48,315 research outputs found
Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion
We study the algebra Sp(n,R) of the symplectic model, in particular for the
cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we
derive a set of partial differential equations for the generators as functions
of classical canonical variables. We obtain a solution to these equations that
represents the classical limit of a boson mapping of the algebra. The
relationship to the collective dynamics is formulated as a theorem that
associates the mapping with an exact solution of the time-dependent Hartree
approximation. This solution determines a decoupled classical symplectic
manifold, thus satisfying the criteria that define an exactly solvable model in
the theory of large amplitude collective motion. The models thus obtained also
provide a test of methods for constructing an approximately decoupled manifold
in fully realistic cases. We show that an algorithm developed in one of our
earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics
The goal of the present account is to review our efforts to obtain and apply
a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic
degrees of freedom, starting from a Hamiltonian system with more or many more
degrees of freedom. The approach is based on an analysis of the classical limit
of quantum-mechanical problems. Initially, we study the classical problem
within the framework of Hamiltonian dynamics and derive a fully self-consistent
theory of large amplitude collective motion with small velocities. We derive a
measure for the quality of decoupling of the collective degree of freedom. We
show for several simple examples, where the classical limit is obvious, that
when decoupling is good, a quantization of the collective Hamiltonian leads to
accurate descriptions of the low energy properties of the systems studied. In
nuclear physics problems we construct the classical Hamiltonian by means of
time-dependent mean-field theory, and we transcribe our formalism to this case.
We report studies of a model for monopole vibrations, of Si with a
realistic interaction, several qualitative models of heavier nuclei, and
preliminary results for a more realistic approach to heavy nuclei. Other topics
included are a nuclear Born-Oppenheimer approximation for an {\em ab initio}
quantum theory and a theory of the transfer of energy between collective and
non-collective degrees of freedom when the decoupling is not exact. The
explicit account is based on the work of the authors, but a thorough survey of
other work is included.Comment: 203 pages, many figure
Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles
We consider free lattice fermions subjected to a static bounded potential and
a time- and space-dependent electric field. For any bounded convex region
() of space, electric fields
within drive currents. At leading order, uniformly
with respect to the volume of and
the particular choice of the static potential, the dependency on
of the current is linear and described by a conductivity distribution. Because
of the positivity of the heat production, the real part of its Fourier
transform is a positive measure, named here (microscopic) conductivity measure
of , in accordance with Ohm's law in Fourier space. This finite
measure is the Fourier transform of a time-correlation function of current
fluctuations, i.e., the conductivity distribution satisfies Green-Kubo
relations. We additionally show that this measure can also be seen as the
boundary value of the Laplace-Fourier transform of a so-called quantum current
viscosity. The real and imaginary parts of conductivity distributions satisfy
Kramers-Kronig relations. At leading order, uniformly with respect to
parameters, the heat production is the classical work performed by electric
fields on the system in presence of currents. The conductivity measure is
uniformly bounded with respect to parameters of the system and it is never the
trivial measure . Therefore, electric fields generally
produce heat in such systems. In fact, the conductivity measure defines a
quadratic form in the space of Schwartz functions, the Legendre-Fenchel
transform of which describes the resistivity of the system. This leads to
Joule's law, i.e., the heat produced by currents is proportional to the
resistivity and the square of currents
Observation of Leggett's collective mode in a multi-band MgB2 superconductor
We report observation of Leggett's collective mode in a multi-band MgB2
superconductor with T_c=39K arising from the fluctuations in the relative phase
between two superconducting condensates. The novel mode is observed by Raman
spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed
mode frequency is consistent with theoretical considerations based on the first
principle computations.Comment: Accepted for PR
Coherent Vector Meson Photoproduction with Nuclear Breakup in Relativistic Heavy Ion Collisions
Relativistic heavy ions are copious sources of virtual photons. The large
photon flux gives rise to a substantial photonuclear interaction probability at
impact parameters where no hadronic interactions can occur. Multiple
photonuclear interactions in a single collision are possible. In this letter,
we use mutual Coulomb excitation of both nuclei as a tag for moderate impact
parameter collisions. We calculate the cross section for coherent vector meson
production accompanied by mutual excitation, and show that the median impact
parameter is much smaller than for untagged production. The vector meson
rapidity and transverse momentum distribution are very different from untagged
exclusive vector meson production.Comment: 14 pages, including 4 figure
Monopole Planets and Galaxies
Spherical clusters of SU(2) BPS monopoles are investigated here. A large
class of monopole solutions is found using an abelian approximation, where the
clusters are spherically symmetric, although exact solutions cannot have this
symmetry precisely. Monopole clusters generalise the Bolognesi magnetic bag
solution of the same charge, but they are always larger. Selected density
profiles give structures analogous to planets of uniform density, and galaxies
with a density decaying as the inverse square of the distance from the centre.
The Bolognesi bag itself has features analogous to a black hole, and this
analogy between monopole clusters and astrophysical objects with or without
black holes in their central region is developed further. It is also shown that
certain exact, platonic monopoles of small charge have sizes and other features
consistent with what is expected for magnetic bags.Comment: 23 pages. Revised version to appear in Physical Review D. New
introduction and conclusions; analogy between monopoles and astrophysical
objects developed furthe
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