Correlations and commuting transfer matrices in integrable unitary circuits

We consider a unitary circuit where the underlying gates are chosen to be \check{R}Ř-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

Volatility Parameterization of Ambient Organic Aerosols at a rural site of the Northern China Plain

The volatility of organic aerosols plays a key role in determining their gas-particle partitioning, which subsequently alters the physicochemical properties and atmospheric fates of aerosol particles. Nevertheless, an accurate estimation of the volatility of organic aerosols (OA) remains challenging. Because most standard particulate organic compounds are scarce, on the other hand, their vapor pressures are too low to estimate by most traditional methods. Here, we deployed an iodide-adduct Long Time-of-Flight Chemical Ionization Mass Spectrometer (LToF-CIMS) coupled with a Filter Inlet for Gases and AEROsols (FIGAERO) to probe the relationship between the molecular formulas of atmospheric organic aerosol’s components and their volatilities. A number of Tmax (i.e., the temperature corresponding to the first signal peak of thermogram) were abstracted and validated from the desorption thermograms of mixed organic and inorganic calibrants which were atomized and then collected onto a Teflon filter. Besides, 30 filter samples of ambient air were collected in winter 2019 at Wangdu station in Beijing-Tianjin-Hebei region, and analyzed by FIGAERO-LToF-CIMS, leading to the identification of 1,448 compounds dominated by the CHO (containing carbon, hydrogen, and oxygen atoms) and CHON (containing carbon, hydrogen, oxygen, and nitrogen atoms) species. Among them, 181 organic formulas including 91 CHO and 90 CHON compounds were then selected since their thermograms can be characterized with clear Tmax values in more than 20 out of 30 filter samples and subsequently divided into two groups according to their O / C ratios. The mean O / C of these two groups are 0.56 ± 0.35 (average ± one standard deviation) and 0.18 ± 0.08, respectively. We then obtained the correlation functions between volatility and elemental composition for the two group compounds. Compared with previous volatility parameterizations, our correlation functions provide a better estimation of the volatility of semi-volatility organic compounds (SVOCs) and low-volatility organic compounds (LVOCs) in the ambient organic aerosols. Furthermore, we suggest that there should be specialized volatility parameterizations for different O / C organic compounds.

Fermi-gas correlators of ADHM theory and triality symmetry

We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d \mathcal{N}=4𝒩=4 ADHM theory with a gauge group U(N)U(N), an adjoint hypermultiplet and ll hypermultiplets which can describe a stack of NN M2-branes at A_{l-1}Al−1 singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.

Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite.

Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions

We show that, when investigating Wilson-fermions correlation functions on the lattice, one is bound to encounter major difficulties in defining their dispersion relation, even at tree level. The problem is indeed quite general and, although we stumbled upon it while studying Coulomb-gauge applications, it also affects gauge fixed studies in covariant gauges, including their most popular version, Landau gauge. In this paper we will discuss a solution to this problems based on a redefinition of the kinematic momentum of the fermion.

Crossing antisymmetric Polyakov blocks + dispersion relation

Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the ‘+ type Polyakov blocks’. These blocks are built from AdSd+1 Witten diagrams. In 1d they encode the ‘+ type’ analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent ‘locality constraints’ in addition to the usual CFT sum rules given by the ‘Polyakov conditions’. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

Correlation functions and transport coefficients in generalised hydrodynamics

We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.