Scientific Series

The Hartle-Hawking-Vilenkin state is defined on mini-superspace and is semiclassically related to inflationary theory.  However, the state suffers a few problems connected to the path integral of Euclidean or the Lorentzian measure of metrics.  In this talk, we will explore a way around these issues by working in the (Ashtekar) connection representation, a real Kodama-Chern-Simons state.  We find a generalized "Fourier Transform" that related the Chern-Simons-Kodama state to the Hartle-Hawking state beyond mini-superspace.  We end with some discussion and open ended questions for cosmology and quantum gravity.

LIGO's successful detection of gravitational waves has revitalized the theoretical understanding of the angular momentum carried away by gravitational radiation. An infinite-dimensional supertranslation ambiguity has presented an essential difficulty for decades of study. Recent advances were made to quantify the supertranslation ambiguity in the context of binary coalescence. In this talk, we will present the first definition of angular momentum in general relativity that is completely free from supertranslation ambiguity. The new definition of angular momentum is derived from the limit of the quasilocal angular momentum we defined previously.

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17^t for T gates). Our algorithm is state-of-the-art for this task:

as an example, in approximately 25 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50 qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. The Compute algorithm calculates the probability of a chosen measurement outcome to machine precision with run-time O(2^t−r(t−r)t) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105 and t=80 T-gates, and then compute the Born rule probability with a run-time consistently less than 104 seconds using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms.

Statistical mechanics is the branch of physics that explains how macroscopic properties of matter emerge from the behavior of its microscopic constituents. Population ecology studies how and why populations change over time and space, primarily due to the interaction among individuals and between individuals and the environment where they thrive. Although seemingly very different, both disciplines aim to explain large-scale phenomena based on a description of their underlying drivers, and statistical mechanics tools have been largely used to formalize population ecology. For over 100 years, however, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. 

In this presentation, I will first discuss why mathematical models are powerful tools to understand ecological processes. Then, I will show how traditional models of population dynamics emerge from ideal gas assumptions for individual movement and briefly touch on our recent efforts to refine those models combining more elaborated tools from statistical physics, random walk theory, and GPS tracking data of natural populations.

In this talk I will discuss the application of the so-called “consistency relations” for large scale structures to the study of primordial non-Gaussianities of the local f_NL type. I will first introduce the consistency relations themselves, commenting on some important aspects and underlying assumptions. I will then verify them (and their violation) using N-body simulations for the matter density in the Universe. This proves consistency relations to be a promising tool to apply in the forthcoming large scale structures surveys. I will conclude describing some work in progress aimed at finding a practical recipe to constrain f_NL from these relations.

We propose a new type of critical quantum liquids, dubbed Stiefel liquids, based on 2+1 dimensional Wess-Zumino-Witten models on target space SO(N)/SO(4). We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N = 5 and N = 6, respectively. Furthermore, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that the theories do not (at least not easily) admit any weakly-coupled UV completion. Such non-Lagrangian states are beyond the paradigm of parton gauge theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of mean-field construction also makes it difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.

It has been proposed that microscopic black holes can catalyze decay of metastable false vacuum. The calculations of the decay rate existing in the literature make use of the Euclidean time formalism developed for equilibrium configurations. This is not the case, however, for a realistic black hole formed by gravitational collapse and emitting Hawking radiation. I will review the motivations to study black hole catalysis of vacuum decay, propose a general method to calculate the decay rate, and illustrate it on a two-dimensional toy model.

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. In this talk, we show that this is not unique to the XXZ model, but happens also to the spin-1/2 Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

In this lecture we will show that the E8 and Leech lattices minimize energy of every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians). This theorem implies recently proven optimality of E8 and Leech lattices as sphere packings and broadly generalizes it to long-range interactions. The key ingredient of the proof is sharp linear programming bounds. To construct the optimal auxiliary functions attaining these bounds, we prove a new interpolation theorem. This is the joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko.

The last decade has seen significant progress in our understanding of scattering in anti-de Sitter (AdS) space. Through the AdS/CFT correspondence, we can reformulate scattering processes in AdS in terms of correlation functions in Conformal Field Theory (CFT), which are sharply defined by the requirements of Conformal Symmetry, Unitarity and a consistent Operator Product expansion. Accordingly, numerous highly effective techniques for the study of scattering in AdS have been developed. This has been driven largely by the Conformal Bootstrap programme, which aims to carve out the space of consistent CFTs (and, in turn, quantum gravities in AdS space) principally through the three basic consistency requirements above. In this talk I will describe some steps towards extending some of these techniques and results to boundary correlators in de Sitter (dS) space. Compared to AdS, we have little grasp of the properties required of consistent correlation functions in Euclidean CFTs dual to physics in dS. The boundaries at infinity in dS are space-like with no standard notion of locality and time, so the basic criteria that underpin the Conformal Bootstrap programme do not directly apply to the corresponding programme in dS, the so-called Cosmological bootstrap. I will show how boundary correlators in AdS and dS can be placed on a similar footing by introducing a Mellin-Barnes representation in momentum space, providing a framework that could facilitate bridging the gap between the Conformal and Cosmological bootstrap programmes. I will then discuss how the Mellin-Barnes representation itself can be a useful tool to study boundary correlators both in AdS and dS.

Following the recommendation of the Update of the European Strategy for Particle Physics and in view of rising interest shown in the US Snowmass process, a new International Muon Collider Collaboration is forming, hosted at CERN. The presentation will introduce the muon collider concept, the reason for the renewed interest and the main challenges and opportunities.