4,189 research outputs found
Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
In this paper, we will see that the symplectic creed by Weinstein "everything
is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and
Lagrange-Poincar\'e reduction. In fact, we show that solutions of the
Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in
one-to-one correspondence with distinguished curves in a Lagrangian submanifold
of a symplectic manifold. For this purpose, we will combine the concept of a
Tulczyjew triple with Marsden-Weinstein symplectic reduction.Comment: 26 page
Field squeeze operators in optical cavities with atomic ensembles
We propose a method of generating unitarily single and two-mode field
squeezing in an optical cavity with an atomic cloud. Through a suitable laser
system, we are able to engineer a squeeze field operator decoupled from the
atomic degrees of freedom, yielding a large squeeze parameter that is scaled up
by the number of atoms, and realizing degenerate and non-degenerate parametric
amplification. By means of the input-output theory we show that ideal squeezed
states and perfect squeezing could be approached at the output. The scheme is
robust to decoherence processes.Comment: Four pages and one figure. Accepted in Physical Review Letter
Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
Most {\em ab initio} calculations on fullerene molecules have been carried
out based on the paradigm of the H\"uckel model. This is consistent with the
restricted nature of the independent-particle model underlying such
calculations, even in single-reference-based correlated approaches. On the
other hand, previous works on some of these molecules using model Hamiltonians
have clearly indicated the importance of short-range inter-atomic spin-spin
correlations. In this work, we consider {\em ab initio} non-collinear
Hartree--Fock (HF) solutions for representative fullerene systems: the bowl,
cage, ring, and pentagon isomers of C, and the larger C,
C, C, C, and C fullerene cages. In all cases but
the ring we find that the HF minimum corresponds to a truly non-collinear
solution with a torsional spin density wave. Optimized geometries at the
generalized HF (GHF) level lead to fully symmetric structures, even in those
cases where Jahn-Teller distortions have been previously considered. The nature
of the GHF solutions is consistent with the -electron space becoming
polyradical in nature: each -orbital remains effectively singly occupied.
The spin frustration, induced by the pentagon rings in an otherwise
anti-ferromagnetic background, is minimized at the HF level by aligning the
spins in non-collinear arrangements. The long-range magnetic ordering observed
is reminiscent of the character of broken symmetry HF solutions in polyacene
systems.Comment: 16 figure
Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
A multi-reference configuration mixing scheme is used to describe the ground
state, characterized by well defined spin and space group symmetry quantum
numbers as well as doping fractions , of one dimensional
Hubbard lattices with nearest-neighbor hopping and periodic boundary
conditions. Within this scheme, each ground state is expanded in a given number
of nonorthogonal and variationally determined symmetry-projected
configurations. The results obtained for the ground state and correlation
energies of half-filled and doped lattices with 30, 34 and 50 sites, compare
well with the exact Lieb-Wu solutions as well as with the ones obtained with
other state-of-the-art approximations. The structure of the intrinsic
symmetry-broken determinants resulting from the variational procedure is
interpreted in terms of solitons whose translational and breathing motions can
be regarded as basic units of quantum fluctuations. It is also shown that in
the case of doped 1D lattices, a part of such fluctuations can also be
interpreted in terms of polarons. In addition to momentum distributions, both
spin-spin and density-density correlation functions are studied as functions of
doping. The spectral functions and density of states, computed with an ansatz
whose quality can be well-controlled by the number of symmetry-projected
configurations used to approximate the electron systems, display
features beyond a simple quasiparticle distribution, as well as spin-charge
separation trends.Comment: 16 pages, 11 figure
Theories of the evolution of cooperative behaviour: A critical survey plus some new results
Gratuitous cooperation (in favour of non-relatives and without repeated interaction) eludes traditional evolutionary explanations. In this paper we survey the various theories of cooperative behaviour, and we describe our own effort to integrate these theories into a self-contained framework. Our main conclusions are as follows. First: altruistic punishment, conformism and gratuitous cooperation co-evolve, and group selection is a necessary ingredient for the co-evolution to take place. Second: people do not cooperate by mistake, as most theories imply; on the contrary, people knowingly sacrifice themselves for others. Third: in cooperative dilemmas conformism is an expression of preference, not a learning rule. Fourth, group-mutations (e.g., the rare emergence of a charismatic leader that brings order to the group) are necessary to sustain cooperation in the long run.Cooperation; altruism; altruistic punishment; conformism; group-selection
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