Simulating lattice gauge theories on a quantum computer

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.Comment: 15 pages, 4 figures, 3 table

Private languages and private theorists

Simon Blackburn objects that Wittgenstein's private language argument overlooks the possibility that a private linguist can equip himself with a criterion of correctness by confirming generalizations about the patterns in which his private sensations occur. Crispin Wright responds that appropriate generalizations would be too few to be interesting. But I show that Wright's calculations are upset by his failure to appreciate both the richness of the data and the range of theories that would be available to the private linguist

Clan Structure Analysis and Rapidity Gap Probability

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA.Comment: (14 pages in Plain TeX plus 5 Postscript Figures, all compressed via uufiles) DFTT 28/9

Specifications for MSE trials for Bluefin tuna in the North Atlantic

This document is a “straw-man” draft of detailed MSE trial specifications for Bluefin tuna in the North Atlantic which, we suggest, are a desirable outcome from the ICCAT meeting on this topic to be held in Monterey over 21-23 January 2016. Such a specification document requires many decisions at a quite complex and detailed level, desirably after full discussion at the meeting. The fact that specific suggestions have been made below is not to suggest that the authors necessarily consider that those reflect the decisions which should be made. Rather their purpose is to assist clarify the totality and nature of decisions required by way of examples. Given this draft nature of this document, and its intended further development during the meeting, the text has yet to be “polished” (to include references, etc.)

Soft-core meson-baryon interactions. II. πN\pi N and K+NK^+ N scattering

The $\pi N$ potential includes the t-channel exchanges of the scalar-mesons $\sigma$ and f_0, vector-meson $\rho$, tensor-mesons f_2 and f_2' and the Pomeron as well as the s- and u-channel exchanges of the nucleon N and the resonances $\Delta$, Roper and S_{11}. These resonances are not generated dynamically. We consider them as, at least partially, genuine three-quark states and we treat them in the same way as the nucleon. The latter two resonances were needed to find the proper behavior of the phase shifts at higher energies in the corresponding partial waves. The soft-core $\pi N$-model gives an excellent fit to the empirical $\pi N$ S- and P-wave phase shifts up to T_{lab}=600 MeV. Also the scattering lengths have been reproduced well and the soft-pion theorems for low-energy $\pi N$ scattering are satisfied. The soft-core model for the $K^+ N$ interaction is an SU_f(3)-extension of the soft-core $\pi N$-model. The $K^+ N$ potential includes the t-channel exchanges of the scalar-mesons a_0, $\sigma$ and f_0, vector-mesons $\rho$, $\omega$ and $\phi$, tensor-mesons a_2, f_2 and f_2' and the Pomeron as well as u-channel exchanges of the hyperons $\Lambda$ and $\Sigma$. The fit to the empirical $K^+ N$ S-, P- and D-wave phase shifts up to T_{lab}=600 MeV is reasonable and certainly reflects the present state of the art. Since the various $K^+ N$ phase shift analyses are not very consistent, also scattering observables are compared with the soft-core $K^+ N$-model. A good agreement for the total and differential cross sections as well as the polarizations is found.Comment: 24 pages, 20 PostScript figures, revtex4, submitted to Phys. Rev.

Multiplicity Distributions and Rapidity Gaps

I examine the phenomenology of particle multiplicity distributions, with special emphasis on the low multiplicities that are a background in the study of rapidity gaps. In particular, I analyze the multiplicity distribution in a rapidity interval between two jets, using the HERWIG QCD simulation with some necessary modifications. The distribution is not of the negative binomial form, and displays an anomalous enhancement at zero multiplicity. Some useful mathematical tools for working with multiplicity distributions are presented. It is demonstrated that ignoring particles with pt<0.2 has theoretical advantages, in addition to being convenient experimentally.Comment: 24 pages, LaTeX, MSUHEP/94071

Higher Resonance Contributions to the Adler-Weisberger Sum Rule in the Large N_c Limit

We determine the $N_c$--dependence of the resonance contributions to the Adler--Weisberger sum rule for the inverse square $1/g_A^2$ of the axial charge coupling constant and show that in the large $N_c$ limit the contributions of the Roper-like excitations scale as $O(1/N_c)$. Consistency with the $1/N_c^2$ scaling of the $1/g_A^2$ term in the sum rule requires these contributions to cancel against each other.Comment: 10 pages, LaTeX, TH Darmstadt preprint IKDA 93/47, REVISE

Hotter, Denser, Faster, Smaller...and Nearly-Perfect: What's the matter at RHIC?

The experimental and theoretical status of the ``near perfect fluid'' at RHIC is discussed. While the hydrodynamic paradigm for understanding collisions at RHIC is well-established, there remain many important open questions to address in order to understand its relevance and scope. It is also a crucial issue to understand how the early equilibration is achieved, requiring insight into the active degrees of freedom at early times.Comment: 10 Pages, 13 Figures, submitted to the proceedings of the Second Meeting of the APS Topical Group on Hadronic Physics, Nashville, TN, October 22-24, 200

Soft-core meson-baryon interactions. I. One-hadron-exchange potentials

The Nijmegen soft-core model for the pseudoscalar-meson baryon interaction is derived, analogous to the Nijmegen NN and YN models. The interaction Hamiltonians are defined and the resulting amplitudes for one-meson-exchange and one-baryon-exchange in momentum space are given for the general mass case. The partial wave projection is carried through and explicit expressions for the momentum space partial wave meson-baryon potentials are presented.Comment: 25 pages, 2 PostScript figures, revtex4, submitted to Phys. Rev.

Random and Correlated Phases of Primordial Gravitaional Waves

The phases of primordial gravity waves is analysed in detail within a quantum mechanical context following the formalism developed by Grishchuk and Sidorov. It is found that for physically relevant wavelengths both the phase of each individual mode and the phase {\it difference} between modes are randomly distributed. The phase {\it sum} between modes with oppositely directed wave-vectors, however, is not random and takes on a definite value with no rms fluctuation. The conventional point of view that primordial gravity waves appear after inflation as a classical, random stochastic background is also addressed.Comment: 14 pages, written in REVTE