119106818
STUDY ON THE NONCOMMUTATIVE REPRESENTATIONS OF GALILEAN GENERATORS
The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed. The Dirac brackets of this model reproduce the original noncommutative algebra. Also, the generators in terms of noncommutative phase-space variables are abstracted from this model in a consistent manner. Finally, the role of Jacobi identities is emphasized to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.
119399108
LAGRANGIAN AND HAMILTONIAN FORMULATIONS OF HIGHER ORDER CHERN–SIMONS THEORIES
We consider models involving the higher (third) derivative extension of the Abelian Chern–Simons (CS) topological term in D = 2 + 1 dimensions. The polarization vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner's little group acts as a gauge generator.
15230645
Critical generation of soliton mode in a gauged O(3) sigma model with interpolating potential
We show that a new soliton mode is generated in a gauged sigma model with interpolating potential when the interpolation parameter decreases below a critical value. pradip@boson.bose.res.in kumar@boson.bose.res.in Recently a class of gauged O(3) sigma models in three dimensions have been studied [1, 2, 3, 4, 5] where a U(1) subgroup of the O(3) symmetry of the model was gauged by coupling the sigma model fields with a gauge field through the corresponding U(1) current. This is different from the minimal coupling via the topological current discussed previously [6]. The motivation behind the new gauged O(3) sigma models was to break the scale invariance of the self dual solutions of the usual O(3) sigma model [7]. Initially the gauge field dynamics was assumed to be dictated by the Maxwell term [1]. Later the extension of the model with the Chern Simons coupling was investigated [2]. A particular form of self interaction was required to be included in these models in order to saturate the Bogomol’nyi bounds [8]. The form of the assumed self interaction potential is of crucial importance. The minima of the potential determine the vaccum structure of the theory. The solutions change remarkably when the vaccum structure exhibits spontaneous breaking of the symmetry of the gauge group. Thus it was demonstrated that the observed degeneracy of the solutions of [1, 2] is lifted when potentials with symmetry breaking minima were incorporated [4, 5]. A generalisation of the models [1, 2] was proposed in [3]where an adjustable real parameter v was introduced in the expression of the self interaction potential. Detailed solutions of the model with the C S coupling were provided. The parameter v interpolates between the symmetric and symmetry breaking phases. The inclusion of such adjustable potential in the corresponding Maxwell coupled model was conjectured, but not fully explored. In this letter we show that this generalisation indeed leads to certain important consequences. The most interesting outcome is a kind of ’critical phenomenon’ where a new self dual soliton mode emerges when the parameter v decreases below v = 1. It will be useful to start with a brief review of the nonlinear O(3) sigma model [7]. The lagrangian of the model is given by, L = 1 2 ∂μφ · ∂ φ (1) Here φ is a triplet of scalar fields constituting a vector in the internal space with unit norm φa = na · φ, (a = 1, 2, 3) (2) φ · φ = φaφa = 1 (3) The vectors na constitute a basis of unit orthogonal vectors in the internal space. We work in the Minkowskian space time with the metric tensor diagonal, gμν = (1,−1,−1). The finite energy solutions of the model (1) satisfies the boundary condition limφ = φa(0) (4) at physiacal infinity. The condition (4) corresponds to one point compactification of the physical infinity. The physical space R2 becomes topologically equivalent to S2 due to this compactification. The static finite energy solutions of the model are then maps from this sphere to the internal sphere. Such solutions are classified by the homotopy [9]
120764089
Bianchi Type-I Space-Time with Variable Cosmological Constant
A spatially homogeneous and anisotropic Bianchi type-I perfect fluid model is considered with variable cosmological constant. Einstein’s field equations are solved by using a law of variation for mean Hubble’s parameter, which is related to average scale factor and that yields a constant value of deceleration parameter. An exact and singular Bianchi-I model is presented, where the cosmological constant remains positive and decreases with the cosmic time. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the model is carried out.
119277312
Mass dependence of various fragments in multi-fragmentation
Based on the isospin-dependent quantum molecular dynamics (IQMD) model, we aim to understand the effect of target fragmentation on various quantities i.e. collision rate, fragments multiplicity etc by simulating the collision between $Au^{197}$ projectile and $C^{12}$, $Al^{26}$, $Cu^{63}$, and $Pb^{208}$ as targets at incident energy 600 MeV/nucleon. The collision geometry is varied from central to peripheral. Our results indicate the rise and fall in the production of intermediate mass fragments with ${Z_{bound}}$ which is in agreement with the experimental data of Aladin collaboration at lower impact parameters, while, some deviation is seen at higher impact parameters.
120654378
Bianchi-I Space-time with Variable Gravitational and Cosmological “Constants”
We consider Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi-I space-time. A law of variation for the Hubble parameter, which is related to the average scale factor and yields a constant value of the deceleration parameter, is assumed to solve the field equations. The gravitational constant is allowed to follow a power-law form. We find that a time-increasing gravitational constant is suitable for describing the present evolution of universe. The solutions reveal the dynamics of a universe, which expands forever. The physical interpretation of the solutions is discussed in detail.
122883207
AN EXACT BIANCHI TYPE-I COSMOLOGICAL MODEL IN LYRA'S MANIFOLD
A spatially homogeneous and anisotropic Bianchi type-I space–time has been studied within the framework of Lyra's geometry. Exact solutions of the Einstein's field equations have been obtained with a time dependent gauge function by using a special law of variation for Hubble's parameter that yields a constant value of deceleration parameter. It has been found that the solutions generalize the solutions obtained by Rahaman et al. [Astrophys. Space Sci.299, 211 (2005)] and are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the model has been carried out.
120879756
Neck formation and deformation effects in a preformed cluster model of exotic cluster decays
Using the nuclear proximity approach and the two center nuclear shape parametrization, the interaction potential between two deformed and pole-to-pole oriented nuclei forming a necked configuration in the overlap region is calculated and its role is studied for the cluster decay half-lives. The barrier is found to move to a larger relative separation, with its proximity minimum lying in the neighborhood of the Q value of decay and its height and width reduced considerably. For cluster decay calculations in the preformed cluster model of Malik and Gupta, due to deformations and orientations of nuclei, the (empirical) preformation factor is found to get reduced considerably and agrees nicely with other model calculations known to be successful for their predictions of cluster decay half-lives. Comparison with the earlier case of nuclei treated as spheres suggests that the effects of both deformations and neck formation get compensated by choosing the position of cluster preformation and the inner classical turning point for penetrability calculations at the touching configuration of spherical nuclei. {copyright} {ital 1997} {ital The American Physical Society}