Engineering topics
Publications and source records attributed to Pisarski, Robert D. [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000278624759).
We present a straightforward derivation of the spectral representation of a scalar field at nonzero temperature, assuming that the field is relativistically invariant in vacuum. This form was first derived by Bros and Buchholz.
Here, we use a low-energy effective approach, the extended linear sigma model, to study realizations of the U(1) A anomaly with different operators, linear and quadratic in the ’t Hooft determinant. After discussing the parameterization in agreement with vacuum’s phenomenology, we investigate the influence of these different anomaly terms on the Columbia plot: the square of the ’t Hooft determinant favors a cross-over for small quark masses. Finally, we also discuss the extension of the ’t Hooft determinant to cases in which different mesonic multiplets interact with each other. Novel chiral anomalous interaction terms involving excited (pseudo)scalar states, pseudovector, and pseudotensor mesons are expressed via a mathematical extension of the determinant, denoted as a polydeterminant.
A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N x N complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.
In confined hadronic matter, the spontaneous breaking and restoration of chiral symmetry can be described by considering nucleons, 𝑁 + (939), and excited states of opposite parity, 𝑁 − (1535). In a cold, dense hadronic phase where chiral symmetry remains spontaneously broken, direct Urca decay processes involving the 𝑁 − are possible, e.g., 𝑁 − → 𝑁 + + 𝑒 − + $\bar{𝜈}_𝑒$. Here, we show that at low temperature and moderate densities, because the 𝑁 − are much heavier than the 𝑁 + , such cooling dominates over standard 𝑁 + direct Urca processes. This provides a strong astrophysical signature of the pattern of chiral symmetry restoration in neutron stars.
The phase diagram of QCD probably exhibits a moat regime over a large region of temperature 𝑇 and chemical potential 𝜇 ≠ 0. A moat regime is characterized by quasiparticle moatons (pions) whose energy is minimal at nonzero spatial momentum. At 𝜇 ≠ 0, higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge-invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.
At nonzero temperatures, the deconfining phase transition can be analyzed using an effective matrix model to characterize the change in holonomy. The model includes gluons and two-dimensional ghost fields in the adjoint representation, or “teens.” As ghosts, the teen fields are responsible for the decrease of the pressure as 𝑇 →𝑇 𝑑 , with 𝑇 𝑑 the transition temperature for deconfinement. Using the solution of this matrix model for a large number of colors, the parameters of the teen fields are adjusted so that the expectation value of the Polyakov loop is close to the values from the lattice. The shear, 𝜂, and bulk, 𝜁, viscosities are computed at nonzero holonomy to leading logarithmic order in weak coupling. In the pure glue theory, the value of the Polyakov loop is relatively large in the deconfined phase, ≈1/2 at 𝑇 𝑑 . Consequently, if 𝑠 is the entropy density, while 𝜂/𝑠 decreases as 𝑇 →𝑇 𝑑 , it is still well above the conformal bound. In contrast, 𝜁/𝑠 is largest at 𝑇 𝑑 , comparable to 𝜂/𝑠, then falls off rapidly with increasing temperature and is negligible by ∼2𝑇 𝑑 .
Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC) 2 -ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable “surrogate constructed” method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC) 2 methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model—quantum electrodynamics for a single, massive fermion in 1 +1 dimensions—and show that our method can be used to accurately extrapolate to the continuum limit.