The String Calculation of QCD Wilson Loops on Arbitrary Surfaces

Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.Comment: 10 pages, LaTeX, no figure

Novel schemes for measurement-based quantum computation

We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique further develops tools from many-body physics - based on finitely correlated or projected entangled pair states - to go beyond the cluster-state based one-way computer. We identify resource states that are radically different from the cluster state, in that they exhibit non-vanishing correlation functions, can partly be prepared using gates with non-maximal entangling power, or have very different local entanglement properties. In the computational models, the randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. Finally, we comment on the possibility of tailoring computational models to specific physical systems as, e.g. cold atoms in optical lattices.Comment: 5 pages RevTeX, 1 figure, many diagrams. Title changed, presentation improved, material adde

Enhancement of kinetic energy fluctuations due to expansion

Global equilibrium fragmentation inside a freeze out constraining volume is a working hypothesis widely used in nuclear fragmentation statistical models. In the framework of classical Lennard Jones molecular dynamics, we study how the relaxation of the fixed volume constraint affects the posterior evolution of microscopic correlations, and how a non-confined fragmentation scenario is established. A study of the dynamical evolution of the relative kinetic energy fluctuations was also performed. We found that asymptotic measurements of such observable can be related to the number of decaying channels available to the system at fragmentation time.Comment: 6 pages, 4 figure

The stability of the spectator, Dirac, and Salpeter equations for mesons

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a time-like vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions

Microcanonical Thermodynamics of First Order Phase Transitions studied in the Potts Model

Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information about the main characteristics of first order phase transitions like the transition temperature, the latent heat, and the interphase surface tension. The characterisitc backbending of the micro- canonical caloric equation of state T(E) (not to be confused with the well known Van der Waals loops in ordinary thermodynamics) leading to a negative specific heat is intimatly linked to the interphase surface entropy.Comment: Latex, 4 eps-figures, graphicx.st

Gauge Fields and Space-Time

In this article I attempt to collect some ideas,opinions and formulae which may be useful in solving the problem of gauge/ string / space-time correspondence This includes the validity of D-brane representation, counting of gauge-invariant words, relations between the null states and the Yang-Mills equations and the discussion of the strong coupling limit of the string sigma model. The article is based on the talk given at the "Odyssey 2001" conference.Comment: 20 page

The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures

Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical mechanics especially its key quantity, entropy. Whereas in conventional thermostatistics, the homogeneity and extensivity of the system and the concavity of its entropy are central conditions, these fail for the systems considered here. For example, at phase separation, the entropy, S(E), is necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as inhomogeneities and surface effects cannot be scaled away, one must be careful with the standard arguments of splitting a system into two subsystems, or bringing two systems into thermal contact with energy or particle exchange. Not only the volume part of the entropy must be considered. As will be shown here, when removing constraints in regions of a negative heat capacity, the system may even relax under a flow of heat (energy) against a temperature slope. Thus the Clausius formulation of the second law: ``Heat always flows from hot to cold'', can be violated. Temperature is not a necessary or fundamental control parameter of thermostatistics. However, the second law is still satisfied and the total Boltzmann entropy increases. In the final sections of this paper, the general microscopic mechanism leading to condensation and to the convexity of the microcanonical entropy at phase separation is sketched. Also the microscopic conditions for the existence (or non-existence) of a critical end-point of the phase-separation are discussed. This is explained for the liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of Chemical Physic

Invariant Connections with Torsion on Group Manifolds and Their Application in Kaluza-Klein Theories

Invariant connections with torsion on simple group manifolds $S$ are studied and an explicit formula describing them is presented. This result is used for the dimensional reduction in a theory of multidimensional gravity with curvature squared terms on $M^{4} \times S$. We calculate the potential of scalar fields, emerging from extra components of the metric and torsion, and analyze the role of the torsion for the stability of spontaneous compactification.Comment: 13 pages, LATEX, UB-ECM-PF 93/1

Calculating the Rest Tension for a Polymer of String Bits

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint, UFIFT-HEP-94