Complexity is Simple

In this note we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and `simple' gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd's assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in Brown et al

Single-spin-flip dynamics of the Ising chain

We consider the most general single-spin-flip dynamics for the ferromagnetic Ising chain with nearest-neighbour influence and spin reversal symmetry. This dynamics is a two-parameter extension of Glauber dynamics corresponding respectively to non-linearity and irreversibility. The associated stationary state measure is given by the usual Boltzmann-Gibbs distribution for the ferromagnetic Hamiltonian of the chain. We study the properties of this dynamics both at infinite and at finite temperature, all over its parameter space, with particular emphasis on special lines and points.Comment: 31 pages, 18 figure

Pilot wave model without configuration or Fock spaces

The goal of this article is to come up with interpretation of quantum phenomena that is both local and deterministic. This is done by the means of envoking two different metrics, $g_o$ and $g_s$. These two metrics give very different "speeds of light": $c_o$ and $c_s$, respectively. The $g_o$ and $c_o$ are, respectively, "ordinary" metric and speed of light that we are used to. On the other hand, $c_s$ is superluminal. In this paper I propose a model in which newly introduced signals, which are subject to $g_s$, are responsible for key quantum phenomena.Comment: 36 pages, no figure

TeV Astrophysics Constraints on Planck Scale Lorentz Violation

We analyze observational constraints from TeV astrophysics on Lorentz violating nonlinear dispersion for photons and electrons without assuming any a priori equality between the photon and electron parameters. The constraints arise from thresholds for vacuum Cerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum Cerenkov radiation.Comment: 4 pages, RevTeX4, 1 figure. Some references and a footnote added, improved discussion on the photon annihilation and GZK cutoff. Minor changes of wording. Main results unchanged. Version to appear as a Rapid Communication in PR

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.Comment: 24 pages, 15 figure

A first look at Landau-gauge propagators in G2 Yang-Mills theory

G_2 Yang--Mills theory is an interesting laboratory to investigate non-perturbative effects. On one hand, no conventional quark confinement via a linearly rising potential is present. On the other hand, its thermodynamic properties are similar to ordinary SU(N) Yang--Mills theory. Finally, it has been conjectured that gluons are removed from the physical spectrum in the same way as in SU(N) Yang--Mills theory. The last claim will be explored by determining the Landau-gauge ghost and gluon propagators, as well as the Faddeev--Popov operator eigenspectrum, in G_2 lattice gauge theory in two and three dimensions. The results are found to agree qualitatively with the SU(2) and SU(3) case. Therefore, the conjecture that Yang--Mills theories with different gauge groups are qualitatively similar on the level of their Landau gauge Green's functions is supported.Comment: 22 pages, 4 figures, 2 tables; in v2: One figure added, added statistics, extended discussion on some topics, various minor change

Quark Masses: An Environmental Impact Statement

We investigate worlds that lie on a slice through the parameter space of the Standard Model over which quark masses vary. We allow as many as three quarks to participate in nuclei, while fixing the mass of the electron and the average mass of the lightest baryon flavor multiplet. We classify as "congenial" worlds that satisfy the environmental constraint that the quark masses allow for stable nuclei with charges one, six, and eight, making organic chemistry possible. Whether a congenial world actually produces observers depends on a multitude of historical contingencies, beginning with primordial nucleosynthesis, which we do not explore. Such constraints may be independently superimposed on our results. Environmental constraints such as the ones we study may be combined with information about the a priori distribution of quark masses over the landscape of possible universes to determine whether the measured values of the quark masses are determined environmentally, but our analysis is independent of such an anthropic approach. We estimate baryon masses as functions of quark masses and nuclear masses as functions of baryon masses. We check for the stability of nuclei against fission, strong particle emission, and weak nucleon emission. For two light quarks with charges 2/3 and -1/3, we find a band of congeniality roughly 29 MeV wide in their mass difference. We also find another, less robust region of congeniality with one light, charge -1/3 quark, and two heavier, approximately degenerate charge -1/3 and 2/3 quarks. No other assignment of light quark charges yields congenial worlds with two baryons participating in nuclei. We identify and discuss the region in quark-mass space where nuclei would be made from three or more baryon species.Comment: 40 pages, 16 figures (in color), 4 tables. See paper for a more detailed abstract. v4: Cleaning up minor typo