6,862 research outputs found
Continuum Singularities of a Mean Field Theory of Collisions
Consider a complex energy for a -particle Hamiltonian and let
be any wave packet accounting for any channel flux. The time independent
mean field (TIMF) approximation of the inhomogeneous, linear equation
consists in replacing by a product or Slater
determinant of single particle states This results, under the
Schwinger variational principle, into self consistent TIMF equations
in single particle space. The method is a
generalization of the Hartree-Fock (HF) replacement of the -body homogeneous
linear equation by single particle HF diagonalizations
We show how, despite strong nonlinearities in this mean
field method, threshold singularities of the {\it inhomogeneous} TIMF equations
are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure
Existence of a Density Functional for an Intrinsic State
A generalization of the Hohenberg-Kohn theorem proves the existence of a
density functional for an intrinsic state, symmetry violating, out of which a
physical state with good quantum numbers can be projected.Comment: 6 page
The quantum dynamics of atomic magnets, co-tunneling and dipolar-biased tunneling
Multi-spins tunneling cross-relaxations in an ensemble of weakly-coupled
Ho ions, mediated by weak anisotropic dipolar interactions, can be
evidenced by ac-susceptibility measurements in a high temperature regime. Based
on a four-body representation, including the rare-earth nuclear spin, two-ions
tunneling mechanisms can be attributed to both dipolar-biased tunneling and
co-tunneling processes. The co-reversal involving entangled pairs of magnetic
moments is discussed with a particular emphasis, giving new evidences to
elucidate the many-body quantum dynamics.Comment: 4 figure
On positive functions with positive Fourier transforms
Using the basis of Hermite-Fourier functions (i.e. the quantum oscillator
eigenstates) and the Sturm theorem, we derive the practical constraints for a
function and its Fourier transform to be both positive. We propose a
constructive method based on the algebra of Hermite polynomials. Applications
are extended to the 2-dimensional case (i.e. Fourier-Bessel transforms and the
algebra of Laguerre polynomials) and to adding constraints on derivatives, such
as monotonicity or convexity.Comment: 12 pages, 23 figures. High definition figures can be obtained upon
request at [email protected] or [email protected]
Move ordering and communities in complex networks describing the game of go
We analyze the game of go from the point of view of complex networks. We
construct three different directed networks of increasing complexity, defining
nodes as local patterns on plaquettes of increasing sizes, and links as actual
successions of these patterns in databases of real games. We discuss the
peculiarities of these networks compared to other types of networks. We explore
the ranking vectors and community structure of the networks and show that this
approach enables to extract groups of moves with common strategic properties.
We also investigate different networks built from games with players of
different levels or from different phases of the game. We discuss how the study
of the community structure of these networks may help to improve the computer
simulations of the game. More generally, we believe such studies may help to
improve the understanding of human decision process.Comment: 14 pages, 21 figure
Distinguishing humans from computers in the game of go: a complex network approach
We compare complex networks built from the game of go and obtained from
databases of human-played games with those obtained from computer-played games.
Our investigations show that statistical features of the human-based networks
and the computer-based networks differ, and that these differences can be
statistically significant on a relatively small number of games using specific
estimators. We show that the deterministic or stochastic nature of the computer
algorithm playing the game can also be distinguished from these quantities.
This can be seen as tool to implement a Turing-like test for go simulators.Comment: 7 pages, 6 figure
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