Influence of the vacuum level upon the growth of carbon nanotubes on silicon carbide surface

We have investigated the influence of the vacuum level upon the growth of carbon nanotubes (CNTs) on 6H-SiC () surface.CNTs of about 160 nm in length were formed densely and uniformly on the 6H-SiC surface during annealing at 1700 °C in a high vacuum (∼10⁻² Pa). CNTs of about 1 μm in length were formed during annealing at 1700 °C in an ultra-high vacuum (∼10⁻⁷ Pa). However, CNTs were not formed and SiO₂ layers were formed on the SiC surface at 1700 °C in air. It is found that longer CNTs can grow up in an ultra-high vacuum, moreover, a little aligned and low-density graphite layers, or carbon nanofibers can also grow up.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Aberrated diffraction patterns of off-axis Gaussian beams

Fraunhofer diffraction patterns of off-axis Gaussian beams passing through an optical system having primary spherical aberration are investigated. The resultant diffraction patterns show a nearly elliptical form with a transverse focal shift which depends on the incident position of the Gaussian beams on the pupil and on their radius.     

57Fe and57Co Mössbauer studies of highT c Y-Ba-Cu oxides

The⁵⁷Co emission Mössbauer spectra from YBa₂Cu₃O_6.92 (1-2-307) and YBa₂Cu₃O_6.00 (1-2-306) have been measured and compared with the⁵⁷Fe absorption spectra from YBa₂Cu_2.95Fe_0.05O_7?δ in order to clarify decisively the site assignments for the⁵⁷Fe quadrupole-split doublets in these compounds. Mössbauer spectra obtained from both specimens consist of four components whose hyperfine interaction parameters well agree with each other. It is shown that the Co and Fe atoms mainly substitute at Cu1 chain sites in 1-2-307, but in 1-2-306 the Co atoms occupy randomly the Cu2 plane sites and indicate magnetically-split sextet which converts to a paramagnetic doublet of S-state Fe³⁺ in 1-2-307 by a post-annealing in O₂ gas.     

Localization transition of <Emphasis Type="Italic">d</Emphasis>-friendly walkers

 Friendly walkers is a stochastic model obtained from independent one-dimensional simple random walks {S ^k _j } _j≥0 , k=1,2,…,d by introducing ``non-crossing condition': and ``reward for collisions' characterized by parameters . Here, the reward for collisions is described as follows. If, at a given time n, a site in ℤ is occupied by exactly m≥2 walkers, then the site increases the probabilistic weight for the walkers by multiplicative factor exp (β _m )≥1. We study the localization transition of this model in terms of the positivity of the free energy and describe the location and the shape of the critical surface in the (d−1)-dimensional space for the parameters . Received: 13 June 2002 / Revised version: 24 August 2002 Published online: 28 March 2003 Mathematics Subject Classification (2000): 82B41, 82B26, 82D60, 60G50 Key words or phrases: Random walks – Random surfaces – Lattice animals – Phase transitions – Polymers – Random walks     

Phase transitions in N—n-propylpyridinium-TCNQ2 and N—n-butylpyridinium-TCNQn at high pressures

The electrical resistivity of N-n-propylpyridinium-TCNQ₂ (NPPy-TCNQ₂) and N-n-butylpyridinium-TCNQ_n (NBPy-TCNQ_n) has been measured as a function of temperature and pressure. Phase transitions in these salts have been studied at high pressures. The transition temperature (T_c) in NPPy-TCNQ₂ at atmospheric pressure increased with increasing pressure at the rate of dT_c/dP = + 12.0 degkbar^?1. The value of volume change calculated from the Clapeylon-Clausius relation was + 4.4 cm³ mol^?1. The electrical resistivity along the a- and c-axis increased with increasing pressure below 7 kbar. This anomalous electrical behaviour is closely related to the crystal structure of NPPy-TCNQ₂. The resistivity dropped sharply at about 11 kbar. This abrupt change may be due to a new pressure induced phase transition.The T_c of the NBPy-TCNQ_n increased remarkably with increasing pressure up to 0.7 kbar, above which the phase transition disappeared. The phase transitions of N-n-alkyl-substituted pyridinium TCNQ salts depend strongly on the nature of cations.     

Recording a binary computer-generated hologram on a thermoplastic film

A computer-generated hologram was recorded on a thermoplastic film using an electron-beam recording device. The hologram was a binary one of detour phase type and of surface relief type. A bright image was reconstructed from the recorded hologram.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Classification of integral trees

A finite poset Q is called integral over a field k if there exists an ASL (algebra with straightening laws) domain on Q{–} over k. We classify all trees (rank one connected posets without cycles) which are integral over an infinite field.