3,094 research outputs found
Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
Quantum transport properties of electron systems driven by strong electric
fields are studied by mapping the Landau-Zener transition dynamics to a quantum
walk on a semi-infinite one-dimensional lattice with a reflecting boundary,
where the sites correspond to energy levels and the boundary the ground state.
Quantum interference induces a distribution localized around the ground state,
and when the electric field is strengthened, a delocalization transition occurs
describing breakdown of the original electron system.Comment: 4 pages, 3 figures, Journal-ref adde
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
Localization of Two-Dimensional Quantum Walks
The Grover walk, which is related to the Grover's search algorithm on a
quantum computer, is one of the typical discrete time quantum walks. However, a
localization of the two-dimensional Grover walk starting from a fixed point is
striking different from other types of quantum walks. The present paper
explains the reason why the walker who moves according to the degree-four
Grover's operator can remain at the starting point with a high probability. It
is shown that the key factor for the localization is due to the degeneration of
eigenvalues of the time evolution operator. In fact, the global time evolution
of the quantum walk on a large lattice is mainly determined by the degree of
degeneration. The dependence of the localization on the initial state is also
considered by calculating the wave function analytically.Comment: 21 pages RevTeX, 4 figures ep
Continuous-time quantum walk on integer lattices and homogeneous trees
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and
infinite homogeneous trees. By using the generating function method, we compute
the limit of the average probability distribution for the general isotropic
walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous
trees. In addition, we compute the asymptotic approximation for the probability
of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page
Wigner formula of rotation matrices and quantum walks
Quantization of a random-walk model is performed by giving a qudit (a
multi-component wave function) to a walker at site and by introducing a quantum
coin, which is a matrix representation of a unitary transformation. In quantum
walks, the qudit of walker is mixed according to the quantum coin at each time
step, when the walker hops to other sites. As special cases of the quantum
walks driven by high-dimensional quantum coins generally studied by Brun,
Carteret, and Ambainis, we study the models obtained by choosing rotation as
the unitary transformation, whose matrix representations determine quantum
coins. We show that Wigner's -dimensional unitary representations of
rotations with half-integers 's are useful to analyze the probability laws
of quantum walks. For any value of half-integer , convergence of all moments
of walker's pseudovelocity in the long-time limit is proved. It is generally
shown for the present models that, if is even, the probability measure
of limit distribution is given by a superposition of terms of scaled
Konno's density functions, and if is odd, it is a superposition of
terms of scaled Konno's density functions and a Dirac's delta function at the
origin. For the two-, three-, and four-component models, the probability
densities of limit distributions are explicitly calculated and their dependence
on the parameters of quantum coins and on the initial qudit of walker is
completely determined. Comparison with computer simulation results is also
shown.Comment: v2: REVTeX4, 15 pages, 4 figure
Entanglement measurement with discrete multiple coin quantum walks
Within a special multi-coin quantum walk scheme we analyze the effect of the
entanglement of the initial coin state. For states with a special entanglement
structure it is shown that this entanglement can be meausured with the mean
value of the walk, which depends on the i-concurrence of the initial coin
state. Further on the entanglement evolution is investigated and it is shown
that the symmetry of the probability distribution is reflected by the symmetry
of the entanglement distribution.Comment: 9 pages, IOP styl
Modeling the coma of 2060 Chiron
Observations of comet-like activity and a resolved coma have established that 2060 Chiron is a comet. Determinations of its radius range from 65 to 200 km. This unusually large size for a comet suggests that the atmosphere of Chiron is intermediate to the tightly bound, thin atmospheres typical of planets and satellite and the greatly extended atmospheres in free expansion typical of cometary comae. Under certain conditions it may gravitationally bind an atmosphere that is thick compared to its size, while a significant amount of gas escapes to an extensive exosphere. These attributes coupled with reports of sporadic outbursts at large heliocentric distances and the identification of CN in the coma make Chiron a challenging object to model. Simple models of gas production and the dusty coma were recently presented but a general concensus on many basic features has not emerged. Development was begun on a more complete coma model of Chiron. The objectives are to report progress on this model and give the preliminary results for understanding Chiron
Quantum walks and orbital states of a Weyl particle
The time-evolution equation of a one-dimensional quantum walker is exactly
mapped to the three-dimensional Weyl equation for a zero-mass particle with
spin 1/2, in which each wave number k of walker's wave function is mapped to a
point \vec{q}(k) in the three-dimensional momentum space and \vec{q}(k) makes a
planar orbit as k changes its value in [-\pi, \pi). The integration over k
providing the real-space wave function for a quantum walker corresponds to
considering an orbital state of a Weyl particle, which is defined as a
superposition (curvilinear integration) of the energy-momentum eigenstates of a
free Weyl equation along the orbit. Konno's novel distribution function of
quantum-walker's pseudo-velocities in the long-time limit is fully controlled
by the shape of the orbit and how the orbit is embedded in the
three-dimensional momentum space. The family of orbital states can be regarded
as a geometrical representation of the unitary group U(2) and the present study
will propose a new group-theoretical point of view for quantum-walk problems.Comment: REVTeX4, 9 pages, 1 figure, v2: Minor corrections made for
publication in Phys.Rev.
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