Manifestations of quantum holonomy in interferometry

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.Comment: Some changes, journal reference adde

Correlation induced non-Abelian quantum holonomies

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the L\'{e}vay geometric phase [2004 {\it J. Phys. A: Math. Gen.} {\bf 37} 1821] in the case of two-qubit systems undergoing local SU(2) evolutions.Comment: Minor corrections; journal reference adde

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

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. 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 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 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

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

A generalized Pancharatnam geometric phase formula for three level systems

We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed generalisation of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3)\/ and its generators in the defining representation, and uses geometrical objects and operations in an eight dimensional real Euclidean space. Implications for an n-level system are also discussed.Comment: 12 pages, Revtex, one figure, epsf used for figure insertio