65,924 research outputs found
Hamiltonian Dynamics of Yang-Mills Fields on a Lattice
We review recent results from studies of the dynamics of classical Yang-Mills
fields on a lattice. We discuss the numerical techniques employed in solving
the classical lattice Yang-Mills equations in real time, and present results
exhibiting the universal chaotic behavior of nonabelian gauge theories. The
complete spectrum of Lyapunov exponents is determined for the gauge group
SU(2). We survey results obtained for the SU(3) gauge theory and other
nonlinear field theories. We also discuss the relevance of these results to the
problem of thermalization in gauge theories.Comment: REVTeX, 51 pages, 20 figure
Dual theory of the superfluid-Bose glass transition in disordered Bose-Hubbard model in one and two dimensions
I study the zero temperature phase transition between superfluid and
insulating ground states of the Bose-Hubbard model in a random chemical
potential and at large integer average number of particles per site. Duality
transformation maps the pure Bose-Hubbard model onto the sine-Gordon theory in
one dimension (1D), and onto the three dimensional Higgs electrodynamics in two
dimensions (2D). In 1D the random chemical potential in dual theory couples to
the space derivative of the dual field, and appears as a random magnetic field
along the imaginary time direction in 2D. I show that the transition from the
superfluid state in both 1D and 2D is always controlled by the random critical
point. This arises due to a coupling constant in the dual theory with replicas
which becomes generated at large distances by the random chemical potential,
and represents a relevant perturbation at the pure superfluid-Mott insulator
fixed point. At large distances the dual theory in 1D becomes equivalent to the
Haldane's macroscopic representation of disordered quantum fluid, where the
generated term is identified with random backscattering. In 2D the generated
coupling corresponds to the random mass of the complex field which represents
vortex loops. I calculate the critical exponents at the superfluid-Bose glass
fixed point in 2D to be \nu=1.38 and z=1.93, and the universal conductivity at
the transition \sigma_c = 0.26 e_{*}^2 /h, using the one-loop field-theoretic
renormalization group in fixed dimension.Comment: 25 pages, 6 Postscript figures, LaTex, references updated, typos
corrected, final version to appear in Phys. Rev. B, June 1, 199
On the existence and scaling of structure functions in turbulence according to the data
We sample a velocity field that has an inertial spectrum and a skewness that
matches experimental data. In particular, we compute a self-consistent
correction to the Kolmogorov exponent and find that for our model it is zero.
We find that the higher order structure functions diverge for orders larger
than a certain threshold, as theorized in some recent work. The significance of
the results for the statistical theory of homogeneous turbulence is reviewed.Comment: 15 pages, 5 figures, to appear in PNA
SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction
In this paper, we present an automated technique SWATI: Synthesizing
Wordlengths Automatically Using Testing and Induction, which uses a combination
of Nelder-Mead optimization based testing, and induction from examples to
automatically synthesize optimal fixedpoint implementation of numerical
routines. The design of numerical software is commonly done using
floating-point arithmetic in design-environments such as Matlab. However, these
designs are often implemented using fixed-point arithmetic for speed and
efficiency reasons especially in embedded systems. The fixed-point
implementation reduces implementation cost, provides better performance, and
reduces power consumption. The conversion from floating-point designs to
fixed-point code is subject to two opposing constraints: (i) the word-width of
fixed-point types must be minimized, and (ii) the outputs of the fixed-point
program must be accurate. In this paper, we propose a new solution to this
problem. Our technique takes the floating-point program, specified accuracy and
an implementation cost model and provides the fixed-point program with
specified accuracy and optimal implementation cost. We demonstrate the
effectiveness of our approach on a set of examples from the domain of automated
control, robotics and digital signal processing
Zero-Temperature Phase Transitions of Antiferromagnetic Ising Model of General Spin on a Triangular Lattice
We map the ground-state ensemble of antiferromagnetic Ising model of spin-S
on a triangular lattice to an interface model whose entropic fluctuations are
proposed to be described by an effective Gaussian free energy, which enables us
to calculate the critical exponents of various operators in terms of the
stiffness constant of the interface. Monte Carlo simulations for the
ground-state ensemble utilizing this interfacial representation are performed
to study both the dynamical and the static properties of the model. This method
yields more accurate numerical results for the critical exponents. By varying
the spin magnitude in the model, we find that the model exhibits three phases
with a Kosterlitz-Thouless phase transition at 3/2<S_{KT}<2 and a locking phase
transition at 5/2 < S_L \leq 3. The phase diagram at finite temperatures is
also discussed.Comment: 15 pages, LaTeX; 10 figures in PostScript files; The revised version
appears in PRB (see Journal-ref). New electronic address of first author,
[email protected]
Simulation of Field Theories in Wavelet Representation
The field is expanded in a wavelet series and the wavelet coefficients are
varied in a simulation of the 2D field theory. The drastically reduced
autocorrelations result in a substantial decrease of computing requirements,
compared to those in local Metropolis simulations. A large part of the
improvement is shown to be the result of an additional freedom in the choice of
the allowed range of change at the Metropolis update of wavelet components,
namely the range can be optimized independently for all wavelet sizes.Comment: 10 pages, LaTeX with 8 figures, Swansea preprint SWAT/3
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