Optimal Quantum Clocks

A quantum clock must satisfy two basic constraints. The first is a bound on the time resolution of the clock given by the difference between its maximum and minimum energy eigenvalues. The second follows from Holevo's bound on how much classical information can be encoded in a quantum system. We show that asymptotically, as the dimension of the Hilbert space of the clock tends to infinity, both constraints can be satisfied simultaneously. The experimental realization of such an optimal quantum clock using trapped ions is discussed.Comment: 4 pages, revtex, 1 figure, revision contains some new result

Product Integral Formalism and Non-Abelian Stokes Theorem

We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.Comment: Latex; condensed version of hep-th/9903221, to appear in Jour. Math. Phy

Configurations of Handles and the Classification of Divergences in the String Partition Function

The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced to geometrical characteristics of the string worldsheet. Some categories of divergences may be eliminated in string theories formulated on compact manifolds.Comment: 24 pages, DAMTP-R/94/1

The role of entanglement in dynamical evolution

Entanglement or entanglement generating interactions permit to achieve the maximum allowed speed in the dynamical evolution of a composite system, when the energy resources are distributed among subsystems. The cases of pre-existing entanglement and of entanglement-building interactions are separately addressed. The role of classical correlations is also discussed.Comment: 5 pages, 1 figure. Revised versio

Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates

The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their explicit evaluation is proposed. A procedure of constructing additional counter-terms to the canonical Hamiltonian that compensate this difference at any finite order is proposed. For the Yukawa model, the light-front Hamiltonian with all of these counter-terms is obtained in a closed form. Possible application of this approach to gauge theories is discussed.Comment: LaTex 2.09, 20 pages, 5 figure

Geometric derivation of the quantum speed limit

The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum mechanical processes in Nature, since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for non-unitary evolution.Comment: 8 pages, 1 figure

Electrons as quasi-bosons in magnetic white dwarfs

A white dwarf star achieves its equilibrium from the balancing of the gravitational compression against the Fermi degeneracy pressure of the electron gas. In field theory there are examples (e.g. the monopole-charge system) where a strong magnetic field can transform a boson into a fermion or a fermion into a boson. In some condensed matter systems (e.g. fractional quantum Hall systems) a strong magnetic field can transform electrons into effective fermions, or effective anyons. Based on these examples we investigate the possibility that the strong magnetic fields of some white dwarfs may transform some fraction of the electrons into effective bosons. This could have consequences for the structure of highly magnetized white dwarfs. It would alter the mass-radius relationship, and in certain instances one could envision a scenario where a white dwarf below the Chandrasekhar limit could nevertheless collapse into a neutron star due to a weakening of the electron degeneracy pressure. In addition the transformation of electrons into effective bosons could result in the electrons Bose condensing, which could speed up the cooling rate of white dwarfs.Comment: 10 pages. To be published IJMP

Shear and bulk viscosities for pure glue matter

Shear $\eta$ and bulk $\zeta$ viscosities are calculated in a quasiparticle model within a relaxation time approximation for pure gluon matter. Below $T_c$ the confined sector is described within a quasiparticle glueball model. Particular attention is paid to behavior of the shear and bulk viscosities near $T_c$. The constructed equation of state reproduces the first-order phase transition for the glue matter. It is shown that with this equation of state it is possible to describe the temperature dependence of the shear viscosity to entropy ratio $\eta/s$ and the bulk viscosity to entropy ratio $\zeta/s$ in reasonable agreement with available lattice data but absolute values of the $\zeta/s$ ratio underestimate the upper limits of this ratio in the lattice measurements typically by an order of magnitude.Comment: 8 pages, 4 figures; the published versio

Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory

We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is $H_{0}+{e^{\prime}}^{2}H_{1}$, where $H_{0}$ is the Hamiltonian of a set of (1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_{1}$ as the interaction Hamiltonian. For gauge group SU(2), we use form factors of the currents of the principal chiral sigma models to compute the string tension for small $e^{\prime}$, after reviewing exact S-matrix and form-factor methods. In the anisotropic regime, the dependence of the string tension on the coupling constant is not in accord with generally-accepted dimensional arguments.Comment: Now 37 pages, Section 5 moved to an appendix, more motivation given in the introduction, a few more typos correcte

Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example

We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected properties in the SG model. Some of them continue to have scale- invariant dynamics even in the presence of the non-conformal cosine interaction. For instance, it is shown that the Mandelstam operator for the bosonic representation of the Fermi field does {\it not} develop a mass term in the SG theory, contrary to what the real Fermi field in the massive Thirring model is expected to do. It is also shown that in the presence of the non-conformal interactions, some vertex operators have unique Lorentz spins, while others do not.Comment: 32 pages, Univ. of Illinois Preprint # ILL-(TH)-93-1