A quantum walk with a delocalized initial state: contribution from a coin-flip operator

A unit evolution step of discrete-time quantum walks is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps delicately depends on the coin-flip operator and an initial condition of the walk. To get the behavior, a lot of long-time limit distributions for the quantum walks starting with a localized initial state have been derived. In the present paper, we compute limit distributions of a 2-state quantum walk with a delocalized initial state, not a localized initial state, and discuss how the walker depends on the coin-flip operator. The initial state induced from the Fourier series expansion, which is called the $(\alpha,\beta)$ delocalized initial state in this paper, provides different limit density functions from the ones of the quantum walk with a localized initial state.Comment: International Journal of Quantum Information, Vol.11, No.5, 1350053 (2013

Relativistic models of magnetars: Nonperturbative analytical approach

In the present paper we focus on building simple nonperturbative analytical relativistic models of magnetars. With this purpose in mind we first develop a method for generating exact interior solutions to the static and axisymmetric Einstein-Maxwell-hydrodynamic equations with anisotropic perfect fluid and with pure poloidal magnetic field. Then using an explicit exact solution we present a simple magnetar model and calculate some physically interesting quantities as the surface elipticity and the total energy of the magnetized star.Comment: 10 pages, LaTe

Quantum Fluctuations of Black Hole Geometry

By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the expansions of null rays as quantum operators. Then, the exact wave function is found as a mass eigenstate, and the radius of the apparent horizon is quantum-mechanically defined. In the evolution of the metric variables, the wave function changes from a WKB solution giving the classical trajectories to a tunneling solution. By virtue of the quantum fluctuations of the metric evolution beyond the WKB approximation, we can observe a static black hole state with the apparent horizon separating from the event horizon.Comment: 18 pages, DPNU-93-3

Moments of inertia of relativistic magnetized stars

We consider principal moments of inertia of axisymmetric, magnetically deformed stars in the context of general relativity. The general expression for the moment of inertia with respect to the symmetric axis is obtained. The numerical estimates are derived for several polytropic stellar models. We find that the values of the principal moments of inertia are modified by a factor of 2 at most from Newtonian estimates.Comment: 7 pages, 3 figures, accepted for publication in Astronomy and Astrophysic

Localization of the Grover walks on spidernets and free Meixner laws

A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.Comment: 32 page

Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein-Maxwell's equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass M = 1.4 Msun and surface magnetic fields of the order of 10^15 G, a quadrupole ellipticity of the order of 10^(-6) - 10^(-5) should be expected. Low mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10^(-3) in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.Comment: 25 pages, 9 figures, submitted to MNRA

Collapse/Flattening of Nucleonic Bags in Ultra-Strong Magnetic Field

It is shown explicitly using MIT bag model that in presence of ultra-strong magnetic fields, a nucleon either flattens or collapses in the direction transverse to the external magnetic field in the classical or quantum mechanical picture respectively. Which gives rise to some kind of mechanical instability. Alternatively, it is argued that the bag model of confinement may not be applicable in this strange situation.Comment: 8 pages, REVTEX, 3 figures .eps files (included

Absorption problems for quantum walks in one dimension

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P, Q, R and S of the vector space of complex 2 times 2 matrices. Our method studied here is a natural extension of the approach in the classical random walk.Comment: 15 pages, small corrections, journal reference adde