Scientific Series

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas. We provide a simplifying perspective onto convolutions through tensor networks (TNs) which allow reasoning about the underlying tensor multiplications by drawing diagrams, and manipulating them to perform function transformations and sub-tensor access. We demonstrate this expressive power by deriving the diagrams of various autodiff operations and popular approximations of second-order information with full hyper-parameter support, batching, channel groups, and generalization to arbitrary convolution dimensions. Further, we provide convolution-specific transformations based on the connectivity pattern which allow to re-wire and simplify diagrams before evaluation. Finally, we probe computational performance, relying on established machinery for efficient TN contraction. Our TN implementation speeds up a recently-proposed KFAC variant up to 4.5x and enables new hardware-efficient tensor dropout for approximate backpropagation.

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Zoom link https://pitp.zoom.us/j/99090845943?pwd=NHBNVTNnbDNSOGNSVzNGS21xcllFdz09

Recently, models with different properties have been proposed for polymerized dust collapse and regular black holes. To fully understand their properties and differences, we provide a systematic procedure to construct effective polymerized spherically symmetric models encoding holonomy corrections as $1+1$d field theory from effective regular cosmological dynamics or stationary effective metrics. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangians in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. The effective dynamics can reproduce known regular black hole solutions, including Bardeen and Hayward, by a suitable choice of holonomy corrections. As a concrete example, we construct an effective model compatible with the improved dynamics of loop quantum cosmology in the decoupled LTB sector. We compare it with several effective polymerized models recently introduced in the context of loop quantum gravity and gain some new insights into the presence of shocks.

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Zoom link https://pitp.zoom.us/j/99966795418?pwd=Ty9mRXNML3NsUXdvcU1WUTdCaWpVZz09

Extreme mass-ratio binary black hole systems, known as EMRIs, are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). We hope to use these systems to probe black hole spacetimes in exquisite detail and make precision measurements of supermassive black hole properties. Accurate models using general relativistic perturbation theory will allow us to unlock the potential of these unique systems. Such models must include post-geodesic corrections, which account for forces driving the smaller black hole away from a geodesic trajectory. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime, introducing post-geodesic correction called the spin-curvature force. In this talk, I will present our calculation of EMRI waveforms that include both spin-curvature forces and the leading backreaction due to gravitational radiation. We use a near-identity transformation to eliminate dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies; such efficiency is crucial for LISA data analysis. Finally, I will discuss what aspects still need to be included in future calculations so that we can use EMRIs for a new era of precision gravitational-wave astronomy, addressing outstanding puzzles in astrophysics, cosmology and fundamental theoretical physics.

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Zoom link https://pitp.zoom.us/j/91917788358?pwd=MWp5OUhxbkRmZDFxWWE4cHR0VlBTUT09

The current ΛCDM concordance model has been widely successful in describing our Universe. However, crucial questions, such as the H0 tension, remain unanswered and are becoming increasingly critical with the continuous release of high-precision cosmological data. This has led to the exploration of modified ΛCDM models, one of them being the coupled quintessence, or Coupled Dark Energy (CDE) model.  Here, we perform for the first time a tomographic analysis of coupled dark energy, where the coupling strength is parametrised and constrained in different redshift bins. We employ cosmic microwave background data from Planck, ACT and SPT, showing the impact of different choices that can be made in combining these datasets. Then, we use a range of low redshift probes to test CDE cosmologies, both for a constant and a tomographic coupling. In particular, we use for the first time data from weak lensing, galaxy clustering, and 3x2pt galaxy-galaxy lensing cross-correlation data. For CMB and background datasets, a tomographic coupling allows for β values up to one order of magnitude larger than in previous works, in particular at z < 1. The use of 3x2pt analysis then becomes important to constrain β at low redshifts, even when coupling is allowed to vary: for 3x2pt we find, at 0.5 < z < 1, β = 0.018+0.007 −0.011, comparable to what CMB and background datasets would give for a constant coupling. This makes upcoming galaxy surveys potentially powerful probes to test CDE models at low redshifts. 

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Zoom link https://pitp.zoom.us/j/94442666279?pwd=OTgrMTZ5dTRzZmc2WFhuMkF3ekJzdz09

The Monster Lie Algebra $\mathfrak m$ has two well-known avatars: It is a Borcherds' algebra that is also a quotient of the physical space of a specific tensor product of vertex algebras. In this talk, I will discuss a construction of vertex algebra elements that project to bases for subalgebras of $\mathfrak m$ isomorphic to $\mathfrak{gl}_2$, corresponding to each of the imaginary simple roots of the Monster Lie algebra.

Furthermore, for a fixed imaginary simple root, I will illustrate how the action of the Monster simple group on the Moonshine module induces an action of the Monster group on the set of the $\mathfrak{gl}_2$ subalgebras constructed this way. I will discuss this action and related open questions.

This talk is based on joint work with Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich, and Scott H. Murray.

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Zoom link TBA

Abstract TBA

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Zoom link https://pitp.zoom.us/j/98123499206?pwd=QWlHcFBJWE8zRTlyT1A5WUVsQS9NUT09

Measuring the temperature of your coffee should not change the amount of coffee in your cup. This holds because the operators representing the coffee’s energy and volume commute. The intuitive assumption that conserved quantities, also known as charges, commute, underpins basic physics derivations, like that of the thermal state's form and Onsager coefficients. Yet, operators' failure to commute plays a key role in quantum theory, e.g. underlying uncertainty relations. Lifting this assumption has spawned a growing subfield of quantum many-body physics [1].

How can one argue that charges’ noncommutation caused a result? To isolate the effects of charges’ noncommutation, we created analogous models that differ in whether their charges commute and discovered more entanglement in the noncommuting-charge model [2]. We further introduce noncommuting charges (an SU(2) symmetry) into monitored quantum circuits, circuits with unitary evolutions and mid-circuit projective measurements. Numerically, we find that the SU(2)-symmetric model has a critical phase in place of the area-law phase typically found in these circuits [3]. I will focus on the results from Ref 2 and 3. Time permitting, I'll briefly explain how one can use Lie Algebra theory to build the Hamiltonians necessary for testing the predictions of noncommuting charge physics [4].

[1] Majidy et al. "Noncommuting conserved charges in quantum thermodynamics and beyond." Nat Rev Phys (2023)
[2] Majidy et al. "Non-Abelian symmetry can increase entanglement entropy.” PRB (2023)
[3] Majidy et al. "Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits." PRB (2023)
[4] Yunger Halpern and Majidy “How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics” npj QI (2022)

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Zoom link https://pitp.zoom.us/j/97193579200?pwd=MkdmbWo1S2lUcUZtUFpORk5VbnFBdz09

We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal (h) fields. We show that, for all h, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional - argued to yield exact results at low frequencies - that expands in powers of a spin glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p-rotor model at nonzero h: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition.

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Zoom link https://pitp.zoom.us/j/98757418107?pwd=U1hiQnpKTDI4ajUyL04zRmQ4dVg3UT09

Using a novel version of the gravitational path integral for compact spatial regions at a moment of time symmetry, I argue that a region of space can encode a larger one. In particular, I show that the entanglement entropy of a region of space equals the area of the boundary of the smallest region that contains it. The key insight is to include the effects of the gravitational edge modes associated with the region in the path integral. This result is consistent with a recent conjecture by Bousso and Penington.

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Zoom link https://pitp.zoom.us/j/93301151464?pwd=Z2t5QlpUQ3hoaEkwQlFZS2tITGpEQT09

Dark matter interactions with Standard Model particles can inject energy at early times, altering the standard evolution of the early universe. In particular, this energy injection can perturb the spectrum of the cosmic microwave background (CMB) away from that of a perfect blackbody, alter the CMB anisotropy spectrum, and affect processes by which the first stars form. For this study, I will discuss recent work to upgrade the DarkHistory code package to more carefully track interactions among low energy electrons, hydrogen atoms, and radiation, in order to accurately compute the evolution of the CMB spectral distortion in the presence of Dark Matter energy injection. I will show results for the contribution to the spectral distortions from redshifts z < 3000 for arbitrary energy injection scenarios, new CMB anisotropy constraints on light dark matter, as well as the effect of exotic energy injection on early star formation.

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Zoom link https://pitp.zoom.us/j/99559611185?pwd=bDFVdmpyVE5CbXVXVHdEL29Md0FXUT09

Driven by rapid advancements in quantum simulation capabilities across diverse physical platforms, open quantum systems are now of great interest, with special focus on thermalization processes of interacting many-body systems. Various techniques have been used to study operator spreading, to characterize entanglement dynamics, and even to identify exotic phases enabled by dynamical symmetries.

This talk will present a novel perspective on dynamical quantum systems that is capable of reproducing many previous results under a single intuitive framework and enables new results in symmetry-constrained systems. This is accomplished via a mapping between the dynamics averaged over Brownian random time evolution and the low-energy spectrum of a Lindblad superoperator, which acts as an effective Hamiltonian in a doubled Hilbert space. Doing so, we identify emergent hydrodynamics governing charge transport in open quantum systems with various symmetries, constraints, and ranges of interactions. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a simple, general, and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution, and by extension, thermalizing quantum systems.

O. Ogunnaike, J. Feldmeier, J.Y. Lee, "Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range Interactions," arXiv:2304.13028 (accepted to PRL)

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The cosmic microwave background is a sensitive probe of early-Universe physics, and yet fundamental constants at recombination can differ from their present-day values due to degeneracies in the standard cosmological model. Such scenarios have been invoked to reconcile discrepant measurements of the present-day expansion rate, but even absent such motivation they raise the intriguing possibility of yet-undiscovered physics coupled directly to Standard Model particles. I will discuss theories in which a new scalar field shifts the electron's mass at early times; viable models are already stringently constrained by measurements of quasar absorption lines, the abundances of light elements, and the universality of free fall. I will show that the remaining parameter space is exactly that which allows not only the primary cosmic microwave background but also low-redshift distances to be consistent with observations. After presenting the results of parameter inference I will discuss additional cosmological and laboratory signatures of the model.

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Zoom link https://pitp.zoom.us/j/99705853481?pwd=MTZRWC9hREkvOXpiZkxCM3UvdnRNQT09