Perturbative Description Research Articles

Noncomoving description of adiabatic radial perturbations of relativistic stars

Noncomoving description of adiabatic radial perturbations of relativistic stars

Linear instability of viscous parallel shear flows: revisiting the perturbation no-slip condition

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behaviour of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid–solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows.

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach.

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

Spatiotemporal nonlinear dynamics and chaos in a mechanical Duffing-type system

This paper investigates spatiotemporal nonlinear dynamics and chaos in a dissipative mechanical Duffing-type system subjected to external stimulus. A nonlinear wave equation with cubic nonlinearity governs the system dynamics. A perturbation description is employed to build mathematical tools that represent different aspects of system dynamics, from local to global behaviors. Lyapunov exponents are defined from the different perturbations allowing the evaluation of local, convective and mean exponents. Different dynamical regimes are investigated considering homogeneous and heterogeneous spatial stimuli. Distinct dynamical responses are observed including periodic, quasi-periodic and chaotic behaviors. A novel concept of chaotic wave is employed to explain the spatial transport of chaos through the media considering heterogeneous conditions. Chaotic wave velocity is measured by the convective Lyapunov exponents.

An analytical description of substructure-induced gravitational perturbations in stellar systems

ABSTRACT Perturbations to stellar systems can reflect the gravitational influence of dark matter substructures. On scales much smaller than the size of a stellar system, we point out analytical connections between the stellar and dark matter distributions. In particular, the density and velocity power spectra of the stars are proportional to the density power spectrum of the perturbing dark matter, scaled by k−4. This relationship allows easy evaluation of the suitability of a stellar system for detecting dark substructure. As examples, we show that the Galactic stellar halo is expected to be sensitive to cold dark matter substructure at wavenumbers k ≲ 0.3 kpc−1, and the Galactic disc might be sensitive to substructure at wavenumbers k ∼ 4 kpc−1. The perturbations considered in this work are short-lived, being rapidly erased by the stellar velocity dispersion, so it may be possible to attribute a detection to dark matter substructure without ambiguity.

Dynamically massive linear covariant gauges: Setup and first results

We discuss the possibility to obtain a massive Landau gauge, based on the local composite operator effective action framework combined with the Zimmermann reduction of couplings prescription. As a way to deal with the gauge ambiguity, we check that the ghost propagator remains positive, a necessary condition for gluon field configurations beyond the Gribov region to be negligible. We pay attention to the Becchi-Rouet-Stora-Tyutin invariance of the construction, allowing for a future generalization to a class of massive linear covariant gauges. As a litmus test, we compare our predictions to the lattice data for the two-point functions in Landau gauge introducing the “dynamically infrared-safe” renormalization scheme, including the renormalization group optimization of both the gap equation and the two-point functions. We also discuss the relation to and differences with the Curci-Ferrari model, the usefulness of which in providing an effective perturbative description of nonperturbative Yang-Mills theories became clear during recent years. Published by the American Physical Society 2024

Emergent M-theory limit

It has been recently proposed that at each infinite distance limit in the moduli space of quantum gravity a perturbative description emerges with fundamental degrees of freedom given by those infinite towers of states whose typical mass scale is parametrically not larger than the ultraviolet cutoff, identified with the species scale. This proposal is applied to the familiar ten-dimensional type IIA and IIB superstring theories, when considering the limit of infinite string coupling. For type IIB, the light towers of states are given by excitations of the D1-brane, as expected from self-duality. Instead, for type IIA at strong coupling, which is dual to M-theory on S1, we make the observation that the emergent degrees of freedom are bound states of transversal M2- and M5-branes with Kaluza-Klein momentum along the circle. We speculate on the interpretation of the necessity of including all these states for a putative quantum formulation of M-theory. Published by the American Physical Society 2024

Codebase release 1.0 for GRIFFIN

This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}'ff‾→f′f‾′ with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation.

GRIFFIN: A C++ library for electroweak radiative corrections in fermion scattering and decay processes

This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}'ff‾→f′f‾′ with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation.

Magnetoacoustic Heating of Plasma Caused by Periodic Magnetosound Perturbations with Discontinuities in a Quasi-Isentropic Magnetic Gas

The magnetoacoustic heating of a plasma by harmonic or periodic saw-tooth perturbations at a transducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wave vector may form an arbitrary angle θ with the equilibrium straight magnetic strength. In view of variable θ and plasma-β, the description of magnetosound perturbations and relative magnetosound heating is fairly difficult. The scenario of heating depends not only on plasma-β and θ, but also on a balance between nonlinear attenuation at the shock front and inflow of energy into a system. Under some conditions, the average over the magnetosound period force of heating may tend to a positive or negative limit, or may tend to zero, or may remain constant when the distance from a transducer tends to infinity. Dynamics of temperature specifying heating differs in thermally stable and unstable cases and occurs unusually in the isentropically unstable flows.

A tail of eternal inflation

Non-trivial inflaton self-interactions can yield calculable signatures of primordial non-Gaussianity that are measurable in cosmic surveys. We calculate the non-Gaussian corrections to Stochastic Inflation within the framework of Soft de Sitter Effective Theory, from which we derive the associated probability distribution for the scalar fluctuations. As a consequence of this new result, we show that the phase transition to slow-roll eternal inflation is often incalculable in these models. Instead, this transition is sensitive to the non-Gaussian tail of the distribution of scalar fluctuations, which probes physics inside the horizon, potentially beyond the cutoff scale of the Effective Field Theory of Inflation. We delineate the parameter space consistent with current observations and weak coupling at horizon crossing in which the large fluctuations relevant for eternal inflation can only be determined by appealing to a UV completion. We also argue that this breakdown of the perturbative description is required for the de Sitter entropy to reflect the number of de Sitter microstates.

SIMPly add a dark photon

Pions of a dark sector gauge group can be strongly interacting massive particle (SIMP) dark matter, produced by the freeze-out of 3 → 2 interactions, with naturally large self-interactions. We study if adding a dark photon to the set-up can do it all: i) maintain thermalization with the visible sector, ii) resonantly enhance the 3 → 2 interactions, thus allowing for a perturbative pion description, and iii) provide a velocity dependent self-interaction that can affect small scale structure formation. For Nf = 3 this minimal setup is marginally excluded, as the required kinetic mixing is too small to maintain thermal equilibrium with the SM. Adding an extra dark quark opens up parameter space, and — perhaps somewhat surprisingly — we find that all bounds can be satisfied for dark pion masses mπ ∼ 250 − 600 MeV. Dropping the small scale structure requirement iii), a viable setup is reproduced for dark charges of αd = 0.01 − 1 and a dark pion mass mπ ≥ 30 MeV. Late time annihilations are non-negligible making the SIMP dark pion a bit WIMPy.

General properties of fidelity in non-Hermitian quantum systems with PT symmetry

The fidelity susceptibility is a tool for studying quantum phase transitions in the Hermitian condensed matter systems. Recently, it has been generalized with the biorthogonal basis for the non-Hermitian quantum systems. From the general perturbation description with the constraint of parity-time (PT) symmetry, we show that the fidelity F is always real for the PT-unbroken states. For the PT-broken states, the real part of the fidelity susceptibility Re[XF] is corresponding to considering both the PT partner states, and the negative infinity is explored by the perturbation theory when the parameter approaches the exceptional point (EP). Moreover, at the second-order EP, we prove that the real part of the fidelity between PT-unbroken and PT-broken states is ReF=12. Based on these general properties, we study the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain. We find that for both interacting and non-interacting systems, the real part of fidelity susceptibility density goes to negative infinity when the parameter approaches the EP, and verifies it is a second-order EP by ReF=12.

Approximately stealth black hole in higher-order scalar-tensor theories

We investigate a generic quadratic higher-order scalar-tensor theory with a scordatura term, which is expected to provide a consistent perturbative description of stealth solutions with a timelike scalar field profile. In the DHOST subclass, exactly stealth solutions are known to yield perturbations infinitely strongly coupled and thus cannot be trusted. Beyond DHOST theories with the scordatura term, such as in ghost condensation and U-DHOST, we show that stealth configurations cannot be realized as exact solutions but those theories instead admit approximately stealth solutions where the deviation from the exactly stealth configuration is controlled by the mass scale M of derivative expansion. The approximately stealth solution is time-dependent, which can be interpreted as the black hole mass growth due to the accretion of the scalar field. From observed astrophysical black holes, we put an upper bound on M as ĉ D1 1/2 M ≲ 2 × 1011 GeV, where ĉ D1 is a dimensionless parameter of order unity that characterizes the scordatura term. As far as M is sufficiently below the upper bound, the accretion is slow and the approximately stealth solutions can be considered as stealth at astrophysical scales for all practical purposes while perturbations are weakly coupled all the way up to the cutoff M and the apparent ghost is as heavy as or heavier than M.

A superconfiguration calculation of opacity with consistent bound and continuum electron treatments using green’s functions

One of the challenges in calculating the opacity of dense plasmas is the difficulty in consistently modeling electrons bound to nuclei and those that exist within the continuum of free states in electronic structure models. We address this issue by adapting the green’s function approach, originally developed for use in average atom calculations, to the determination of superconfiguration (SC) electronic structure. The spectra created using these SCs indicate that a consistent treatment of continuum electronic structure is important for phenomena involving electrons near ionization thresholds, such as the pressure ionization of bound states and the opacity due to transitions near bound-free edges. Though important for dense plasmas, the detailed incorporation of continuum electrons into structure calculations does not have significant impact on the recent discrepancies between the predicted and measured opacity of hot, dense iron (Bailey et al 2015 Nature 517 56). We find that the inclusion of plasma effects through an ion-sphere model along with our treatment of continuum electronic states gives a description of pressure ionization in hot, dense aluminum that is in better agreement with experiment than methods that rely on perturbative descriptions of the plasma environment (Hoarty et al 2013 Phys. Rev. Lett. 110 265003).

Continuous absorption and emission of light by the heteronuclear rare gas (ArXe)+ and (KrXe)+ ions

Studies of radiative transitions between ground and charge transfer excited terms of heteronuclear rare-gas (ArXe)+ and (KrXe)+ ions with small and moderate dissociation energies (D0 ArXe+ =179 and D0 KrXe+ =389 meV) are reported. Potential energy curves and dipole transition matrix elements are evaluated using ab initio calculations based on the CASSCF method followed by the NEVPT2 treatment and perturbative description of relativistic effects as implemented in the ORCA suite. We develop an efficient approach for the calculations of Boltzmann-averaged cross sections, rate constants, and absorption and emission coefficients associated with the integral contributions of bound-bound and bound-free transitions from a manifold of rovibrational states of the (RgXe)+ ion. A similar approach is used for the description of the free-free and free-bound transitions between different electronic terms of a quasimolecular (RgXe)+ ion temporarily formed during a collision of Ar or Kr atoms with Xe+ ions. Our method is based on the quantal version of the theory of non-adiabatic transitions in molecular and quasimolecular systems combined with the approximation of a quasicontinuum for rovibrational energy levels. This allowed us to obtain a semianalytic expression for the integral absorption properties particularly relevant at elevated temperatures. We perform a comprehensive analysis of the identified radiative processes in local thermodynamic equilibrium plasmas of rare gas Rg/Xe mixtures containing both atomic, Xe+, and molecular, RgXe+, ions and determine their role in the formation of the absorption and emission spectra in a wide range of wavelengths and gas temperatures. The results obtained are in good agreement with the available experimental data.

Semiclassical strong-field theory of phase delays in ω−2ω above-threshold ionization

Phase and time delays of atomic above-threshold ionization were recently experimentally explored in an $\omega -2\omega$ setting [Zipp et al, Optica 1, 361 (2014)]. The phases of wavepackets ejected from argon by a strong $2\omega$ pulse were probed as a function of the relative phase of a weaker $\omega$ probe pulse. Numerical simulations solving the time-dependent Schr\"{o}dinger equation (TDSE) displayed a sensitive dependence of the doubly differential momentum distribution on the relative phase between the $\omega$ and $2\omega$ fields. Moreover, a surprisingly strong variation of the extracted phase delays on the intensity of the probe pulse was found. We present a semiclassical strong-field description of the phase delays in the emission of electrons in an $\omega -2\omega$ setting and apply it to atomic hydrogen. Non-perturbative effects in both the $2\omega$ pump and the $\omega$ probe field are included. The semiclassical description allows tracing phase delays to path interferences between emission during different points in time of emission within the temporal unit cell of the two-color laser field. We find good agreement between the semiclassical saddle-point approximation, the full strong field approximation (SFA), and previous results applicable in the perturbative limit of probe fields. We show that the RABBIT-like perturbative description of phase delays breaks down for stronger fields and higher-energy electron emission. In this regime, characterization of the ionization signal requires an entire ensemble of phase delays {$\delta_i(E)$} with $i=1,2,\ldots$ the difference in photon numbers of the strong $2\omega$ field involved in the interfering paths. Comparison between SFA and TDSE calculations reveals the influence of the Coulomb field even in this strong-field scenario.

Investigating the structure of gluon fluctuations in the proton with incoherent diffraction at HERA

Impact parameter dependent dipole models are ideal tools for investigating the spatial structure of the proton. We investigate the incoherent ep cross section in exclusive J/psi photoproduction as measured by HERA, and find that as |t| increases, the models need several levels of substructure of gluon density fluctuations in order to describe the measured data well. In lieu of a perturbative description, we add this substructure by hand. This substructure is modelled as hotspots within hotspots. This enables us to describe measurements for |t|> 1 GeV^2, which is necessary for describing any observable which integrate over the t-spectrum, such as the rapidity or W_{gamma p}. We find that three levels of proton substructure are adequate for a good description of all available ep data up to |t|=30 GeV^2. We note that the gluonic density fluctuation structure follows a scaling behaviour, such that the logarithms of the number of hotspots and their size fall on a line, effectively reducing the available parameter space of the model. Our findings systematically constrains and provides a benchmark for the development of a perturbative model of spatial gluon fluctuations in nucleons.

Weak ergodicity breaking in Josephson-junction arrays

We study the quantum dynamics of Josephson-junction arrays. We find isolated groups of low-entanglement eigenstates that persist even when the Josephson interaction is strong enough to destroy the overall organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates lie in the inner part of the spectrum, far from the spectral edge, and provide a weak ergodicity breaking, reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity probes, we find that the system tends toward more ergodicity for increasing system size: The parameter range where the bulk of the eigenstates look nonergodic shrinks for increasing system size. We study two geometries, a one-dimensional chain and a two-leg ladder. In the latter case, adding a magnetic flux makes the system more ergodic.

Gravitational waves from first-order electroweak phase transition in a model with light sgoldstinos

We study previously unexplored possibility of triggering the first order electroweak phase transition (EWPT) by interactions of the Standard Model (SM) particles with the sector responsible for low scale supersymmetry breaking. The low-energy theory apart from the SM particles contains additional scalar degrees of freedom — sgoldstinos — which contribute to the effective scalar potential and thus can trigger the first order EWPT. Remarkably, the latter requires only moderate couplings in the scalar sector. The perturbative description in terms of the effective theory seems formally to be applicable upto the scale of supersymmetry breaking: the Landau pole in the scalar sector is above 108-109 GeV. We calculate the gravitational wave signal generated at this transition (it can be tested, e.g. by LISA, BBO and DECIGO) and briefly discuss the collider phenomenology of this scenario.