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

Does a black hole rotate in Chern-Simons modified gravity?

Rotating black hole solutions in the (3+1)-dimensional Chern-Simons modified gravity theory are discussed by taking account of perturbation around the Schwarzschild solution. The zenith-angle dependence of a metric function related to the frame-dragging effect is determined from a constraint equation independently of a choice of the embedding coordinate. We find that at least within the framework of the first-order perturbation method, the black hole cannot rotate for finite black hole mass if the embedding coordinate is taken to be a timelike vector. However, the rotation can be permitted in the limit of $M/r \to 0$ (where $M$ is the black hole mass and $r$ is the radius). For a spacelike vector, the rotation can also be permitted for any value of the black hole mass.Comment: 4 pages, Accepted for publication in Phys. Rev.

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 $(2j+1)$-dimensional unitary representations of rotations with half-integers $j$'s are useful to analyze the probability laws of quantum walks. For any value of half-integer $j$, 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 $(2j+1)$ is even, the probability measure of limit distribution is given by a superposition of $(2j+1)/2$ terms of scaled Konno's density functions, and if $(2j+1)$ is odd, it is a superposition of $j$ 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

Site-bond representation and self-duality for totalistic probabilistic cellular automata

We study the one-dimensional two-state totalistic probabilistic cellular automata (TPCA) having an absorbing state with long-range interactions, which can be considered as a natural extension of the Domany-Kinzel model. We establish the conditions for existence of a site-bond representation and self-dual property. Moreover we present an expression of a set-to-set connectedness between two sets, a matrix expression for a condition of the self-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde

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

The QWalk Simulator of Quantum Walks

Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very important for the development of this area, since it allows the researchers to focus on the mathematical and physical aspects of the research instead of deviating the efforts to the implementation of specific numerical simulations. In this paper we present QWalk, a quantum walk simulator for one- and two-dimensional lattices. Finite two-dimensional lattices with generic topologies can be used. Decoherence can be simulated by performing measurements or by breaking links of the lattice. We use examples to explain the usage of the software and to show some recent results of the literature that are easily reproduced by the simulator.Comment: 21 pages, 11 figures. Accepted in Computer Physics Communications. Simulator can be downloaded from http://qubit.lncc.br/qwal

Design of a 3 DOFs parallel actuated mechanism for a biped hip joint

Proceedings of the 2002 IEEE International Conference on Robotics & Automation, Washington, DC, May 200

Distribution of chirality in the quantum walk: Markov process and entanglement

The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial conditions, and it also determines the asymptotic value of the entanglement between the coin and the position. It is shown that for given asymptotic values of both the entanglement and the chirality distribution it is possible to find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions. Moreover it is shown that the entanglement also measures the degree of Markovian randomness of the distribution of chirality.Comment: 5 pages, 3 figures, It was accepted in Physcial Review

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda