3,344 research outputs found
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
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
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 -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
Innermost stable circular orbits around magnetized rotating massive stars
In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an
approximate analytical formula for the radius of the innermost stable circular
orbit (ISCO) of a neutral test particle around a massive, rotating and deformed
source. In the present paper, we generalize their expression by including the
magnetic dipole moment. We show that our approximate analytical formulas are
accurate enough by comparing them with the six-parametric exact solution
calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the
numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for
realistic neutron stars. As a main result, we find that in general, the radius
at ISCO exhibits a decreasing behavior with increasing magnetic field. However,
for magnetic fields below 100GT the variation of the radius at ISCO is
negligible and hence the non-magnetized approximate expression can be used. In
addition, we derive approximate analytical formulas for angular velocity,
energy and angular momentum of the test particle at ISCO.Comment: 8 pages, 3 figure
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