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Nonequilibrium Aspects of Integrable Models

Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Temporal entanglement entropy as a probe of renormalization group flow

The recently introduced concept of timelike entanglement entropy has sparked a lot of interest. Unlike the traditional spacelike entanglement entropy, timelike entanglement entropy involves tracing over a timelike subsystem. In this work, we propose an extension of timelike entanglement entropy to Euclidean space (“temporal entanglement entropy”), and relate it to the renormalization group (RG) flow. Specifically, we show that tracing over a period of Euclidean time corresponds to coarse-graining the system and can be connected to momentum space entanglement. We employ Holography, a framework naturally embedding RG flow, to illustrate our proposal. Within cutoff holography, we establish a direct link between the UV cutoff and the smallest resolvable time interval within the effective theory through the irrelevant $T\bar{T}$ deformation. Increasing the UV cutoff results in an enhanced capability to resolve finer time intervals, while reducing it has the opposite effect. Moreover, we show that tracing over a larger Euclidean time interval is formally equivalent to integrating out more UV degrees of freedom (or lowering the temperature). As an application, we point out that the temporal entanglement entropy can detect the critical Lifshitz exponent z in non-relativistic theories which is not accessible from spatial entanglement at zero temperature and density.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Renormalized quark masses using gradient flow

We propose a new and simple method for determining the renormalized quark masses from lattice simulations. Renormalized quark masses are an important input to many phenomenological applications, including searching and modeling physics beyond the Standard Model. The nonperturbative renormalization is performed using gradient flow combined with the short-flow-time expansion that is improved by renormalization group (RG) running to match to the $\overline{MS}$ scheme. Implementing the RG running perturbatively, we demonstrate this method works reliably at least up to the charm-quark mass and exhibits an easily attainable “windowing condition.” Using RBC/UKQCD’s (2+1)-flavor Shamir domain-wall fermion ensembles with Iwasaki gauge action, we find 𝑚 $\overline{MS}$ 𝑠⁡ (𝜇 = 2 GeV) = 89⁢(3) MeV and 𝑚 $\overline{MS}$ 𝑐 ⁡(𝜇 = 3 GeV) = 972⁢(16) MeV. These results predict the scale-independent ratio 𝑚 𝑐 /𝑚 𝑠 = 12.1⁢(4). Generalization to other observables is possible, providing an efficient approach to determine nonperturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals

Abstract We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the binary as a composite particle. We spell out our procedure to study such effects: assembling tree amplitudes via generalized-unitarity methods and employing the closed-time-path formalism to derive the causal effective actions, which encompass the full conservative and dissipative dynamics. We push through to a new state of the art for these higher-order effects, up to the third subleading tail effect, at order$$ {G}_N^5 $$ G N 5 and the 5-loop level, which corresponds to the 8.5PN order. We formulate the consequent dissipated energy for these higher-order corrections, and carry out a renormalization analysis, where we uncover new subleading RG flow of the quadrupole coupling. For all higher-order tail effects we find perfect agreement with partial observable results in PN and self-force theories, where available.

Physics↗

Apparent fine tunings for field theories with broken space-time symmetries

We exhibit a class of effective field theories that have hierarchically small Wilson coefficients for operators that are not protected by symmetries but are not finely tuned. These theories possess bounded target spaces and vacua that break space-time symmetries. We give a physical interpretation of these theories as generalized solids with open boundary conditions. We show that these theories realize unusual RG flows where higher dimensional (seemingly irrelevant) operators become relevant even at weak coupling. Finally, we present an example of a field theory whose vacuum energy relaxes to a hierarchically small value compared to the UV cut-off.

Physics↗

Background independent quantum field theory and gravitating vacuum fluctuations

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein’s equation. Self-consistent background spacetimes are scale dependent, and therefore “going on-shell” at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this “rigid picture” breaks down after a very short RG time already (less than one decade of scales) because of a “scale horizon” that forms. Furthermore, we critically reanalyze and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

In-Situ Detection of Process-Induced Porosity During Cure of Out-of-Autoclave Composites

Composite materials offer unique benefits in aerospace applications, including high strength-to-weight ratio, and are becoming increasingly used by industry manufacturers. Current manufacturing and processing methods can lead to defects in the composites, which are identified after fabrication using inspection methods. This study utilized a high-temperature ultrasonic inspection system to detect process-induced porosity in an out-of-autoclave (OOA) composite panel during cure. In order to perform ultrasonic scans in-situ during cure, the system needed to be able to operate at oven temperatures up to 200 °C. There are no commercially available ultrasonic scanning systems that can operate continuously at these temperatures, so an enclosure was fabricated to insulate the ultrasonic system in the curing oven. The enclosure housed a MISTRAS® motorized X-Y raster scanner and contact transducer (Olympus® X2002). The Olympus® X2002 contact transducer is a continuous high-temperature delay line transducer with a center frequency of 2.25 MHz. In order to prevent the inside of the enclosure from reaching high temperatures, a sparge pipe inside the cooling enclosure was connected to a liquid nitrogen (LN2) tank outside of the oven via insulated hoses. The cooling system was automatically controlled by a temperature controller that was programmed to open a solenoid valve along the hose at 31 ℃ and close at 28 ℃ inside the cooling enclosure. When the solenoid valve was open, LN2 would flow from the LN2 tank and vaporize prior to reaching cooling enclosure. A U-shaped sparge pipe had holes drilled along its length to uniformly introduce cold nitrogen gas into the cooling enclosure. This prevented the motors from ever reaching the maximum desired operating temperature of 38 ℃. In the bottom of the enclosure, the tool plate was placed with the composite facing the outside of the enclosure, exposing it to the temperatures of the oven. The tool plate was 63.5 mm thick borosilicate glass, which was chosen for its low ultrasonic attenuation and moderate thermal conductivity. A thin layer of ultrasonic couplant was placed on the tool plate. The transducer sent and received ultrasonic waves through the tool plate into the composite. A MISTRAS® Remote UT System performed all wave generation, analog to digital conversion, and data acquisition and processing. The transducer was connected directly to the Remote UT System via a high-temperature BNC cable (CD International, RG-316). Polyimide insulated copper wire was used to connect the scanner to a 2-axis motor drive, which was connected to the Remote UT System. The motor drive and Remote UT System were located outside the industrial oven. A diagram of the ultrasonic system is shown in Figure 1. Figure 1: Diagram of ultrasonic in-situ defect detection system. In this study, a porosity gradient was introduced into the carbon fiber reinforced polymer (CFRP) composite through a misfit of the part and caul plate. A 24-ply quasi-isotropic ([0/90, ±45]12S) composite panel was laid up using Newport® AS4C-M/NB321 out-of-autoclave (OOA) plain weave (PW) prepreg (42% resin content, 195 g/m2). The first 16 plies were 203 mm × 203 mm. Ply drops were incorporated into the panel by decreasing the length of plies 17-24. The sizes of each ply are included in Table 1. All plies were centered along their length (x-axis) creating a trapezoidal type cross-section. Table 1: Ply sizes Plies Length (mm) Width (mm) 1-16 203 203 17-18 102 203 19-20 85 203 21-22 68 203 23-24 51 203 A 15-5 stainless steel caul plate (Size: 203 × 203 × 1.2 mm) was placed on the laminate. The composite and caul plate were vacuum bagged to the tool plate. Per the product datasheet, Newport 321 can be cured between 121 °C and 149 °C, depending on service temperature, with a hold for 90-120 minutes. Based on prior thermal testing of the cooling enclosure, the desired composite temperature cycle could be attained when the air temperature of the oven was ramped to 160 °C at a rate of 1.7 °C/min with a 3 hour hold. The extended hold was not necessary to cure the composite, but did allow for additional scans at the cure temperature during preliminary testing. The composite panel was under vacuum pressure for the entire cure cycle. Under vacuum, the caul plate deformed causing high and low pressure regions. The low-pressure regions formed high porosity in the composite part. The ultrasonic data collected showed that the inspection system was able to monitor the evolution of porosity within the composite throughout the cure cycle. Fifty scans of a 203 mm × 51 mm (8 in. × 2 in.) area of the composite were completed throughout the cure cycle. The scan speed was set to 43 mm/s in the x-direction and 36 mm/s in the y-direction, with a 1.0 mm/pixel resolution in both directions. Each scan took approximately five minutes to complete. Figure 2 shows C-scan amplitude data (top view) from one scan during the cure cycle. The color map indicates the maximum amplitude (%) measured with a time gate that contains reflections from the back surface (furthest from the transducer in contact with the caul plate) of the composite. Because porosity in the composite increases the ultrasonic attenuation in the composite part, a higher amplitude (red) indicates low porosity and a lower amplitude (blue) indicates high porosity. The regions where the caul plate was applying increased pressure (center and ends of the panel) resulted in reduced porosity, whereas the ply drop regions had reduced pressure and thus had higher porosity. Figure 2: Amplitude C-scan (top view) of OOA composite from one scan during the 160 °C temperature hold. Higher amplitude (red) indicates low porosity. Lower amplitude (blue) indicates high porosity. A B-scan is a two-dimensional image plotting the ultrasonic signals from a single y-position at every x-location of the composite panel. The travel time (μs) of the ultrasonic wave (representing the through-thickness location) is plotted along the y-axis, and the ultrasonic wave signal is represented as a contour map. Based on the B-scan data, the location of the defects with respect to the composite thickness was able to be determined. The ply drop regions had high porosity near the front (tool plate) surface of the composite (Figure 3). Figure 3: B-scan (cross-section view) of OOA composite from one scan during the 160 °C temperature hold. Using the data obtained from amplitude C-scans and B-scans throughout the cure cycle, the high and low porosity regions within the composite laminate were detected and localized with high spatial resolution. This paper will discuss the evolution of porosity content in the OOA composite during cure. OOA tests aided the transition of this system to an autoclave, which is the primary method of curing aerospace-grade thermoset composites.

Tyler B. Hudson↗