Counting Cubic Extensions with given Quadratic Resolvent

Given a number field $k$ and a quadratic extension $K_2$, we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of $k$ whose Galois closure contains $K_2$ as quadratic subextension, ordered by the norm of their relative discriminant ideal. The main tool is Kummer theory. We also study in detail the error term of the asymptotics and show that it is $O(X^{\alpha})$, for an explicit $\alpha<1$.Comment: 19 page

Quantum pumping and dissipation in closed systems

Current can be pumped through a closed system by changing parameters (or fields) in time. Linear response theory (the Kubo formula) allows to analyze both the charge transport and the associated dissipation effect. We make a distinction between adiabatic and non-adiabatic regimes, and explain the subtle limit of an infinite system. As an example we discuss the following question: What is the amount of charge which is pushed by a moving scatterer? In the low frequency (DC) limit we can write dQ=-GdX, where dX is the displacement of the scatterer. Thus the issue is to calculate the generalized conductance $G$.Comment: 12 pages, 6 figures, Lecture notes for the proceedings of the conference "Frontiers of Quantum and Mesoscopic Thermodynamics" [Prague, July 2004

Trends in Special Library Buildings

published or submitted for publicatio

Diffusion Enhances Spontaneous Electroweak Baryogenesis

We include the effects of diffusion in the electroweak spontaneous baryogenesis scenario and show that it can greatly enhance the resultant baryon density, by as much as a factor of $1/\alpha_w^4 \sim 10^6$ over previous estimates. Furthermore, the baryon density produced is rather insensitive to parameters characterizing the first order weak phase transition, such as the width and propagation velocity of the phase boundary.Comment: 15 pages, uses harvmac and epsf macro

On Lie Algebras Generated by Few Extremal Elements

We give an overview of some properties of Lie algebras generated by at most 5 extremal elements. In particular, for any finite graph {\Gamma} and any field K of characteristic not 2, we consider an algebraic variety X over K whose K-points parametrize Lie algebras generated by extremal elements. Here the generators correspond to the vertices of the graph, and we prescribe commutation relations corresponding to the nonedges of {\Gamma}. We show that, for all connected undirected finite graphs on at most 5 vertices, X is a finite-dimensional affine space. Furthermore, we show that for maximal-dimensional Lie algebras generated by 5 extremal elements, X is a point. The latter result implies that the bilinear map describing extremality must be identically zero, so that all extremal elements are sandwich elements and the only Lie algebra of this dimension that occurs is nilpotent. These results were obtained by extensive computations with the Magma computational algebra system. The algorithms developed can be applied to arbitrary {\Gamma} (i.e., without restriction on the number of vertices), and may be of independent interest.Comment: 19 page

The Large N_c Baryon-Meson I_t = J_t Rule Holds for Three Flavors

It has long been known that nonstrange baryon-meson scattering in the 1/N_c expansion of QCD greatly simplifies when expressed in terms of t-channel exchanges: The leading-order amplitudes satisfy the selection rule I_t = J_t. We show that I_t = J_t, as well as Y_t = 0, also hold for the leading amplitudes when the baryon and/or meson contain strange quarks, and also characterize their 1/N_c corrections, thus opening a new front in the phenomenological study of baryon-meson scattering and baryon resonances.Comment: 12 pages, 0 figures, ReVTe

Excited Baryons in Large NcN_c QCD

This talk reviews recent developments in the use of large $N_c$ QCD in the description of baryonic resonances. The emphasis is on the model-independent nature of the approach. Key issues discussed include the spin-flavor symmetry which emerges at large $N_c$ and the direct use of scattering observables. The connection to quark model approaches is stressed.Comment: Talk at "Baryons 04", Palaiseau, October 200

Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation

We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic physics can be regarded as two special results of the general formulation. We assume a time-dependent Hamiltonian $H(Q,P;x(t))$ with $x(t)=Vt$, where $V$ is slow in a classical sense. The rate-of-change $V$ is not necessarily slow in the quantum-mechanical sense. Dissipation means an irreversible systematic growth of the (average) energy. It is associated with the stochastic spreading of energy across levels. The latter can be characterized by a transition probability kernel $P_t(n|m)$ where $n$ and $m$ are level indices. This kernel is the main object of the present study. In the classical limit, due to the (assumed) chaotic nature of the dynamics, the second moment of $P_t(n|m)$ exhibits a crossover from ballistic to diffusive behavior. We define the $V$ regimes where either perturbation theory or semiclassical considerations are applicable in order to establish this crossover in the quantal case. In the limit $\hbar\to 0$ perturbation theory does not apply but semiclassical considerations can be used in order to argue that there is detailed correspondence, during the crossover time. In the perturbative regime there is a lack of such correspondence. Namely, $P_t(n|m)$ is characterized by a perturbative core-tail structure that persists during the crossover time. In spite of this lack of (detailed) correspondence there may be still a restricted correspondence as far as the second-moment is concerned. Such restricted correspondence is essential in order to establish the universal fluctuation-dissipation relation.Comment: 46 pages, 6 figures, 4 Tables. To be published in Annals of Physics. Appendix F improve

Translated tori in the characteristic varieties of complex hyperplane arrangements

We give examples of complex hyperplane arrangements for which the top characteristic variety contains positive-dimensional irreducible components that do not pass through the origin of the character torus. These examples answer several questions of Libgober and Yuzvinsky. As an application, we exhibit a pair of arrangements for which the resonance varieties of the Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic varieties are not isomorphic. The difference comes from translated components, which are not detected by the tangent cone at the origin.Comment: Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Application

Very Special Relativity in Curved Space-Times

The generalization of Cohen and Glashow's Very Special Relativity to curved space-times is considered. Gauging the SIM(2) symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2) invariant Lagrangians can always be constructed. For space-times with SIM(2) holonomy, they describe chiral fermions propagating freely as massive particles.Comment: 7 page