776 research outputs found
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
Phase ordering in chaotic map lattices with conserved dynamics
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in
contact with a thermal bath, is numerically studied. The model here proposed is
equivalent to a conserved Ising model with coupligs which fluctuate over the
same time scale as spin moves. When couplings fluctuations and thermal
fluctuations are both important, this model does not belong to the class of
universality of a Langevin equation known as model B; the scaling exponents are
continuously varying with the temperature and depend on the map used. The
universal behavior of model B is recovered when thermal fluctuations are
dominant.Comment: 6 pages, 4 figures. Revised version accepted for publication on
Physical Review E as a Rapid Communicatio
NĂveis de fĂłsforo disponĂvel e tamanho de partĂcula do fosfato bicĂĄlcico na dieta de poedeiras comerciais de 24 a 58 semanas de idade
Sistemas de alimentação e suplementação de farinha de casca de ostras sobre o desempenho e a qualidade da casca dos ovos de poedeiras comerciais
Nearest Neighbor Distances on a Circle: Multidimensional Case
We study the distances, called spacings, between pairs of neighboring energy
levels for the quantum harmonic oscillator. Specifically, we consider all
energy levels falling between E and E+1, and study how the spacings between
these levels change for various choices of E, particularly when E goes to
infinity. Primarily, we study the case in which the spring constant is a badly
approximable vector. We first give the proof by Boshernitzan-Dyson that the
number of distinct spacings has a uniform bound independent of E. Then, if the
spring constant has components forming a basis of an algebraic number field, we
show that, when normalized up to a unit, the spacings are from a finite set.
Moreover, in the specific case that the field has one fundamental unit, the
probability distribution of these spacings behaves quasiperiodically in log E.
We conclude by studying the spacings in the case that the spring constant is
not badly approximable, providing examples for which the number of distinct
spacings is unbounded.Comment: Version 2 is updated to include more discussion of previous works. 17
pages with five figures. To appear in the Journal of Statistical Physic
Experimental Study of the Shortest Reset Word of Random Automata
In this paper we describe an approach to finding the shortest reset word of a
finite synchronizing automaton by using a SAT solver. We use this approach to
perform an experimental study of the length of the shortest reset word of a
finite synchronizing automaton. The largest automata we considered had 100
states. The results of the experiments allow us to formulate a hypothesis that
the length of the shortest reset word of a random finite automaton with
states and 2 input letters with high probability is sublinear with respect to
and can be estimated as $1.95 n^{0.55}.
Very-high energy gamma-ray astronomy: A 23-year success story in high-energy astroparticle physics
Very-high energy (VHE) gamma quanta contribute only a minuscule fraction -
below one per million - to the flux of cosmic rays. Nevertheless, being neutral
particles they are currently the best "messengers" of processes from the
relativistic/ultra-relativistic Universe because they can be extrapolated back
to their origin. The window of VHE gamma rays was opened only in 1989 by the
Whipple collaboration, reporting the observation of TeV gamma rays from the
Crab nebula. After a slow start, this new field of research is now rapidly
expanding with the discovery of more than 150 VHE gamma-ray emitting sources.
Progress is intimately related with the steady improvement of detectors and
rapidly increasing computing power. We give an overview of the early attempts
before and around 1989 and the progress after the pioneering work of the
Whipple collaboration. The main focus of this article is on the development of
experimental techniques for Earth-bound gamma-ray detectors; consequently, more
emphasis is given to those experiments that made an initial breakthrough rather
than to the successors which often had and have a similar (sometimes even
higher) scientific output as the pioneering experiments. The considered energy
threshold is about 30 GeV. At lower energies, observations can presently only
be performed with balloon or satellite-borne detectors. Irrespective of the
stormy experimental progress, the success story could not have been called a
success story without a broad scientific output. Therefore we conclude this
article with a summary of the scientific rationales and main results achieved
over the last two decades.Comment: 45 pages, 38 figures, review prepared for EPJ-H special issue "Cosmic
rays, gamma rays and neutrinos: A survey of 100 years of research
Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV
Results are presented from a search for a W' boson using a dataset
corresponding to 5.0 inverse femtobarns of integrated luminosity collected
during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV.
The W' boson is modeled as a heavy W boson, but different scenarios for the
couplings to fermions are considered, involving both left-handed and
right-handed chiral projections of the fermions, as well as an arbitrary
mixture of the two. The search is performed in the decay channel W' to t b,
leading to a final state signature with a single lepton (e, mu), missing
transverse energy, and jets, at least one of which is tagged as a b-jet. A W'
boson that couples to fermions with the same coupling constant as the W, but to
the right-handed rather than left-handed chiral projections, is excluded for
masses below 1.85 TeV at the 95% confidence level. For the first time using LHC
data, constraints on the W' gauge coupling for a set of left- and right-handed
coupling combinations have been placed. These results represent a significant
improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe
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