Free Fields Research Articles

A theoretical model for compressible bubble dynamics considering phase transition and migration

A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form, with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller–Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapour proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapour proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with decreasing Mach number and increasing vapour proportion. The energy analyses of the bubble reveal that the presence of vapour inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.

Modularity in d > 2 free conformal field theory

We derive new closed form expressions for the partition functions of free conformally-coupled scalars on S2D−1 × S1 which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions.

Perturbations of classical fields by gravitational shockwaves

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of point-like sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes.

Quotient quiver subtraction

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the SU(n) hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3dN=4 unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.

Entanglement in ( 1+1 )-dimensional free scalar field theory: Tiptoeing between continuum and discrete formulations

We review some classic works on ground state entanglement entropy in (1+1)-dimensional free scalar field theory. We point out identifications between the methods for the calculation of entanglement entropy and we show how the formalism developed for the discretized theory can be utilized in order to obtain results in the continuous theory. We specify the entanglement spectrum and we calculate the entanglement entropy for the theory defined on an interval of finite length L. Finally, we derive the modular Hamiltonian directly, without using the modular flow, via the continuum limit of the expressions obtained in the discretized theory. In a specific coordinate system, the modular Hamiltonian assumes the form of a free field Hamiltonian on the Rindler wedge. Published by the American Physical Society 2024

A perturbative approach to the non-relativistic string spectrum

In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS5×S5 spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions.

Higher-rank sectors in the hexagon formalism and marginal deformations

Abstract The hexagon approach provides an integrability framework for the computation of structure constants in N = 4 super Yang-Mills theory in four dimensions. Three-point functions are cut into two hexagonal patches, on which the excitations of the long-range Bethe ansatz of the spectrum problem scatter. To this end, the Bethe states representing the operators also need to be cut into two parts. In rank-one sectors such entangled states are fairly straightforward to construct so that most applications of the method have so far been restricted to this simplest case. In this article we construct entangled states for operators in psu(1, 1|2) sectors, importing a minimum of information from the nested Bethe ansatz. The idea is successfully tested against free field theory for a sample set of correlators with up to three higher-rank operators.
Further, we take a look at the same correlators in the presence of marginal deformations of the theory. While a systematic modification of the hexagon procedure remains out of reach for now, in practical applications the undeformed amplitudes are surprisingly efficient, especially for a certain one-parameter deformation.

Three-Dimensional Site Response Analysis of Clay Soil Considering the Effects of Soil Behavior and Type

To understand changes in bedrock motion at the ground surface, frequency effects, and spatial distribution within the soil, it is important to look at how a site responds to earthquakes. This is important for soil–structure interaction in structural and geotechnical earthquake engineering. This study deals with the effect of classifying clays according to shear wave velocity (stiff/medium/soft) and nonlinearity in behavior (linear/nonlinear) on the analysis of the site response. A 3D soil model with a combination of free fields and quiet boundaries and advanced constitutive models for soil to obtain accurate results was used to conduct this study. A strong TABAS earthquake was used to excite the compliant base of the model after converting the velocity record of TABAS to an equivalent surface traction force using a horizontal force–time history proportional to the velocity–time history. This study reveals that the site response analysis is affected by the type of clay soil and the soil material behavior, with soft clay soil causing higher PGV and PGV values in the linear case and lower values in the nonlinear case due to soil yielding, which causes soil response attenuation. This results in extremely conservative and expensive building designs when linear soil behavior is adopted. On the other hand, the applied earthquake exhibits greater attenuation at longer frequencies and greater amplification at mid and short frequencies. However, at frequencies near the applied earthquake frequency, neither attenuation nor amplification occurs. Furthermore, nonlinear soil behavior is crucial for soil evaluation and foundation design due to higher octahedral shear strain and settlement values, especially in softer soils, resulting from extensive plastic deformation.

Quantizing Carrollian field theories

Carrollian field theories have recently emerged as a candidate dual to flat space quantum gravity. We carefully quantize simple two-derivative Carrollian theories, revealing a strong sensitivity to the ultraviolet. They can be regulated upon being placed on a spatial lattice and working at finite inverse temperature. Unlike in conventional field theories, the details of the lattice-regulated Carrollian theories remain important at long distances even in the limit that the lattice spacing is sent to zero. We use that limit to define interacting continuum models with a tractable perturbative expansion. The ensuing theories are those of generalized free fields, with non-Gaussian correlations suppressed by positive powers of the lattice spacing, and an unbroken supertranslation symmetry.

Degradation mechanism for epoxy resins under combined electric, thermal and compressive stresses

Epoxy resins are widely used in equipment such as ultra-high voltage dry-type bushings, which are subjected to severe electric, thermal, and compressive stresses. Some physical mechanisms have already been proposed to explain the degradations generated by these different stresses, however their effects have not yet been quantified.. The degradation characteristics of epoxy resin under combined stresses of 8 kV/mm, 40 °C-120 °C, and 0–60 MPa were investigated in experiments. The results showed that the degradation characteristics turned significantly with the increase of compressive stress. With the increase in compressive stress, initially the partial discharge initiation voltage, tree initiation voltage and time to breakdown increased, and fractal dimension decreased. While the compressive stress exceeded the turning point, the characteristics were reversed. It can be suggested that opposing mechanisms exist. The free volume and phase field theories dominate at lower and higher stresses, respectively. A novel degradation model of the epoxy resin was proposed based on the theories above. When the compressive stress was low, the reduction of free volume played a dominant role in slowing down the degradation. When the compressive stress was high, the partial energy density concentration accelerated the degradation and played a dominant role. The molecular dynamics and finite element simulation of degradation process stress was carried out and proved consistent with experiments. It confirmed the proposed degradation model reliable and valid.

Recommendations for Psychosocial Support for Long-Distance Caregivers of Terminally Ill Patients

ContextThe provision of appropriate psychosocial support has a significant impact on quality of life for informal caregivers of terminally ill patients. Long-distance caregivers have specific wishes and needs for psychosocial support. ObjectivesTo date, no formal support measures for long-distance caregivers of terminally ill patients have been developed in Germany. The national Delphi study aimed at systematically and empirically generating recommendations for psychosocial support measures, tailored to this population. MethodsRecommendations were formulated on the basis of qualitative interviews exploring the support experiences and unmet needs of long-distance caregivers of terminally ill patients. Experts from hospice and palliative care rated the relevance and feasibility of 10 recommendations using two 4-point Likert-type scales. Additionally, suggestions for improvement were captured via free text fields. Recommendations were deemed to have achieved consensus when ≥ 80% of participants indicated “strongly agree” or “somewhat agree” for both relevance and feasibility. ResultsA total of 26 experts completed two Delphi rounds. Following the first round, eight of the 10 recommendations were revised according to participant feedback. After the second round, consensus was achieved for five of these revised recommendations. Three recommendations were rejected, as participants regarded them unfeasible due to a perceived lack of personnel resources. ConclusionThe consensus-based recommendations represent the first empirically grounded guidelines in Germany aimed at addressing the psychosocial needs of long-distance caregivers of terminally ill patients. The recommendations seek to raise awareness among both professional and voluntary workers regarding the specific support requirements of this understudied population.

A∞ perspective to Sen's formalism

Sen's formalism is a mechanism for eliminating constraints on the dynamical fields that are imposed independently from equations of motion by employing spurious free fields. In this note a cyclic homotopy associative algebra underlying Sen's formalism is developed. The novelty lies in the construction of a symplectic form and cyclic A∞ maps on an extended algebra that combines the dynamical and spurious fields. This algebraic presentation makes the gauge invariance of theories using Sen's formulation manifest.

Dimer piling problems and interacting field theory

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large-N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

Experimental Analysis of Noise Characteristics on Different Types of Pavements inside and outside Highway Tunnels

Aiming to reduce noise pollution and optimize the acoustic quality in highway tunnels, the noise characteristics on different types of pavements were analyzed and compared in this research, based on the on-site noise measurement in two tunnels with the free fields as a control group. Specifically, the noise characteristics include two aspects: various noise and noise time attenuation performance. Various noise includes on-board sound intensity (OBSI) noise and cabin noise. The noise time attenuation performance uses the indicator of reverberation time. Three types of pavements were measured, including dense-graded asphalt concrete (DAC) and single-layered and double-layered porous asphalt (PA) pavement. The results showed that, for the same type of pavement, compared with the free fields, the difference in OBSI noise in tunnels was within a range of less than 1 dBA; the cabin noise increased by 3.4 dBA~6.6 dBA. The noise level in tunnels was greater than that outside tunnels, and the longer tunnel exhibited higher traffic noise and worse noise time attenuation performances. For the same tunnel, PA pavement could reduce the cabin noise by 3.8 dBA~6.7 dBA. PA pavement also exhibited shorter reverberation time. The application of PA pavement could effectively improve the acoustic quality in the tunnel. This research contributes to noise pollution abatement and the improvement of the comfort and safety of drivers in tunnels.

Bosonic and fermionic coherence of N-partite states in the background of a dilaton black hole

We study the N-partite coherences of GHZ and W states for free bosonic and fermionic fields when any n observers hover near the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. We derive the more general analytical expressions for N-partite coherence, encompassing both physically accessible and inaccessible coherences in the context of the dilaton black hole. It has been found that the coherence of the bosonic field is greater than that of the fermionic field, while the entanglement of the fermionic field is greater than that of the bosonic field in dilaton spacetime. Additionally, the coherence of the W state is greater than that of the GHZ state, whereas the entanglement of the GHZ state is greater than that of the W state in curved spacetime. These results suggest that we should utilize suitable quantum resources and different types of particles for relativistic quantum information tasks.

Supersymmetric charge constraints on AdS black holes from free fields

Supersymmetric AdS black hole solutions exist only when their angular momenta and charges satisfy a certain constraint that depends on the dimension. We show that these nonlinear relations on the conserved charges agree with a computation in the dual supersymmetric CFT in its free limit, with interactions entering only through a uniform rescaling of all charges. Our computations apply to the highly non-trivial charge constraints for AdS4, AdS5 and AdS7 black holes, and generalize an earlier one for the analogous constraint in AdS3. Our results suggest a microscopic understanding of AdS black holes beyond the scope of supersymmetric indices.

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Quantum field theories of relativistic Luttinger fermions

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models. Published by the American Physical Society 2024

Theory of the cubic autoproduct and its utility for noisy direction of arrival estimation

Autoproducts are quadratic or higher products of frequency-domain acoustic fields that can mimic genuine fields at frequencies within or outside the original field's bandwidth. Past studies have found a variety of interesting autoproduct properties but have been limited to quadratic autoproducts. This paper presents cubic autoproduct theory and documents how noise suppression may be attained with the cubic frequency-difference autoproduct, a product of three frequency-domain acoustic fields. The cubic autoproduct's field equations, developed from the inhomogeneous Helmholtz equation, and analytical results in single- and two-path environments justify interpretating the cubic autoproduct as a pseudofield and underscore its similarities to the quadratic autoproducts. For nonzero field bandwidth, many frequency triplets satisfy the relationship for a single cubic autoproduct frequency. Thus, bandwidth averaging can lead to serendipitous noise suppression and is shown herein to facilitate field-phase-structure recovery from ideal free space fields corrupted by Gaussian noise. Cubic-autoproduct-based direction of arrival (DOA) estimation using signal and noise recordings collected in the ocean are found to be more accurate than conventional DOA estimates from the same data. In particular, cubic autoproduct results showed a 3–5 dB noise suppression advantage for 4- and 6-kHz direct- and reflected-path sounds broadcast 200 m to a four-element receiving array.

Type II string theory on AdS3×S3×T4 and symmetric orbifolds

We discuss in detail the 1+1-dimensional superconformal field theory dual to type II string theory on AdS3×S3×T4, emphasizing the string theoretic aspects of this duality. For one unit of Neveu-Schwarz (NS-NS) 5-brane flux (Q5=1), this string theory has been suggested to be dual to a grand-canonical ensemble of T4N/SN free symmetric orbifold conformal field theories (CFTs). We show how the string genus expansion emerges to all orders for the free orbifold grand-canonical correlation functions. We also discuss how the strong coupling limit of the NS-NS string theory arises (even at large N) in the free orbifold description, and argue why this limit does not have a weakly coupled RR description. The dual conformal field theory (CFT) includes (for all values of Q5) an extra T4 factor that is decoupled from perturbative string theory. We discuss the exactly marginal deformations that relate the different values of Q5, including the precise JJ¯ deformations mixing this extra T4 with the symmetric orbifold. Published by the American Physical Society 2024