We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to these two degrees of freedom, it is allowed to stay at the same position. We calculate rigorously the wavefunction of the particle starting from the origin for any initial qubit state, and show the spatial distribution of probability of finding the particle. In contrast with the Hadamard walk with two inner states on a line, the probability of finding the particle at the origin does not converge to zero even after infinite time steps except special initial states. This implies that the particle is trapped near the origin after long time with high probability.

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.

Particle trapping in multi-state quantum walk on a circle is studied. The timeaveraged probability distribution of a particle which moves four different lattice sites according to four internal states is calculated exactly. In contrast with "Hadamard walk" with only two internal states, the particle remains at the initial position with high probability. The time-averaged probability of finding the particle decreases exponentially as distance from a center of a spike. This implies that the particle is trapped in a narrow region. This striking difference is minutely explained from difference between degeneracy of eigenvalues of the time-evolution matrices. The dependence of the particle distribution on initial conditions is also considered.

In secondary ion mass spectrometry (SIMS) of organic substances, the dissociation of the sample molecules is crucial. We have developed SIMS equipment capable of bombardment, where the primary ions are argon cluster ions with kinetic energy per atom controllable down to 1  eV. We previously reported the detection of intact ions of insulin and cytochrome C using this equipment. In this paper, we present a detailed characterization of the emission of secondary ions from insulin, focusing on the difference in secondary ion yield between intact ions and fragment ions by varying the incident angle of the cluster ions. The emission intensity of the intact ions was changed drastically due to the exposed dosage and incident angle of the cluster ions in contrast to the fragment ions. We discuss these results based on the manner in which the argon-cluster ions collide with the organic solid.

Using a molecular dynamics simulation, we examine the actuation of nanodrums consisting of a single graphene sheet. The membrane of the nanodrum, which contains 190 carbon atoms, is bent by collision with a cluster consisting of 10 argon atoms. The choice of an appropriate cluster velocity enables nanometre deformation of the membrane in sub-picosecond time without rupturing the graphene sheet. Theoretical results predict that, if an adsorbed molecule exists on the graphene sheet, the quick deformation due to the impact with the cluster can break the weak bonding between the adsorbed molecule and the graphene sheet and release the molecule from the surface; this suggests that this system has attractive potential applications for purposes of molecular ejection.

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A size-selected argon (Ar) gas-cluster ion beam (GCIB) was applied to the secondary ion mass spectrometry (SIMS) of a 1,4-didodecylbenzene (DDB) thin film. The samples were also analyzed by SIMS using an atomic Ar(+) ion projectile and X-ray photoelectron spectroscopy (XPS). Compared with those in the atomic-Ar(+) SIMS spectrum, the fragment species, including siloxane contaminants present on the sample surface, were enhanced several hundred times in the Ar gas-cluster SIMS spectrum. XPS spectra during beam irradiation indicate that the Ar GCIB sputters contaminants on the surface more effectively than the atomic Ar(+) ion beam. These results indicate that a large gas-cluster projectile can sputter a much shallower volume of organic material than small projectiles, resulting in an extremely surface-sensitive analysis of organic thin films.

We introduce a parity conserving version of the contact process, which can be treated using a series expansion technique. Both Padé approximants for the series and numerical simulations for the derivative of the order parameter show that the critical exponent b is consistent with the conjecture b 1. Dynamical Monte Carlo simulations confirm that the model belongs to the branching annihilating random walk with an even number of offsprings universality class. [S0031-9007 (98)06309-1] PACS numbers: 64.60.Ak, 05.40. + j, 64.60.Ht Contact process (CP) [1,2] is a nonequilibrium model exhibiting an extinction-survival second order dynamical phase transition. The basic CP introduced by Harris [1]has a unique absorbing state and belongs to the directed percolation (DP) universality class [3][4][5]. Many other nonequilibrium models such as A-model [6,7], branching annihilating random walk [8,9] with an odd number of offsprings, and Reggon field theory [10] are believed to belong to the same universality class as the basic contact process, which is often regarded as a minimal example of a broad class of interacting particle systems, similarly to the role of the Ising system in equilibrium critical phenomena.Another important universality class for nonequilibrium models is branching annihilating random walk with even offsprings universality class (BAWe) [11,12]. The first model belonging to a non-DP, and now believed to belong to the BAWe universality class was a probabilistic cellular automaton studied by Grassbeger et al. [13]. Recently, a number of models belonging to BAWe universality, such as certain kinetic Ising models [14], the interacting monomer-dimer model (MDM) [15,16], three species monomer-monomer model [17], and modified DomanyKinzel model [18] introduced by Hinrichsen [19] attracted much attention. While for DP universality models series expansion treatment proved to be most effective in estimating critical values (see references above), so far models in BAWe universality relied exclusively on Monte Carlo simulations.Although the DP universality class is very wide and includes models with rather simple rules, no model in it has been solved exactly [20]. Guttmann and Enting [21] suggested that DP models will never be solved exactly in the sense of being expressed in terms of D-finite functions due to an absence of pattern in series expansion coefficients. Furthermore, based on numerical data Jensen and Guttmann [5] conjectured that critical exponents for DP should not be expected to be simple rational fractions.On the other hand, Jensen conjectured that combinations of critical exponents of BAWe can be represented as b͞n Ќ 1 2 and n Ќ ͞n k 7͞4 [11]. Intuitively, it would suggest that BAWe universality is "simpler" than DP universality; one could even speculate concerning the possibility of an exact solution.In this Letter, we introduce a extended CP, which while belonging to BAWe universality allows a series expansion treatment. We use the series expansion technique [22][23][24] in order to clarify the value o...