Discreteness and the origin of probability in quantum mechanics

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.Comment: 5 pages, revtex, 1 figure. Revised version, to appear in Physics Letters B. (Small clarifcation, references added.

New AdS non Abelian black holes with superconducting horizons

We present arguments for the existence of higher dimensional asymptotically AdS non Abelian black holes with a Ricci flat event horizon and analyze their basic properties. Unlike higher dimensional black holes with a curved horizon, of the usual Einstein-Yang-Mills system, these solutions have finite mass-energy. Below some non-zero critical temperature, they are thermodynamically preferred over the Abelian configurations.Comment: 11 pages, 4 figure

The angular distribution of the reaction νˉe+p→e++n\bar{\nu}_e + p \to e^+ + n

The reaction $\bar{\nu}_e + p \to e^+ + n$ is very important for low-energy ($E_\nu \lesssim 60$ MeV) antineutrino experiments. In this paper we calculate the positron angular distribution, which at low energies is slightly backward. We show that weak magnetism and recoil corrections have a large effect on the angular distribution, making it isotropic at about 15 MeV and slightly forward at higher energies. We also show that the behavior of the cross section and the angular distribution can be well-understood analytically for $E_\nu \lesssim 60$ MeV by calculating to ${\cal O}(1/M)$, where $M$ is the nucleon mass. The correct angular distribution is useful for separating $\bar{\nu}_e + p \to e^+ + n$ events from other reactions and detector backgrounds, as well as for possible localization of the source (e.g., a supernova) direction. We comment on how similar corrections appear for the lepton angular distributions in the deuteron breakup reactions $\bar{\nu}_e + d \to e^+ + n + n$ and $\nu_e + d \to e^- + p + p$. Finally, in the reaction $\bar{\nu}_e + p \to e^+ + n$, the angular distribution of the outgoing neutrons is strongly forward-peaked, leading to a measurable separation in positron and neutron detection points, also potentially useful for rejecting backgrounds or locating the source direction.Comment: 10 pages, including 5 figure

Giant Gravitons - with Strings Attached (III)

We develop techniques to compute the one-loop anomalous dimensions of operators in the ${\cal N}=4$ super Yang-Mills theory that are dual to open strings ending on boundstates of sphere giant gravitons. Our results, which are applicable to excitations involving an arbitrary number of open strings, generalize the single string results of hep-th/0701067. The open strings we consider carry angular momentum on an S$^3$ embedded in the S$^5$ of the AdS$_5\times$S$^5$ background. The problem of computing the one loop anomalous dimensions is replaced with the problem of diagonalizing an interacting Cuntz oscillator Hamiltonian. Our Cuntz oscillator dynamics illustrates how the Chan-Paton factors for open strings propagating on multiple branes can arise dynamically.Comment: 66 pages; v2: improved presentatio

Q2Q^2--Dependence of the Gerasimov-Drell-Hearn Sum Rule

We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating the total photon absorption cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$ on the nucleon via photon excitation of baryon resonances in the constituent quark model. A total of seventeen, low-lying, non-strange baryon resonances are included in this calculation. The transverse and longitudinal interference cross section, $\sigma_{1/2}^{TL}$, is found to play an important role in the study of the $Q^2$ variation of the sum rule. The results show that the GDH sum rule is saturated by these resonances at a confidence level of 94%. In particular, the $P_{33}(1232)$ excitation largely saturates the sum rule at $Q^2 = 0$, and dominates at small $Q^2$. The GDH integral has a strong $Q^2$-dependence below $Q^2= 1.0 {GeV}^2$ and changes its sign around $Q^2= 0.3 {GeV}^2$. It becomes weakly $Q^2$-dependent for $Q^2 > 1.0 {GeV}^2$ because of the quick decline of the resonance contributions. We point out that the $Q^2$ variation of the GDH sum rule is very important for understanding the nucleon spin structure in the non-perturbative QCD region.Comment: revtex, 17 pages, 3 ps figs include

Nonlinear evolution of the momentum dependent condensates in strong interaction: the ``pseudoscalar laser''

We discuss the relaxation of the scalar and pseudoscalar condensates after a rapid quench from an initial state with fluctuations. If we include not only the zero-mode but also higher modes of the condensates in the classical evolution, we observe parametric amplification of those ``hard'' modes. Thus, they couple nonlinearly to the ``soft'' modes. As a consequence, domains of coherent pi-field emerge long after the initial spinodal decomposition. The momentum-space distribution of pions emerging from the decay of that momentum-dependent condensate is discussed.Comment: 6 Pages, REVTEX, 8 Figures; one reference and one figure adde

The Proton Spin and Flavor Structure in the Chiral Quark Model

After a pedagogical review of the simple constituent quark model and deep inelastic sum rules, we describe how a quark sea as produced by the emission of internal Goldstone bosons by the valence quarks can account for the observed features of proton spin and flavor structures. Some issues concerning the strange quark content of the nucleon are also discussed.Comment: 59 pages with table of contents, Lecture delivered at the Schladming Winter School (March 1997), to be published by Springer-Verlag under the title "Computing Particle Properties" (eds. C. B. Lang and H. Gausterer

Challenges and Obstacles for a Bouncing Universe in Brane Models

A Brane evolving in the background of a charged AdS black-hole displays in general a bouncing behaviour with a smooth transition from a contracting to an expanding phase. We examine in detail the conditions and consequences of this behaviour in various cases. For a cosmological-constant-dominated Brane, we obtain a singularity-free, inflationary era which is shown to be compatible only with an intermediate-scale fundamental Planck mass. For a radiation-dominated Brane, the bouncing behaviour can occur only for background-charge values exceeding those allowed for non-extremal black holes. For a matter-dominated Brane, the black-hole mass affects the proper volume or the expansion rate of the Brane. We also consider the Brane evolving in an asymmetric background of two distinct charged AdS black hole spacetimes being bounded by the Brane and find that, in the case of an empty critical Brane, bouncing behaviour occurs only if the black-hole mass difference is smaller than a certain value. The effects of a Brane curvature term on the bounce at early and late times are also investigated.Comment: 23 pages, Latex file, comments and references added, version to appear in Phys. Rev.

Finite size corrections for open strings/open chains in planar AdS/CFT

We identify the leading finite-size (Luscher-type) correction to the energy of open strings ending on maximal giant gravitons. In particular we obtain the leading finite size correction at weak 't Hooft coupling and in the planar limit to the energy of very short vacuum states. These results are shown to agree with certain 1, 2, 3 and 4-loop dual gauge theory perturbative calculations, which we also perform.Comment: 31 pages; v2: comments and references added; v3: clarifications and references adde

Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory

The quantum time evolution of \phi^4-field theory for a spatially homogeneous system in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym equations including the tadpole and sunset self-energies. Whereas the tadpole self-energy yields a dynamical mass, the sunset self-energy is responsible for dissipation and an equilibration of the system. In particular we address the dynamics of the spectral (`off-shell') distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. The investigation explicitly demonstrates that the only translation invariant solutions representing the stationary fixed points of the coupled equation of motions are those of full thermal equilibrium. They agree with those extracted from the time integration of the Kadanoff-Baym equations in the long time limit. Furthermore, a detailed comparison of the full quantum dynamics to more approximate and simple schemes like that of a standard kinetic (on-shell) Boltzmann equation is performed. Our analysis shows that the consistent inclusion of the dynamical spectral function has a significant impact on relaxation phenomena. The different time scales, that are involved in the dynamical quantum evolution towards a complete thermalized state, are discussed in detail. We find that far off-shell 1 3 processes are responsible for chemical equilibration, which is missed in the Boltzmann limit. Finally, we address briefly the case of (bare) massless fields. For sufficiently large couplings $\lambda$ we observe the onset of Bose condensation, where our scheme within symmetric \phi^4-theory breaks down.Comment: 77 pages, 26 figure