Conference

In the Statistics literature there are three main frameworks for causal modeling: counterfactuals (aka potential outcomes), non-parametric structural equation models (NPSEMs) and graphs (aka path diagrams or causal Bayes nets). These approaches are similar and, in certain specific respects, equivalent. However, there are important conceptual differences and each formulation has its own strengths and weaknesses. These divergences are of relevance both in theory and when the approaches are applied in practice. This talk will introduce the different frameworks, and describe, through examples, both the commonalities and dissimilarities. In particular, we will see that the “default” assumptions within these frameworks lead to different identification results when quantifying mediation and, more generally, path-specific effects.

Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell’s theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell’s result is an early foray into the field of causal inference and that the insights derived from almost 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This tutorial will highlight some of what is happening at the intersection of these two fields.

This work investigates the ferroelectric properties of γ − In₂Se₃, a material that uniquely retains its spontaneous polarization at the nano-scale, making it resistant to depolarizing fields. With a direct band gap of 1.8 eV and the ability to switch between insulating and semiconducting phases at room temperature, γ − In₂Se₃ holds promise for next-gen memory devices, where its stable ferroelectricity could revolutionize data storage and processing.

The black hole information paradox is a fundamental conflict between the quantum-mechanical and thermodynamic descriptions of black holes, specifically of their particle-emission process known as the Hawking radiation. The paradox concerns whether the radiation of a black hole is a unitary time evolution or a thermal process that erases most information about the initial state of the black hole. Multiple black hole models (e.g. [1,2]) were shown to exhibit the Page curve behavior, suggesting the unitarity of the Hawking radiation. However, without a verified theory of quantum gravity, the exact structure of black holes remains undetermined, and we need a model-independent way to test black hole unitarity. My project thus aims to develop a general framework for testing black hole unitarity by searching for its physical signatures. In particular, we employ the "hybrid" RST model [3], which possesses a Page-curve behavior, and study whether the unitarity is manifested in the transition rate of the Unruh-DeWitt particle detector. [1] Hong Zhe Chen, Robert C. Myers, Dominik Neuenfeld, Ignacio A. Reyes, Joshua Sandor. Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane". https://doi.org/10.48550/arXiv.2010.00018. [2] Yohan Potaux, Sergey N. Solodukhin, and Debajyoti Sarkar. "Spacetime Structure, Asymptotic Radiation, and Information Recovery for a Quantum Hybrid State.” Physical Review Letters 130, no. 26 (June 30, 2023): 261501. https://doi.org/10.1103/PhysRevLett.130.261501. [3] Yohan Potaux, Debajyoti Sarkar, and Sergey N. Solodukhin. "Quantum States and Their Back-Reacted Geometries in 2D Dilaton Gravity.” Physical Review D 105, no. 2 (January 12, 2022): 025015. https://doi.org/10.1103/PhysRevD.105.025015.

It may be the case that a spacetime exhibits no asymptotia where gauge invariant observables can be defined in a natural way. On such occasions the introduction of a timeline boundary may be helpful. We therefore discuss the initial boundary value problem in the context of General Relativity.

The theory $S = \int\text{d}^{4-\epsilon}x\left(\frac{1}{2}|\partial\phi|^2 - \frac{m^2}{2}|\phi|^2-\frac{g}{16}|\phi|^4\right)$ exhibits a global $U(1)$ symmetry, and the operators $\phi^n$ ($\bar\phi^n$) have charge $n$ ($-n$) with respect to this symmetry. By rescaling the fields and the coupling constant, it is possible to work in a double limit $n\to\infty$, $g\to 0$ with $\lambda = gn$ kept constant. In this way, it is possible to compute 2-point functions of the form $\langle \phi^n(x) \bar\phi^n(0) \rangle$ in the large $n$ limit, either diagrammatically by a resummation of the leading contribution at all orders in $g$, or using semiclassical methods through the saddle point approximation. This second approach is particularly powerful because it can also be applied to the theory on a curved background. This allows obtaining the form of the 2-point function for an arbitrary metric, and by functionally differentiating with respect to it, it is also possible to obtain, in the flat theory, the 3-point function $\langle T^{ij}(z) \phi^n(x) \bar \phi^n(0) \rangle$ in which an energy-momentum tensor has been inserted. This allows for a non-trivial check of the conformal symmetry of this sector of the theory by verifying the Ward identities that this 3-point function should satisfy.

We discuss the concept of spontaneous symmetry breaking and illustrate it with a general example. We consider Wigner-Weyl and Nambu-Goldstone realisations of symmetry in the quantum theory. Next, we state Goldstone’s theorem and sketch its proof. We discuss why quantum chromodynamics is not realised in the Wigner-Weyl mode.

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and high-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but does directly probe on the free function that defines the event horizon. Based on these, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

In this work, we propose a systematic method to obtain the effective field theory of the quantum dissipative systems which nonlinearly realize symmetries. We focus on the high temperature or Brownian limit, in which the effective action of the dissipative dynamics is localized in time. We first introduce a microscopic model at the linear response level, which shows how the dissipative dynamics on Lie group emerges effectively through the reduced dynamics of a system interacting with a thermal bath. The model gives a systematic method to give the Langevin equation which is covariant with respect to the symmetries of the system. In addition, the model shows a systematic way to go beyond the Gaussian white noise and the interaction between the noise and dissipation. Then, using the dynamical KMS symmetry, without any reference to the microscopic structure of the bath, we obtain the most general effective action of the nonlinearly realized dissipative dynamics at high temperature. The universal dissipative coefficients are larger than the case of the linear response approximation. Then, we focus on the case of Ohmic friction where the corresponding dissipative coefficients are more restricted; we suggest an alternative model, the bulk model, to describe any Ohmic dissipative system at high temperature. The Bulk model provides a geometrical picture for the noise in the case of Ohmic friction.

This talk will be based on SciPost Phys. 17, 021 (2024). Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this talk, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the $g$-function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators $\Delta^{+0}_\alpha$ and changing operators $\Delta^{+-}_\alpha$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results $g=0.602(2),\Delta^{+0}_0=0.108(5)$ and $\Delta^{+-}_0=0.84(5)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.

The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing, with next-leading-order non-unital perturbative behaviour. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. This work is based on forthcoming work with Diego Martin, Zoe Holmes, and Marco Cerezo, in affiliation with Los Alamos National Laboratory.