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 $^{28}$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 $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ 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 $\mathcal{R}$, 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 $0\,\mathrm{d}\nu$. 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