Fundamental cosmic strings

Cosmic strings are linear concentrations of energy that may be formed at phase transitions in the very early universe. At one time they were thought to provide a possible origin for the density inhomogeneities from which galaxies eventually develop, though this idea has been ruled out, primarily by observations of the cosmic microwave background (CMB). Fundamental strings are the supposed building blocks of all matter in superstring theory or its modern version, M-theory. These two concepts were originally very far apart, but recent developments have brought them closer. The `brane-world' scenario in particular suggests the existence of macroscopic fundamental strings that could well play a role very similar to that of cosmic strings. In this paper, we outline these new developments, and also analyze recent observational evidence, and prospects for the future.Comment: Review to appear in Contemporary Physic

Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy density in their core reaches that of the prior symmetric vacuum) but topologically stable (the whole manifold would have to be rearranged to get rid of the defect). We show how, in a paradigmatic model of a quantum phase transition, a topological defect can be put in a non-local superposition, so that - in a region large compared to the size of its core - the order parameter of the system is "undecided" by being in a quantum superposition of conflicting choices of the broken symmetry. We demonstrate how to exhibit such a "Schr\"odinger kink" by devising a version of a double-slit experiment suitable for topological defects. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyze environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure

Gravity with de Sitter and Unitary Tangent Groups

Einstein Gravity can be formulated as a gauge theory with the tangent space respecting the Lorentz symmetry. In this paper we show that the dimension of the tangent space can be larger than the dimension of the manifold and by requiring the invariance of the theory with respect to 5d Lorentz group (de Sitter group) Einstein theory is reproduced unambiguously. The other possibility is to have unitary symmetry on a complex tangent space of the same dimension as the manifold. In this case the resultant theory is Einstein-Strauss Hermitian gravity. The tangent group is important for matter couplings. We show that in the de Sitter case the 4 dimensional space time vector and scalar are naturally unified by a hidden symmetry being components of a 5d vector in the tangent space. With a de Sitter tangent group spinors can exist only when they are made complex or taken in doublets in a way similar to N=2 supersymmetry.Comment: 23 pages, one reference added.To be published in JHE

Ortho-para transition in molecular hydrogen

The radiative ortho-para transition in the molecular hydrogen is studied. This highly forbidden transition is very sensitive to relativistic and subtle nonadiabatic effects. Our result for the transition rate in the ground vibrational level \Gamma(J=1\to J=0) = 6.20(62)\cdot 10^{-14} \iyr is significantly lower in comparison to all the previous approximate calculations. Experimental detection of such a weak line by observation of, for example, the cold interstellar molecular hydrogen is at present unlikely.Comment: 4 pages, submitted to Phys. Rev.

The Fluctuations of the Quark Number and of the Chiral Condensate

The distributions of the quark number and chiral condensate over the gauge fields are computed for QCD in Euclidean space at nonzero quark chemical potential. As both operators are non-hermitian the distributions are in the complex plane. Moreover, because of the sign problem, the distributions are not real and positive. The computations are carried out within leading order chiral perturbation theory and give a direct insight into the delicate cancellations that take place in contributions to the total baryon number and the chiral condensate.Comment: 19 pages, 2 figure

Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of the Magnus force and escape into the container volume where they are detected individually with nuclear magnetic resonance. The larger the superflow velocity the smaller the rings which can expand. Thus it is possible to obtain information about the morphology of the initial defect network. We suggest that the nucleation of vortices during the rapid cool-down into the superfluid phase is similar to the formation of defects during cosmological phase transitions in the early universe.Comment: 4 pages, LaTeX file, 4 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-95009.p

Lagrange Anchor for Bargmann-Wigner equations

A Poincare invariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin s > 1/2 in four-dimensional Minkowski space. By making use of this Lagrange anchor, we assign a symmetry to each conservation law.Comment: A contribution to Proceedings of the XXXI Workshop on the Geometric Methods in Physic

Differential Geometry of Quantum States, Observables and Evolution

The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.Comment: 20 pages, comments are welcome

Parameters of Pseudo-Random Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random circuits, with the goal of identifying relevant trade-offs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudo-random circuits and approximate $t$-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudo-random second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be theoretically and practically useful to optimize the efficiency of random state and operator generation.Comment: 17 pages, 14 figures, 2 Appendice