arXiv subjects

Paul M. Saffin

Publications and source records attributed to Paul M. Saffin.

At least 37 records · Page 2Linked to original sources

arXiv2021

Gravitational collapse of quantum fields and Choptuik scaling

Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. By choosing a convenient coherent state, this formalism taps into well-established techniques used for classical collapse and adds on the evolution of the mode functions of the quantum field operator. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classical results in gravitational collapse, and identifying the difference due to the quantum effects. We also find that Choptuik scaling in critical collapse survives in the semiclassical simulation, and furthermore the quantum deviation from the classical Choptuik scaling decreases when the system approaches the critical point.

hep-th↗

arXiv2021

Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions

We elucidate the regulator-sourced 2PI and average 1PI approaches for deriving exact flow equations in the case of a zero dimensional quantum field theory, wherein the scale dependence of the usual renormalisation group evolution is replaced by a simple parametric dependence. We show that both approaches are self-consistent, while highlighting key differences in their behaviour and the structure of the would-be loop expansion.

hep-th↗

arXiv2021

Gravitational collapse with quantum fields

Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. This formalism utilizes well-established techniques used for classical collapse by choosing a convenient coherent state, and simulates the matter fields quantum mechanically. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classical results in gravitational collapse, and identifying the difference due to quantum effects.

gr-qc↗

arXiv2021

Alternative flow equation for the functional renormalization group

We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point source of the 2PI effective action to be associated consistently with the regulator of the renormalization group flow. We show that this procedure leads to a flow equation that differs from that obtained in the standard approach based on the average one-particle irreducible effective action.

hep-th↗

arXiv2021

Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation

Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.

hep-th↗

arXiv2021

Charge-Swapping Q-balls and Their Lifetimes

For scalar theories accommodating spherically symmetric Q-balls, there are also towers of quasi-stable composite Q-balls, called charge swapping Q-balls (CSQs). We investigate the properties, particularly the lifetimes, of these long-lived CSQs in 2+1D and 3+1D using numerical simulations with efficient second order absorbing boundary conditions. We find that the evolution of a CSQ typically consists of 4 distinct stages: initial relaxation, first plateau (CSQ stage), fast decay and second plateau (oscillon stage). We chart the lifetimes of CSQs for different parameters of the initial conditions and of the potential, and show the attractor behavior and other properties of the CSQs.

hep-th↗

arXiv2020

Deconstructing higher order clockwork gravity

We consider the higher order clockwork theory of gravitational interactions, whereby a number of gravitons are coupled together with TeV strength, but nevertheless generate a Planck scale coupling to matter without the need for a dilaton. It is shown that the framework naturally lends itself to a five-dimensional geometry, and we find the 5D continuum version of such deconstructed 4D gravitational clockwork models. Moreover, the clockwork picture has matter coupled to particular gravitons, which in the 5D framework looks like a braneworld model, with the Randall-Sundrum model being a special case. More generally, the gravitational clockwork leads to a family of scalar-tensor braneworld models, where the scalar is not a dilaton.

hep-th↗

arXiv2020

Simulations of a bubble wall interacting with an electroweak plasma

We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymmetry. A number of technical details necessary for a proper numerical implementation are developed.

hep-th↗

arXiv2020

Classical Decay Rates of Oscillons

Oscillons are extremely long-lived, spatially-localized field configurations in real-valued scalar field theories that slowly lose energy via radiation of scalar waves. Before their eventual demise, oscillons can pass through (one or more) exceptionally stable field configurations where their decay rate is highly suppressed. We provide an improved calculation of the non-trivial behavior of the decay rates, and lifetimes of oscillons. In particular, our calculation correctly captures the existence (or absence) of the exceptionally long-lived states for large amplitude oscillons in a broad class of potentials, including non-polynomial potentials that flatten at large field values. The key underlying reason for the improved (by many orders of magnitude in some cases) calculation is the systematic inclusion of a spacetime-dependent effective mass term in the equation describing the radiation emitted by oscillons (in addition to a source term). Our results for the exceptionally stable configurations, decay rates, and lifetime of large amplitude oscillons (in some cases $\gtrsim 10^8$ oscillations) in such flattened potentials might be relevant for cosmological applications.

hep-th↗

arXiv2020

Black holes in self-tuning cubic Horndeski cosmology

Observations of neutron star mergers in the late Universe have given significant restrictions to the class of viable scalar-tensor theories. In this paper we construct black holes within the "self-tuning" class of this restricted set, whereby the bare cosmological constant is absorbed by the dynamics of the scalar, giving a lower effective cosmological constant. We use analytic expansions at the singularity, black hole and cosmological horizon, and asymptotic region, coupled with numerical solutions, to find well-behaved black holes that asymptote to the self-tuned de Sitter geometry. The geometry differs from standard general relativity black holes near the horizon, and the scalar field velocity provides a hair for the black holes.

gr-qc↗

arXiv2019

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the dynamic part of the path integral which corresponds to the integration over field variables at all later times. This turns the path integral into a two-stage problem where, for each initial condition, there exits one and only one critical point and hence a single thimble in the complex space, whose existence and uniqueness are guaranteed by the characteristics of the initial value problem. In this paper, we test the method for a fully quantum mechanical phenomenon, quantum tunnelling in quantum mechanics. We compare the method to solving the Schrödinger equation numerically, and to the classical-statistical approximation, which emerges naturally in a well-defined limit. We find that the Picard-Lefschetz result matches the expectation from quantum mechanics and that, for this application, the classical-statistical approximation does not.

hep-th↗

arXiv2019

Visualising quantum effective action calculations in zero dimensions

We present an explicit treatment of the two-particle-irreducible (2PI) effective action for a zero-dimensional quantum field theory. The advantage of this simple playground is that we are required to deal only with functions rather than functionals, making complete analytic approximations accessible and full numerical evaluation of the exact result possible. Moreover, it permits us to plot intuitive graphical representations of the behaviour of the effective action, as well as the objects out of which it is built. We illustrate the subtleties of the behaviour of the sources and their convex-conjugate variables, and their relation to the various saddle points of the path integral. With this understood, we describe the convexity of the 2PI effective action and provide a comprehensive explanation of how the Maxwell construction arises in the case of multiple, classically stable saddle points, finding results that are consistent with previous studies of the one-particle-irreducible (1PI) effective action.

hep-th↗

arXiv2019

A new functional RG flow: regulator-sourced 2PI versus average 1PI

We derive the renormalization group evolution of the quartic scalar theory with spontaneous symmetry breaking from an alternative flow equation, obtained within the externally sourced two-particle irreducible framework due to Garbrecht and Millington. In order to make a straightforward comparison with the evolution from the standard Wetterich-Morris-Ellwanger equation, we employ the Litim regulator, work to lowest order in the derivative expansion and neglect anomalous scaling. By this means, we illustrate the leading differences between analytic expressions for the resulting threshold and (non-perturbative) beta functions. In four dimensions, we find that the positions of the potential minima and the cosmological constant evolve more rapidly with scale compared to the standard approach, whereas the quartic coupling evolves more slowly, albeit by a small amount. These differences may have implications for the asymptotic safety programme, as well as our understanding of the non-perturbative scale evolution of the Standard Model Higgs sector.

hep-th↗

arXiv2019

Real-time quantum dynamics, path integrals and the method of thimbles

Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the complex plane, where the integral is better behaved. By Cauchy's theorem, the final value of the path integral is unchanged. Previous analyses have considered the case of real scalar fields in thermal equilibrium, employing a closed Schwinger-Keldysh time contour, allowing the evaluation of the full quantum correlation functions. Here we extend the analysis by not requiring a closed time path, instead allowing for an initial density matrix for out-of-equilibrium initial value problems. We are able to explicitly implement Gaussian initial conditions, and by separating the initial time and the later times into a two-step Monte-Carlo sampling, we are able to avoid the phenomenon of multiple thimbles. In fact, there exists one and only one thimble for each sample member of the initial density matrix. We demonstrate the approach through explicitly computing the real-time propagator for an interacting scalar in 0+1 dimensions, and find very good convergence allowing for comparison with perturbation theory and the classical-statistical approximation to real-time dynamics.

hep-lat↗

arXiv2019

Well-Tempered Cosmology

We examine an approach to cosmology, known as Well-Tempering, that allows for a de Sitter phase whose expansion is independent of the cosmological constant. Starting from a generic scalar-tensor theory compatible with the recent gravitational wave observation, we impose the Well-Tempering conditions and derive a system that is capable of tuning away the cosmological constant within a sub-class of Horndeski theory, where the scalar has a canonical kinetic term and a general potential. This scenario improves upon the Fab-Four approach by allowing a standard fluid-cosmology before entering the de Sitter phase, and we present an explicit example of our general solution.

gr-qc↗

arXiv2018

Higher Order Clockwork Gravity

We present a higher order generalisation of the clockwork mechanism starting from an underlying non-linear multigravity theory with a single scale and nearest neighbour ghost-free interactions. Without introducing any hierarchies in the underlying potential, this admits a family of Minkowski vacua around which massless graviton fluctuations couple to matter exponentially more weakly than the heavy modes. Although multi-diffeomorphisms are broken to the diagonal subgroup in our theory, an asymmetric distribution of conformal factors in the background vacua translates this diagonal symmetry into an asymmetric shift of the graviton gears. In particular we present a TeV scale multigravity model with ${\cal O}(10)$ sites that contains a massless mode whose coupling to matter is Planckian, and a tower of massive modes starting at a TeV mass range and with TeV strength couplings. This suggests a possible application to the hierarchy problem as well as a candidate for dark matter.

hep-th↗

arXiv2018

Dark energy after GW170817, revisited

We revisit the status of scalar-tensor theories with applications to dark energy in the aftermath of the gravitational wave signal GW170817 and its optical counterpart GRB170817A. At the level of the cosmological background, we identify a class of theories, previously declared unviable in this context, whose anomalous gravitational wave speed is proportional to the scalar equation of motion. As long as the scalar field is assumed not to couple directly to matter, this raises the possibility of compatibility with the gravitational wave data, for any cosmological sources, thanks to the scalar dynamics. This newly "rescued" class of theories includes examples of generalised quintic galileons from Horndeski theories. Despite the promise of this leading order result, we show that the loophole ultimately fails when we include the effect of large scale inhomogeneities.

gr-qc↗

arXiv2018

Boltzmann equations for preheating

We derive quantum Boltzmann equations for preheating by means of the density matrix formalism, which account for both the non-adiabatic particle production and the leading collisional processes between the produced particles. In so doing, we illustrate the pivotal role played by pair correlations in mediating the particle production. In addition, by numerically solving the relevant system of Boltzmann equations, we demonstrate that collisional processes lead to a suppression of the growth of the number density even at the very early stages of preheating.

hep-th↗