• Volume 42, Issue 6

      June 1994,   pages  447-494

    • Universality in the length spectrum of integrable systems

      Debabrata Biswas

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      The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M1,…,Mf} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(TTM), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.

    • On phases and length of curves in a cyclic quantum evolution

      Arun Kumar Pati

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      The concept of a curve traced by a state vector in the Hilbert space is introduced into the general context of quantum evolutions and its length defined. Three important curves are identified and their relation to the dynamical phase, the geometric phase and the total phase are studied. These phases are reformulated in terms of the dynamical curve, the geometric curve and the natural curve. For any arbitrary cyclic evolution of a quantum system, it is shown that the dynamical phase, the geometric phase and their sums and/or differences can be expressed as the integral of the contracted length of some suitably-defined curves. With this, the phases of the quantum mechanical wave function attain new meaning. Also, new inequalities concerning the phases are presented.

    • On a time-dependent system of noncentral anharmonic oscillators in two dimensions

      R S Kaushal

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      A new system of time-dependent anharmonic and anisotropic oscillators in two space-dimensions which corresponds to unequal but related spring constants, having Hamiltonian structure, admitting quadratic invariants and accounting also for the fractional powers in the coupling terms, is found.

    • Cosmological models with constant deceleration parameter in Nordtvedt’s theory

      V B Johri Kalyani Desikan

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      Exact solutions of the field equations of Nordtvedt’s theory for spatially flat FRW models with constant deceleration parameter have been obtained. Singular solutions with (i) power-law (ii) exponential expansion have been studied in Nordtvedt’s theory where the coupling parameterω is a function of the scalar fieldφ.

    • Some exact solutions in Bianchi VI0 string cosmology

      Ramesh Tikekar L K Patel

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      Following the techniques used by Letelier and Stachel some new physically relevant explicit Bianchi VI0 solutions of string cosmology with magnetic field are reported. They include two models describing distributions of Takabayashi strings and geometric strings respectively.

    • Quark distribution in light nuclei

      Nazakat Ullah

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      The distribution of quarks in light nuclei is given using the quark cluster wave function. An analytic expression for the nucleus4He is obtained. The distribution so obtained is compared with the one obtained using a different theoretical formulation called mapping.

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