On the Relation Between Quantum Mechanical and Classical Parallel Transport

We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators whose commutators yield diagonal operators; or in Lie algebras those operators whose commutators are in the (diagonal) Cartan subalgebra.Comment: 3 pages, no figure

Investigation of electrochemical behavior of plasma nitrided Ti-6Al-7Nb alloy in Hanks’ Solution

Titanium alloy Ti-6Al-7Nb was plasma nitrided using inductively coupled RF Plasma with 100% Nitrogen at 750, 800 and 850°C for 4 h. Micro Raman studies show the formation of titanium nitrides. Potentiodynamic polarization studies in Hanks’ solution show the corrosion resistance of the untreated samples to be better than the treated samples. Electrochemical Impedance Spectroscopy (EIS) studies show higher charge transfer resistance and lower double layer capacitance for the substrate compared to the nitrided samples. FESEM images of samples immersed in SBF show that growth of apatite is more and the size of deposits are larger on nitrided samples as compared to that on the untreated substrate. Nitrided samples immersed in Hanks’ solution for 7 days show higher amount of calcium, phosphorous and oxygen than the substrate

Geometric phases for mixed states in interferometry

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection-form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.Comment: Two column, 4 pages, Latex file, No figures, Few change

Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $\rho(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\rho(0) E = \rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ from $t = 0$ to $T$ is unity. Generically $E(T) \neq E$ and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.Comment: 16 pages, latex; new material and references adde

Reply to `Singularities of the mixed state phase'

The only difference between Bhandari's viewpoint [quant-ph/0108058] and ours [Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo $2\pi$, whereas Bhandari argues that two phases that differ by $2\pi n$, $n$ integer, may be distinguished experimentally in a history-dependent manner.Comment: 2 page

Model for Entangled States with Spin-Spin Interaction

A system consisting of two neutral spin 1/2 particles is analyzed for two magnetic field perturbations: 1) an inhomogeneous magnetic field over all space, and 2) external fields over a half space containing only one of the particles. The field is chosen to point from one particle to the other, which results in essentially a one-dimensional problem. A number of interesting features are revealed for the first case: the singlet, which has zero potential energy in the unperturbed case, remains unstable in the perturbing field. The spin zero component of the triplet evolves into a bound state with a double well potential, with the possibility of tunneling. Superposition states can be constructed which oscillate between entangled and unentangled states. For the second case, we show that changes in the magnetic field around one particle affect measurements of the spin of the entangled particle not in the magnetic field nonlocally. By using protective measurements, we show it is possible in principle to establish a nonlocal interaction using the two particles, provided the dipole-dipole potential energy does not vanish and is comparable to the potential energy of the particle in the external field

The non-Abelian state-dependent gauge field in optics

The covariant formulation of the quantum dynamics in CP(1) should lead to the observable geometrodynamical effects for the local dynamical variable of the light polarization states.Comment: 8 pages, 3 figures, LaTe

On the spin of gravitational bosons

We unearth spacetime structure of massive vector bosons, gravitinos, and gravitons. While the curvatures associated with these particles carry a definite spin, the underlying potentials cannot be, and should not be, interpreted as single spin objects. For instance, we predict that a spin measurement in the rest frame of a massive gravitino will yield the result 3/2 with probability one half, and 1/2 with probability one half. The simplest scenario leaves the Riemannian curvature unaltered; thus avoiding conflicts with classical tests of the theory of general relativity. However, the quantum structure acquires additional contributions to the propagators, and it gives rise to additional phases.Comment: Honorable mention, 2002 Gravity Research Foundation Essay

Comments on Proposed Gravitational Modifications of Schrodinger Dynamics and their Experimental Implications

We discuss aspects of gravitational modifications of Schrodinger dynamics proposed by Diosi and Penrose. We consider first the Diosi-Penrose criterion for gravitationally induced state vector reduction, and compute the reduction time expected for a superposition of a uniform density cubical solid in two positions displaced by a small fraction of the cube side. We show that the predicted effect is much smaller than would be observable in the proposed Marshall et al. mirror experiment. We then consider the ``Schrodinger -Newton'' equation for an N-particle system. We show that in the independent particle approximation, it differs from the usual Hartree approximation applied to the Newtonian potential by self-interaction terms, which do not have a consistent Born rule interpretation. This raises doubts about the use of the Schrodinger-Newton equation to calculate gravitational effects on molecular interference experiments. When the effects of Newtonian gravitation on molecular diffraction are calculated using the standard many-body Schrodinger equation, no washing out of the interference pattern is predicted.Comment: Tex, 17