174,379 research outputs found
A nonperturbative Real-Space Renormalization Group scheme
Based on the original idea of the density matrix renormalization group
(DMRG), i.e. to include the missing boundary conditions between adjacent blocks
of the blocked quantum system, we present a rigorous and nonperturbative
mathematical formulation for the real-space renormalization group (RG) idea
invented by L.P. Kadanoff and further developed by K.G. Wilson. This is
achieved by using additional Hilbert spaces called auxiliary spaces in the
construction of each single isolated block, which is then named a superblock
according to the original nomenclature. On this superblock we define two maps
called embedding and truncation for successively integrating out the small
scale structure. Our method overcomes the known difficulties of the numerical
DMRG, i.e. limitation to zero temperature and one space dimension.Comment: 13 pages, 5 figures, late
Notes on a paper of Mess
These notes are a companion to the article "Lorentz spacetimes of constant
curvature" by Geoffrey Mess, which was first written in 1990 but never
published. Mess' paper will appear together with these notes in a forthcoming
issue of Geometriae Dedicata.Comment: 26 page
Approximating the coefficients in semilinear stochastic partial differential equations
We investigate, in the setting of UMD Banach spaces E, the continuous
dependence on the data A, F, G and X_0 of mild solutions of semilinear
stochastic evolution equations with multiplicative noise of the form dX(t) =
[AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical
Brownian motion on a Hilbert space H. We prove continuous dependence of the
compensated solutions X(t)-e^{tA}X_0 in the norms
L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n
are uniformly sectorial and converge to A in the strong resolvent sense, and
that the approximating nonlinearities F_n and G_n are uniformly Lipschitz
continuous in suitable norms and converge to F and G pointwise. Our results are
applied to a class of semilinear parabolic SPDEs with finite-dimensional
multiplicative noise.Comment: Referee's comments have been incorporate
Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to 6Li and 10B
We calculate properties of A=6 system using the accurate charge-dependent
nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory.
By application of the ab initio no-core shell model (NCSM) and a variational
calculation in the harmonic oscillator basis with basis size up to 16 hbarOmega
we obtain the 6Li binding energy of 28.5(5) MeV and a converged excitation
spectrum. Also, we calculate properties of 10B using the same NN potential in a
basis space of up to 8 hbarOmega. Our results are consistent with results
obtained by standard accurate NN potentials and demonstrate a deficiency of
Hamiltonians consisting of only two-body terms. At this order of chiral
perturbation theory three-body terms appear. It is expected that inclusion of
such terms in the Hamiltonian will improve agreement with experiment.Comment: 9 pages, 14 figure
Noncommutative Bayesian Statistical Inference from a wedge of a Bifurcate Killing Horizon
Expanding a remark of my PHD-thesis the noncommutative bayesian statistical
inference from one wedge of a bifurcate Killing horizon is analyzed looking at
its inter-relation with the Unruh effectComment: some correction performed; to appear in "International Journal of
Theoretical Physics
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