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

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.

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

Case report: Cytokine therapy and an intracoronary autologous bone marrow-derived cell infusion with Impella support in a patient with dilated cardiomyopathy and a severely reduced ejection fraction

INTRODUCTION: This is the first reported case of a patient with dilated cardiomyopathy (DCM) and severely impaired left ventricular function to receive a combined treatment of granulocyte colony-stimulating factor therapy and an intracoronary delivery of autologous bone marrow-derived mononuclear cells with percutaneous circulatory assistance (the Impella CP device; Abiomed, Danvers, MA). MAIN SYMPTOMS AND OUTCOME: Three months post-treatment, the gentleman in his early 70s demonstrated an improvement in left ventricular ejection fraction (13–17%) and a reduction in New York Heart Association class from III to class I. There was also an improvement in his 6-minute walk test (147–357 meters), N-terminal pro-brain natriuretic peptide level (14,099–7,129 ng/l) and quality of life scores. There were no safety concerns during the treatment or follow-up. CONCLUSION: This case report suggests combined cell and cytokine therapy with adjunctive circulatory support could be a safe and promising treatment for patients with DCM and severely reduced ejection fraction

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