1,561 research outputs found
Cancellation of energy-divergences and renormalizability in Coulomb gauge QCD within the Lagrangian formalism
In Coulomb gauge QCD in the Lagrangian formalism, energy divergences arise in
individual diagrams. We give a proof on cancellation of these divergences to
all orders of perturbation theory without obstructing the algebraic
renormalizability of the theory.Comment: 13 pages, 7 figure
Continuous deformations of the Grover walk preserving localization
The three-state Grover walk on a line exhibits the localization effect
characterized by a non-vanishing probability of the particle to stay at the
origin. We present two continuous deformations of the Grover walk which
preserve its localization nature. The resulting quantum walks differ in the
rate at which they spread through the lattice. The velocities of the left and
right-traveling probability peaks are given by the maximum of the group
velocity. We find the explicit form of peak velocities in dependence on the
coin parameter. Our results show that localization of the quantum walk is not a
singular property of an isolated coin operator but can be found for entire
families of coins
Critical behavior for mixed site-bond directed percolation
We study mixed site-bond directed percolation on 2D and 3D lattices by using
time-dependent simulations. Our results are compared with rigorous bounds
recently obtained by Liggett and by Katori and Tsukahara. The critical
fractions and of sites and bonds are extremely well
approximated by a relationship reported earlier for isotropic percolation,
, where and are the critical fractions in
pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]
Many-spinon states and the secret significance of Young tableaux
We establish a one-to-one correspondence between the Young tableaux
classifying the total spin representations of N spins and the exact eigenstates
of the the Haldane-Shastry model for a chain with N sites classified by the
total spins and the fractionally spaced single-particle momenta of the spinons.Comment: 4 pages, 3 figure
Limit Theorem for Continuous-Time Quantum Walk on the Line
Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric
distribution on the line, whose evolution is described by the Hadamard
transformation, it was proved by the author that the following weak limit
theorem holds: X^{(d)}_t /t \to dx / \pi (1-x^2) \sqrt{1 - 2 x^2} as t \to
\infty. The present paper shows that a similar type of weak limit theorems is
satisfied for a {\it continuous-time} quantum walk X^{(c)}_t on the line as
follows: X^{(c)}_t /t \to dx / \pi \sqrt{1 - x^2} as t \to \infty. These
results for quantum walks form a striking contrast to the central limit theorem
for symmetric discrete- and continuous-time classical random walks: Y_{t}/
\sqrt{t} \to e^{-x^2/2} dx / \sqrt{2 \pi} as t \to \infty. The work deals also
with issue of the relationship between discrete and continuous-time quantum
walks. This topic, subject of a long debate in the previous literature, is
treated within the formalism of matrix representation and the limit
distributions are exhaustively compared in the two cases.Comment: 15 pages, title correcte
Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.
The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod.
Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly
method. Reliable estimate was found for the critical exponent, based on
moderate sized () clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]
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