168 research outputs found
The spectral dimension of random trees
We present a simple yet rigorous approach to the determination of the
spectral dimension of random trees, based on the study of the massless limit of
the Gaussian model on such trees. As a byproduct, we obtain evidence in favor
of a new scaling hypothesis for the Gaussian model on generic bounded graphs
and in favor of a previously conjectured exact relation between spectral and
connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section
I
The statistical geometry of scale-free random trees
The properties of scale-free random trees are investigated using both
preconditioning on non-extinction and fixed size averages, in order to study
the thermodynamic limit. The scaling form of volume probability is found, the
connectivity dimensions are determined and compared with other exponents which
describe the growth. The (local) spectral dimension is also determined, through
the study of the massless limit of the Gaussian model on such trees.Comment: 21 pages, 2 figures, revtex4, minor changes (published version
Spectral partitions on infinite graphs
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic
behaviour at macroscopic scales. This phenomenon is of geometrical origin and
may be properly described in terms of spectral partitions into subgraphs with
well defined spectral dimensions and spectral weights. These subgraphs are
shown to be thermodynamically homogeneous and effectively decoupled.Comment: 8 pages, to appear on Journal of Physics
Pemodelan Produksi Minyak Dan Gas Bumi Di PT. âZâ Menggunakan Metode ARIMA, FFNN, Dan Hybrid ARIMA-FFNN
Proses pengambilan produksi minyak dan produksi gas bumi yang dilakukan secara terus menerus di bawah tanah oleh PT. âZâ dapat mengakibatkan produksi tersebut menurun. Oleh karena itu, penelitian ini dilakukan dengan tujuan untuk meramalkan produksi minyak dan produksi gas bumi pada beberapa periode mendatang dengan menggunakan metode ARIMA, FFNN, dan Hybrid ARIMA-FFNN. Data yang digunakan adalah produksi minyak dan produksi gas bumi per hari pada platform âSâ mulai 01 Januari sampai dengan 31 Desember 2015. Hasil penelitian dengan menggunakan metode ARIMA, FFNN, dan Hybrid ARIMA-FFNN menghasilkan kesimpulan bahwa model terbaik untuk produksi minyak bumi adalah menggunakan metode FFNN dengan jumlah neuron pada hidden layer sebanyak sembilan. Sedangkan model terbaik untuk produksi gas bumi menggunakan metode Hybrid ARIMA-FFNN dengan jumlah neuron pada hidden layer sebanyak sepuluh
An improved time-dependent Hartree-Fock approach for scalar \phi^4 QFT
The model in a finite volume is studied within a
non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of
equilibrium, with particular attention to the structure of the ground state and
of certain dynamical features in the broken symmetry phase. The mean-field
coupled time-dependent Schroedinger equations for the modes of the scalar field
are derived and the suitable procedure to renormalize them is outlined. A
further controlled gaussian approximation of our tdHF approach is used in order
to study the dynamical evolution of the system from non-equilibrium initial
conditions characterized by a uniform condensate. We find that, during the slow
rolling down, the long-wavelength quantum fluctuations do not grow to a
macroscopic size but do scale with the linear size of the system, in accordance
with similar results valid for the large approximation of the O(N) model.
This behavior undermines in a precise way the gaussian approximation within our
tdHF approach, which therefore appears as a viable mean to correct an unlikely
feature of the standard HF factorization scheme, such as the so-called
``stopping at the spinodal line'' of the quantum fluctuations. We also study
the dynamics of the system in infinite volume with particular attention to the
asymptotic evolution in the broken symmetry phase. We are able to show that the
fixed points of the evolution cover at most the classically metastable part of
the static effective potential.Comment: Accepted for publication on Phys. Rev.
Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
Boundary conditions compatible with integrability are obtained for two
dimensional models by solving the factorizability equations for the reflection
matrices . For the six vertex model the general solution
depending on four arbitrary parameters is found. For the models all
diagonal solutions are found. The associated integrable magnetic Hamiltonians
are explicitly derived.Comment: 9 pages,latex, LPTHE-PAR 92-4
Sine-Gordon Model - Renormalization Group Solutions and Applications
The sine-Gordon model is discussed and analyzed within the framework of the
renormalization group theory. A perturbative renormalization group procedure is
carried out through a decomposition of the sine-Gordon field in slow and fast
modes. An effective slow modes's theory is derived and re-scaled to obtain the
model's flow equations. The resulting Kosterlitz-Thouless phase diagram is
obtained and discussed in detail. The theory's gap is estimated in terms of the
sine-Gordon model paramaters. The mapping between the sine-Gordon model and
models for interacting electrons in one dimension, such as the g-ology model
and Hubbard model, is discussed and the previous renormalization group results,
obtained for the sine-Gordon model, are thus borrowed to describe different
aspects of Luttinger liquid systems, such as the nature of its excitations and
phase transitions. The calculations are carried out in a thorough and
pedagogical manner, aiming the reader with no previous experience with the
sine-Gordon model or the renormalization group approach.Comment: 44 pages, 7 figure
Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain
We propose a set of nonlinear integral equations to describe on the excited
states of an integrable the spin 1 chain with anisotropy. The scaling
dimensions, evaluated numerically in previous studies, are recovered
analytically by using the equations. This result may be relevant to the study
on the supersymmetric sine-Gordon model.Comment: 15 pages, 2 Figures, typos correcte
Integrabilities of the Model with Impurities
The hamiltonian with magnetic impurities coupled to the strongly correlated
electron system is constructed from model. And it is diagonalized exactly
by using the Bethe ansatz method. Our boundary matrices depend on the spins of
the electrons. The Kondo problem in this system is discussed in details. The
integral equations are derived with complex rapidities which describe the bound
states in the system. The finite-size corrections for the ground-state energies
are obtained.Comment: 24 pages, Revtex, To be published in J. Phys.
Scalar potential effect in an integrable Kondo model
To study the impurity potential effect to the Kondo problem in a Luttinger
liquid, we propose an integrable model of two interacting half-chains coupled
with a single magnetic impurity ferromagnetically. It is shown that the scalar
potential effectively reconciles the spin dynamics at low temperatures.
Generally, there is a competition between the Kondo coupling and the
impurity potential . When the ferromagnetic Kondo coupling dominates over
the impurity potential (), the Furusaki-Nagaosa many-body singlet can
be perfectly realized. However, when the impurity potential dominates over the
Kondo coupling (), the fixed point predicted by Furusaki and
Nagaosa is unstable and the system must flow to a weak coupling fixed point. It
is also found that the effective moment of the impurity measured from the
susceptibility is considerably enlarged by the impurity potential. In addition,
some quantum phase transitions driven by the impurity potential are found and
the anomaly residual entropy is discussed.Comment: volume enlarged, some new references are adde
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