Topological phase in two flavor neutrino oscillations

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between non-orthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.Comment: 11 pages, 3 figures, accepted in Phys. Rev.

The geometric phase and the dynamics of quantum phase transition induced by a linear quench

We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time $\tau_q$ across the critical point from a paramagnetic to ferromagnetic phase. Our argument is based on the fact that the spin fluctuation occurring during the critical slowing down causes random fluctuation in the ground state geometric phase at the critical regime. The correlation function of the random geometric phase determines the excitation probability of the quasiparticles, which are excited during the transition from the inital paramagnetic to the ferromagnetic phase. This helps us to evaluate the number density of the kinks formed during the transition, which is found to scale as $\tau_q^{-\frac{1}{2}}$. In addition, we have also estimated the spin-spin correlation at criticality.Comment: 10 pages, accepted in J. Phys. A: Math and Theor. (Special issue on Quantum Phases

Cross-National Logo Evaluation Analysis: An Individual Level Approach

The universality of design perception and response is tested using data collected from ten countries: Argentina, Australia, China, Germany, Great Britain, India, the Netherlands, Russia, Singapore, and the United States. A Bayesian, finite-mixture, structural-equation model is developed that identifies latent logo clusters while accounting for heterogeneity in evaluations. The concomitant variable approach allows cluster probabilities to be country specific. Rather than a priori defined clusters, our procedure provides a posteriori cross-national logo clusters based on consumer response similarity. To compare the a posteriori cross-national logo clusters, our approach is integrated with Steenkamp and Baumgartner’s (1998) measurement invariance methodology. Our model reduces the ten countries to three cross-national clusters that respond differently to logo design dimensions: the West, Asia, and Russia. The dimensions underlying design are found to be similar across countries, suggesting that elaborateness, naturalness, and harmony are universal design dimensions. Responses (affect, shared meaning, subjective familiarity, and true and false recognition) to logo design dimensions (elaborateness, naturalness, and harmony) and elements (repetition, proportion, and parallelism) are also relatively consistent, although we find minor differences across clusters. Our results suggest that managers can implement a global logo strategy, but they also can optimize logos for specific countries if desired.adaptation;standardization;Bayesian;international marketing;design;Gibbs sampling;concomitant variable;logos;mixture models;structural equation models

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach

We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and ${1/2}(n-1)(n-2)$ algebraically independent 4-vertex Bargmann invariants. In the process of establishing this result we develop a canonical form for U(n) matrices which is useful in its own right. We show that the recently discovered `off-diagonal' geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.Comment: 13 pages, latex, no figure

Quantum anomaly and geometric phase; their basic differences

It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two notions are more profound and fundamental. As an explicit example, we analyze in detail a quantum mechanical model proposed by M. Stone, which is supposed to show the above connection. We show that the geometric term in the model, which is topologically trivial for any finite time interval $T$, corresponds to the so-called ``normal naive term'' in field theory and has nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental level, the difference between the two notions is stated as follows: The topology of gauge fields leads to level crossing in the fermionic sector in the case of chiral anomaly and the {\em failure} of the adiabatic approximation is essential in the analysis, whereas the (potential) level crossing in the matter sector leads to the topology of the Berry phase only when the precise adiabatic approximation holds.Comment: 28 pages. The last sentence in Abstract has been changed, the last paragraph in Section 1 has been re-written, and the latter half of Discussion has been replaced by new materials. New Conclusion to summarize the analysis has been added. This new version is to be published in Phys. Rev.

Cross-National Logo Evaluation Analysis: An Individual Level Approach

The universality of design perception and response is tested using data collected from ten countries: Argentina, Australia, China, Germany, Great Britain, India, the Netherlands, Russia, Singapore, and the United States. A Bayesian, finite-mixture, structural-equation model is developed that identifies latent logo clusters while accounting for heterogeneity in evaluations. The concomitant v

Positioning in cyberspace: evaluating telecom web sites using correspondence analysis

The growth of presence in the marketspace of the Web has been exponential, both in general and within specific industries. While the academic literature on the phenomena is still in its infancy, there exists a pressing need to establish methodologies to evaluate and map Web sites within and between industries. With the exception of a few notable papers little or no theoretical, descriptive, or normative research has been conducted into Web site positioning and evaluation. This article goes a little towards addressing this lacuna. Specifically, Web sites from the Telecom Industry are evaluated and mapped using correspondence analysis. The technique of correspondence analysis and the interpretation of the maps produced are described in detail. The implications for management are also discussed.</p

A retail category management model integrating shelf space and inventory levels

A retail category management model that considers the interplay of optimal product assortment decisions, space allocation and inventory quantities is presented in this paper. Specifically, the proposed model maximizes the total net profit in terms of decision variables expressing product assortment, shelf space allocation and common review period. The model takes into consideration several constraints such as the available shelf space, backroom inventory space, retailer's financial resources, and estimates of rate of demand for products based on shelf space allocation and competing products. The review period can take any values greater than zero. Results of the proposed model were compared withthe results of the current industry practice for randomly generated product assortments of size six, ten and fourteen. The model also outperformed the literature benchmark. The paper demonstrates that the optimal common review period is flexible enough to accommodate the administrative restrictions of delivery schedules for products, without significantly deviating from the optimal solution

The impact of power and relationship commitment on the integration between manufacturers and customers in a supply chain

Supply chain integration (SCI) has received increasing attention from scholars and practitioners in recent years. However, our knowledge of what influences SCI is still very limited. Although marketing and management researchers have investigated power and relationship commitment issues between organizations, few have examined their impact on SCI. This paper extends the power–relationship commitment theory established in Western marketing literature and links it with SCI in China, through examining the relationship between power, relationship commitment and the integration between manufacturers and their customers. We propose and empirically test a model using data collected from 617 manufacturing companies in China. The results show that different types of customer power impact manufacturers’ relationship commitment in different ways. Expert power, referent power and reward power are important in improving manufacturers’ normative relationship commitment, while reward power and coercive power enhance instrumental relationship commitment. We also found that normative relationship commitment had a greater impact on customer integration than instrumental relationship commitment. These findings are interpreted in light of national culture differences between China and the U.S. in terms of power distance and collectivism, which provide a new perspective on SCI