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  • 1
    Electronic Resource
    Electronic Resource
    The action of product tensor operators within and between pure and mixed configurations (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 3950-3963 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Atomic and nuclear shell Hamiltonians can be represented in terms of one- and two-body product tensor operators which act both in spin and orbital spaces. In this paper, equivalence conditions for the matrix elements of these operators are used to find their normalization constant. The results obtained for one-body operators are tabulated for all pure and mixed shells with l≤3. The normalization constants for two-body operators are proved to be products of two one-body normalization constants with the corresponding ranks. Subsequently, expressions for the matrix elements of one- and two-body double tensor operators within all pure configurations are found for arbitrary ranks. Since these generalized product tensor operators may include polar components, they are allowed to participate in configuration mixing. Therefore, reduced matrix elements for these operators have also been calculated both within mixed configurations and between all possible combinations of mixed and pure configurations. These formulas have been used in a computer program and selected numerical results have been provided in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450917
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  • 2
    Electronic Resource
    Electronic Resource
    The method of coherent structures and metamagnetism (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 5454-5456 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A number of metallic compounds such as FeRh, Mn3GaC, and FeCl2 exhibit the interesting property of metamagnetism, i.e., the presence of order–order magnetic-phase transitions. The microscopic Hamiltonian that is commonly used to describe this class of systems is of the Heisenberg type with competing exchange interactions between the nearest- and next-nearest neighbors. Starting from this quantum Hamiltonian, through several transformations, it is possible to obtain an effective Hamiltonian which has a two-body interaction term. A recent method of analyzing such Hamiltonians is then applied based on exact calculations for the corresponding nonlinear equation of motion. This is followed by quantization about the classical solutions. Stability conditions imposed on the classical solutions agree with earlier results. Their violation is interpreted in terms of modulational instability of the associated Landau–Ginzburg Hamiltonian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.345841
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  • 3
    Electronic Resource
    Electronic Resource
    Exact solutions of the multidimensional classical φ6-field equations obtained by symmetry reduction (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2194-2212 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The often used φ6 model of classical critical phenomena is studied in (3+1)-dimensional Minkowski and Euclidean spaces. The Euler–Lagrange equations describing the kinetics of the scalar order parameter are in this case nonlinear Klein–Gordon equations. The method of symmetry reduction is systematically applied to derive all the solutions invariant under subgroups with generic orbits of codimension 1. Whenever the obtained ordinary differential equations have the Painlevé property, they can be transformed to one of two standard forms. These are then solved in terms of elliptic functions or elementary ones. This results in a large number of new exact solutions. Particularly interesting solutions are found in the immediate vicinity of the tricritical point. Our treatment of the φ6 theory is complete only for the four-dimensional spaces M(3,1) and E(4), but many of the results are given for the more general cases of M(n,1) and E(n+1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527813
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  • 4
    Electronic Resource
    Electronic Resource
    The role of fluctuations in spontaneous metamagnetism (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 64 (1988), S. 5633-5635 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A Landau–Ginzburg Hamiltonian involving coupled sublattice magnetizations as order parameters for spontaneous metamagnets is studied. A brief review of the mean field results is followed by an analysis of the role of fluctuations which arise due to the inhomogeneity terms in the Hamiltonian. Using a Gaussian approach the specific heat contribution from the normal modes is studied neglecting mode-mode coupling. A non-Gaussian approach to the problem is also outlined. While for finite sizes specific heat shows no anomalies, in the thermodynamic limit classical exponents are recovered. The kinetics of the transition is described by the Euler–Lagrange equations for sublattice magnetizations which result in two nonlinearly coupled nonlinear Klein–Gordon equations. Special solutions obtained from a particular ansatz include solitons and elliptic waves whose physical interpretation is provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.342305
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  • 5
    Electronic Resource
    Electronic Resource
    Improved calculations of magnetoelastic properties in collinear metamagnets (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 3918-3920 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Metamagnets such as Mn3GaC, Fe-Rh, Mn2−xCrxSb, and Mn1−xCrxSb exhibit strong magnetoelastic couplings via strain dependence of exchange integrals. The purpose of this paper is to improve the calculations of the relevant elastic and magnetic ensemble averages for model Hamiltonians using some novel non-Gaussian approximations. The results derived are applicable to a wide range of magnetically ordered spin systems placed on anharmonic crystal lattices in the presence of an exchange-striction mechanism. It is found that the commonly invoked polynomial series expansions for the temperature dependence of the displacement and magnetization are valid only at sufficiently low temperatures. At significantly higher temperatures exponential series expansions are found to be more appropriate. Intermediate temperature ranges involve special functions of the parabolic cylinder type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.340605
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  • 6
    Electronic Resource
    Electronic Resource
    The derivation of a symmetry-adapted generalized spin Hamiltonian (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 4001-4004 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The formulation of a generalized spin Hamiltonian using the decomposition of double tensor operators into products of single tensor operators is reexamined critically using their transformation properties under parity, time reversal, charge and Hermitian conjugation, as well as the imposition of symmetry constraints. These properties depend on their polar or axial vector classification. It is concluded that limitations in the parameterization of experimental EPR and ENDOR spectral data are associated with an excessively restrictive interpretation of the constraints imposed in the derivation of phenomenological and generalized spin Hamiltonians. It is shown that the correct imposition of these constraints using the double tensor formulation leads to a symmetry adapted generalized spin Hamiltonian which includes additional zero field splitting terms characteristic of the various crystallographic groups and described by odd rank tensor operators whose matrix elements are nonzero provided account is taken of configuration interactions. It is noted that the conclusions derived are applicable to all physical systems that can be described by Hamiltonians formulated in terms of tensor operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449114
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  • 7
    Electronic Resource
    Electronic Resource
    Comments on the information, information gain and efficiency of self-organizing systems (1987)
    Springer
    The European physical journal 65 (1987), S. 375-379 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Haken recently applied the slaving principle to decompose expressions for information, information gain and efficiency of self-organizing systems into two parts. The first part in each case depends on the order parameter while the second on the slaved modes. Close to the instability points the latter contribution can be ignored. In this paper we elaborate on the formulas given by Haken and find exact expressions which are analytical in the entire domain of the values of control parameters. We also find their asymptotic limits in the immediate proximity of the instability point and far away from it. Our results provide a direct way of relating information, information gain and efficiency of nonequilibrium critical systems to their control parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303726
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  • 8
    Electronic Resource
    Electronic Resource
    Group theory and solutions of classical field theories with polynomial nonlinearities (1993)
    Springer
    Foundations of physics 23 (1993), S. 633-665 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v〉c). We first present a complete set of translationally invariant solutions for the φ4 model and demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ4 and φ6 cases since they provide the most realistic models of elementary particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01883770
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  • 9
    Electronic Resource
    Electronic Resource
    Fröhlich's condensation in a biological membrane viewed as a Davydov soliton (1989)
    Springer
    Journal of biological physics 17 (1989), S. 41-50 
    Details
    ISSN: 1573-0689
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract A model Hamiltonian is postulated for a biological membrane involving phospholipid tails and heads accounting for the presence of dielectrically-active material. It is subsequently demonstrated that under specific conditions, Bose condensation of dipolar oscillations of the head groups may take place in support of Fröhlich's earlier conjecture. A new effect is found here that this condensation phenomenon can be interpreted as the emergence of a Davydov soliton in the momentum space for dipole oscillations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00393325
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  • 10
    Electronic Resource
    Electronic Resource
    Application of the Fröhlich theory to the modelling of rouleau formation in human erythrocytes (1989)
    Springer
    Journal of biological physics 17 (1989), S. 19-40 
    Details
    ISSN: 1573-0689
    Keywords: Erythrocytes ; rouleau formation ; Fröhlich theory ; dipole-dipole interactions ; van der Waals forces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract The details of Fröhlich's theory and some recent experiments on the rouleau formation of human erythrocytes which exhibit a strong interaction that appears to satisfy the prerequisites of the Fröhlich theory, are summarized. To verify whether the Fröhlich theory of long-range coherence in biological systems is applicable to the phenomenon of rouleau formation in human erythrocytes, the interactions between erythrocytes are modelled as those between two large, coupled oscillating dipoles. Relevant expressions for the resonant long-range and the van der Waals interaction are then derived. Using the available numerical data, the eigenfrequencies and the interaction energies corresponding to the experimental conditions are then derived. In the range of postulated frequencies (1011–1012 Hz) the effective interaction coefficient Ξ due to the resonant long-range forces is, indeed, found to agree with its experimental value of 3.0. However, the same value of Ξ can also be achieved through the ordinary van der Waals interactions between dipoles oscillating at lower frequencies. It is concluded that the resonant long-range interaction between erythrocytes may be responsible for the onset of rouleau formation. However, other mechanisms cannot be ruled out at this stage, especially since the Fröhlich mechanism requires a number of unconfirmed preconditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00393324
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