Minimal Uncertainty in Momentum: The Effects of IR Gravity on Quantum Mechanics

The effects of the IR aspects of gravity on quantum mechanics is investigated. At large distances where due to gravity the space-time is curved, there appears nonzero minimal uncertainty $\Delta p_{0}$ in the momentum of a quantum mechanical particle. We apply the minimal uncertainty momentum to some quantum mechanical interferometry examples and show that the phase shift depends on the area surrounded by the path of the test particle . We also put some limits on the related parameters. This prediction may be tested through future experiments. The assumption of minimal uncertainty in momentum can also explain the anomalous excess of the mass of the Cooper pair in a rotating thin superconductor ring.Comment: 8 pages, revised version accepted by PR

Quantal interferometry with dissipative internal motion

In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds of external influences on quantal interference. The concept of mixed-state phase and concomitant gauge invariance is extended to dissipative internal motion. The resulting complex-valued mixed-state interference effects lead to well-known results in the unitary limit and in the case of dissipative motion of pure quantal states. Dissipative interferometry is applied to fault-tolerant geometric quantum computation.Comment: Slight revision, journal reference adde

Comment on "Neutron Interferometric Observation of Noncyclic Phase"

A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].Comment: 5 pages, 0 figures, submitted to Phys.Rev.Let

Geometric Phase in Entangled Systems: A Single-Neutron Interferometer Experiment

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase.Comment: 10 pages 9 figure

The Quartic Higgs Coupling at Hadron Colliders

The quartic Higgs self-coupling is the final measurement in the Higgs potential needed to fully understand electroweak symmetry breaking. None of the present or future colliders are known to be able to determine this parameter. We study the chances of measuring the quartic self-coupling at hadron colliders in general and at the VLHC in particular. We find the prospects challenging.Comment: 5 pages, 4 figure

The Lax pairs for the Holt system

By using non-canonical transformation between the Holt system and the Henon-Heiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the known Lax representations for the Henon-Heiles system.Comment: 7 pages, LaTeX2e, a4.st

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

New Aspects of Geometric Phases in Experiments with polarized Neutrons

Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.Comment: 17 pages, 9 figure

On the influence of resonance photon scattering on atom interference

Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d_p/\lambda_i = y'_{12} (2\pi/kd\lambda_i), where y'_{12} is distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic center-of-mass motion, $d$ is the grating constant and \lambda_i is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of "which-way" information for the interference visibility.Comment: 9 pages, 1 figur