor product space Vλ2⊗Vλ1, which arises in the coupling of two irreducible representations λ1 and λ2 of a semisimple Lie algebra G, in the limit in which one of the highest weights becomes asymptotically large. The construction of asymptotic coupling coefficients is considered.
Nonlinear realizations of the diffeomorphism group in metric-affine gauge theory of gravity
Authors: Giachetta Giovanni
Published: July 2002

The action of diffeomorphisms on coupled metric and spinor fields on a world manifold X is interpreted in terms of nonlinear realizations of the group GL∼+(4,R), the universal twofold covering group of the general linear group GL+(4,R), on the quotient manifold (GL∼+(4,R)×V)/SL(2,C), where SL(2,C) is the spin group and V is the spinor space. By using nonlinear realizations the connection of a metric-affine world manifold couples naturally to standard spinor fields. This enables us not to exceed the scope of usual spinor models as in the case in which infinite-dimensional representations of GL∼+(4,R) are considered. As an application, by starting from the familiar Lagrangian for spin-1/2 models and using the nonlinear realization method, a Lagrangian density for spinor fields which has GL∼+(4,R) as invariance group is constructed. The total Lagrangian density is obtained by adding the Lagrangian of the metric-affine gravity. The energy-momentum current associated with every vector field on the world manifold X is calculated explicitly. It turns out that spinor fields do not contribute to the corresponding superpotential, which takes a form similar to that obtained by Komar.
Flavor symmetry of the tensor Dirac theory
Authors: Reifler Frank , Morris Randall
Published: July 2002

Recently, the Dirac and Einstein equations were unified in a tetrad formulation of a Kaluza–Klein model with gauge group SL(2,R)×U(1). In this model, the self-adjoint modes of the tetrad describe gravity, whereas the isometric modes of the tetrad together with a scalar field describe fermions. This model gives precisely the usual Dirac–Einstein Lagrangian. In this paper we generalize the tensor Dirac theory to the larger gauge group SL(2,C)×U(1) acting on bispinors. We show that each SL(2,R)×U(1) subgroup of SL(2,C)×U(1) corresponds to a different factorization of the second-order Klein–Gordon equation into a first-order Dirac equation. Since the Noether currents are different for each factorization, the solutions describe different flavors of fermions. We show that electric charge, lepton number, and baryon number are conserved in this generalization of the Dirac theory.
Howe duality for the quantum groups Uqu(m,n), Uqu(M)
Authors: Green Gavin
Published: July 2002

A dual pair is defined to be a pair of mutually centralizing subgroups of the real symplectic group. Let (G,G′) be a dual pair of reductive groups in which G is also compact and consider the decomposition of the metaplectic representation of the symplectic group into GG′-irreducibles. Each such irreducible is a tensor product of an irreducible of G with one of G′, and it turns out there is a bijective correspondence between them, a particular irreducible of G only occurring with a particular one of G′ and vice versa. This so-called Howe duality is here generalized to the quantum group case (Uqu(m,n),Uqu(M)) for q not a root of unity. A metaplectic representation for this dual pair is given in terms of the q-oscillator algebra and a Uqu(m,n)×Uqu(M)-covariant Heisenberg–Weyl algebra is also constructed and realized on Fock space. The heart of the proof lies in showing that Uqu(m,n) and Uqu(M) are essentially mutual commutants on Fock space. The duality follows using the compactness of Uqu(M). The proof is independent of the classical theory. As a consequence, given any two unitary highest weight representations of a quantum pseudo-unitary group (which arise from the restriction of a metaplectic representation), the decomposition of their tensor product is the same as in the classical case.
Explicit formulas for reproducing kernels of generalized Bargmann spaces on Cn
Authors: Askour Nour Eddine , Intissar Ahmed , Mouayn Zouhaı̈r
Published: July 2002

We introduce a class of generalized Bargmann spaces on Cn for which we establish explicit formulas of their reproducing kernels. Some applications of the obtained formulas are given.
On phase transitions in a Fermi liquid. II. Transition associated with translational symmetry breaking
Authors: Peletminsky A. S. , Peletminsky S. V. , Slyusarenko Yu. V.
Published: July 2002

The phase transition in a Fermi liquid, associated with translational symmetry breaking and the formation of periodic structures is considered. Special attention is paid to the formation of one-dimensional long-periodic structures in a three-dimensional Fermi liquid. The relation between the formation of such structures and kinetic and thermodynamic stability of the normal state of the Fermi liquid is analyzed.
Growth and dissolution kinetics of He3 inclusions in phase-separated He3–4He solid mixtures
Authors: Gan’shin A. N. , Grigor’ev V. N. , Maı̆danov V. A. , Omelaenko N. F. , Penzev A. A. , Rudavskiı̆ E. Ya. , Rybalko A. S. , Tokar Yu. A.
Published: July 2002

Comprehensive experimental results on growth, dissolution, and melting kinetics of solid inclusions of He3 formed as a result of phase separation of solid mixtures of He3 in He4 are described. A new method developed for obtaining high- quality crystals by cycling the temperature of a solid mixture within the separation region makes it possible to obtain reproducible values of time constants for growth and dissolution of inclusions. Precise measurements of pressure in the crystal at constant volume are used for obtaining data on effective mass diffusion of He3 atoms in the crystal. It is shown that quantum diffusion is strongly suppressed at low temperatures due to elastic fields induced near the boundaries of inclusions. Abnormally rapid transport of matter of the threshold type is observed during dissolution of inclusions. The observed effects can be explained qualitatively in the proposed model of multistage dissolution of He3 inclusions. The data on the variation of pressure as a result of melting and crystallization of He3 inclusions are also obtained. It is proposed that a part of He3 remains in the liquid phase after crystallization.
Influence of intrinsic point defects on the electrophysical properties of NbSe3
Authors: Mamaluı̆ A. A. , Shelest T. N. , Chashka Kh. B.
Published: July 2002

The temperature dependence of the electrical resistivity of quasi-one-dimensional NbSe3 is investigated in the interval 78–550 K in the thermodynamic equilibrium and nonequilibrium states. At temperatures of 300–550 K one observes an exponential deviation from the linear dependence on account of the formation of thermodynamic equilibrium Se vacancies. The influence of intrinsic defects (vacancies) on the properties of NbSe3 at 78–300 K is investigated by the quenching method. For samples with excess vacancies an anomalously large deviation from the Matthiessen rule (up to 150%) is observed.
Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules
Authors: Sone Yoshio , Ohwada Taku , Aoki Kazuo
Published: July 2002

A semi-infinite expanse of a rarefied gas over a plane wall where there is a constant heat flow normal to the wall from infinity is considered. The behavior of the gas is analyzed numerically by a finite difference method on the basis of the standard linearized Boltzmann equation for hard-sphere molecules with diffuse reflection at the wall. From the result the temperature jump coefficient and its associated Knudsen layer of a slightly rarefied gas flow around a body are derived.
Large-scale horizontal mixing in planetary atmospheres
Authors: Pierrehumbert R. T.
Published: July 2002

Some implications of chaotic advection for mixing of potential vorticity and chemical species by large-scale, two-dimensional, atmospheric flows are examined. It is argued that such mixing is important in the Earth’s atmosphere and in those of the other rapidly rotating planets, but that the essential features of the mixing cannot be captured by an effective diffusivity. A means of identifying and characterizing chaotic mixing regions by examining patterns of spatial variation of finite-time estimates of the Lyapunov exponents is proposed, and tested on a number of idealized cases. Some preliminary results on application of the method to Northern Hemisphere atmospheric data are reported. The principal mixing zones, characteristic mixing time, and barriers to transport are identified.
Numerical investigation of instability and transition in rotating plane Poiseuille flow
Authors: Yang Kyung-Soo , Kim John
Published: July 2002

Instability and transition in plane Poiseuille flow with spanwise system rotation is studied via direct numerical simulations with initial small-amplitude random disturbances. The results confirm and clarify the recent experimental findings of Alfredsson and Persson [J. Fluid Mech. 202, 543 (1989)]. A large computational domain is used to allow natural selection of the dominant spanwise wavelength of the observed streamwise vortices, and also the streamwise wavelength of the dominant secondary modes which subsequently develop in the presence of the streamwise vortices. Temporal evolutions of these vortices for several different cases are studied in detail. It is found that the spanwise wavelength of the streamwise vortices can be significantly different from that obtained from linear stability analysis. In all cases examined, the unstable primary three-dimensional waves, which develop during the linear stage, are still persistent in the nonlinear stage. It is also found that for the cases in which the primary three-dimensional waves decay, the finite-amplitude streamwise vortices can become unstable to two different three-dimensional secondary modes of instability, depending on the range of Reynolds number (Re) and rotation number (Ro). The first mode has a streamwise wavelength an order of magnitude longer than the spanwise wavelength; the other, referred to by Alfredsson and Persson as the ‘‘twisting mode’’ because of its visual appearance, has a streamwise wavelength comparable to the spanwise wavelength, and is shown to consist of counter-rotating streamwise vortices whose centers oscillate mostly in the vertical direction. It is shown that these modes are nondispersive traveling waves.
The partial-equilibrium approximation in reacting flows
Authors: Rein Martin
Published: July 2002

Complex reaction systems that are subject to the partial-equilibrium approximation are analyzed. In order to take proper account of equilibrium and finite rate reactions, a distinction is made between linearly independent and dependent species and reactions, respectively. The assumption of partial equilibrium removes short time scales from the problem and leads to a reduction in the number of independent thermodynamic variables. Making use of a fundamental property of equilibrium reactions, a general formulation for partial chemical equilibrium in complex reaction systems is obtained. Furthermore, a partially frozen sound speed is defined and an analytical expression for this sound speed is given. The concept of partial chemical equilibrium is applied to high-speed reacting flows. A characteristic formulation of the conservation and rate equations is presented. Finally, a high-enthalpy flow, namely the expansion of high-temperature air through the axisymmetric nozzle of a shock tunnel, is calculated using the method of lines.
Long periodic internal waves
Authors: Vanden-Broeck Jean-Marc , Turner Robert E. L.
Published: July 2002

Long periodic waves propagating in a channel bounded above and below by horizontal walls are considered. The fluid consists of two layers of constant densities separated by a region in which the density varies continuously. The problem is solved numerically by a finite difference scheme coupled with boundary integral equation techniques. It is shown that there are long periodic waves characterized by a train of ripples in their troughs. The numerical results suggest the existence of a wave with one large crest flanked on either side by a small-amplitude oscillatory wave extending to infinity, in anology with the ‘‘solitary wave with oscillatory tail,’’ known to exist for surface waves with small surface tension.
Analytic axisymmetric magnetohydrodynamic equilibria of a plasma torus with toroidal mass flow
Authors: Throumoulopoulos G. N. , Pantis G.
Published: July 2002

Several classes of analytic equilibria of a toroidal axisymmetric plasma with toroidal mass flow are obtained for isothermal as well as isentropic magnetic surfaces under various pressure and toroidal current density profiles. The effects of flow on certain global equilibrium and stability characteristics are examined. It is shown that for a wide family of equilibria the average beta 〈 β〉 does not depend explicitly on flow and falls within the limits of static equilibria. In particular, for the case of field-reversed configurations 〈 β〉 is totally independent of plasma flow. Calculations based on a specific equilibrium solution for a tokamak with fixed average toroidal magnetic energy show that plasma elongation is an increasing function of the Mach number whereas the safety factor is a decreasing function of it.
The scaling of absolutely unstable, stimulated Raman scattering from planar, laser-produced plasmas
Authors: Drake R. P.
Published: July 2002

A study of the scaling of the fraction, fSRS, of the laser energy scattered by stimulated Raman scattering (SRS) is reported. A simple model of SRS as an absolute instability is presented, leading to the hypothesis that fSRS will be determined by the depth of the plasma producing SRS. The results of a number of experiments are used to test this hypothesis. The experiments analyzed used irradiating wavelengths of 1.06, 0.53, and 0.35 μm. In all cases, the plasmas were planar and the electron–ion collision rate was small compared to the homogeneous SRS growth rate. The depth of the plasma, as opposed to the laser intensity or laser wavelength, is found to be the primary determinant of fSRS. In addition, as the depth of the plasma increases, the angular distribution of the scattering is observed to broaden. The implications of these results for analysis of SRS as an absolute instability and for laser fusion are discussed.
Narrow Raman spectra: The competition between collisional and Landau damping
Authors: Drake R. P. , Williams E. A. , Young P. E. , Estabrook Kent , Kruer W. L. , Montgomery D. S. , Baldis H. A. , Johnston T. W.
Published: July 2002

Narrow Raman spectra can be produced when the collisional damping rate becomes comparable to the homogeneous growth rate for stimulated Raman scattering (SRS). Landau damping limits the SRS spectrum at short wavelength, and collisional damping can limit it at long wavelength through the variation of the damping rate with plasma density. Data are shown to demonstrate this effect for the first time, from experiments in which constant-intensity pulses of 0.35 μm light irradiated 3 μm thick CH targets at intensities up to 2×1014 W/cm2. The observed spectra have a peak wavelength, spectral width, spectral shape, and shift of the peak in time that are consistent with the anticipated effects of damping. Reduction of the emission from the plasma to near thermal levels at heavily damped frequencies is also demonstrated. In addition, the application of two specific models of SRS to these data is discussed.