Stationary State Entanglement of Two Atoms Inside an Optical Cavity under Noise

In this paper, the entanglement properties of a system of two atoms inside an optical cavity in a stochastic interaction with field are studied by the Jaynes-Cummings Model. The phase telegraph noise is considered as a noise term and an exact solution to the model is obtained. The solution reveals the resulting decoherence effects of the noise on the entanglement properties of the system. It shows that under the noise the individual atoms do not entangle with the cavity field. However, a strong atom-atom entanglement is observed in a stationary state. It is seen that a relatively strong noise is cooperative in the construction of the steady state atom-atom entanglement.     

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model

In this study we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological model by considering variable cosmological constant term Λ of the form: , and Λ∼ρ in the presence of strange quark matter with domain wall. The various physical aspects of the model are also discussed.     

On Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups

In [Contemp. Math. 258 (2000) 1-19], by using Fredholm index we developed a version of Quillen's geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In this work, by using Quinn's Transversality Theorem [Proc. Sympos. Pure. Math. 15 (1970) 213-222], it will be shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It will be shown that the Thom isomorphism in this theory will be satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps will be proved. After we discuss the relation between this theory and classical cobordism, we describe some applications to the complex cobordism of flag varieties of loop groups and we do some calculations.     

Some Aspects of LrW1 (G) n L(p, q, W2dμ)(G)

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of LrW1 (G) n L(p, q, W2dμ)(G) spaces. Then the necessary conditions for compact embeddings of the spaces LrW1 ( Rd) N L(p, q, W2dμ)( Rd) are showed.     

Some Aspects of Lw1^r （G）∩ L（p,q, w2dμ）（G）

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of Lw1^r （G）∩ L（p, q, w2dμ）（G） spaces. Then the necessary conditions for compact embeddings of the spaces Lw1^r （R^d）∩ L（p, q, w2dμ）（R^d） are showed.     

MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES

Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1(G) to A is algebrically isomorphic and homeomorphic to A.