Scientific Series

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.

Large surveys of the positions of galaxies in the Universe are becoming increasingly powerful to shed light on some of the unsolved problems of cosmology, including the question of what caused the early Universe to expand. The analysis of the data is challenging, however, because the signal is small, the data is difficult to model, and its probability distribution is not fully known. I will present some recent ideas to approach these challenges.

The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size --- from logarithmic to extensive to fractal. We show how these outcomes in non-unitary circuits (that are ``spacetime-dual" to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets ``radiated away'' from one edge of the system. In spacetime-duals of chaotic unitary circuits, this mapping allows us to uncover a non-thermal volume-law entangled phase with a logarithmic correction to the entropy distinct from other known examples. Most notably, we also find novel steady state phases with fractal entanglement scaling, $S(\ell) \sim \ell^{\alpha}$ with tunable $0 < \alpha < 1$ for subsystems of size $\ell$ in one dimension. These fractally entangled states add a qualitatively new entry to the families of many-body quantum states that have been studied as energy eigenstates or dynamical steady states, whose entropy almost always displays either area-law, volume-law or logarithmic scaling. We also present an experimental protocol for preparing these novel steady states with only a very limited amount of postselection via a type of ``teleportation" between spacelike and timelike slices of quantum circuits.

The prepare-and-measure scenario is ubiquitous in physics. However, beyond the paradigmatic example of dense coding, there is little known about the correlations p(b|x,y) that can be generated between a sender with input x and a receiver with input y and outcome b. Contrasting dense coding, we show that the most powerful protocols based on qubit communication require high-dimensional entanglement. This motivates us to systematically characterise the sets of correlations achievable with classical and quantum communication, respectively, assisted by a potentially unbounded amount of entanglement. We obtain two different SDP hierarchies for both the classical and quantum case: one based on NPA and one based on informationally-restricted correlations. In the talk, I will discuss the advantages and drawbacks of each, and show that they can be used obtain tight or nearly-tight bounds on in several concrete case studies. As examples of applications, these new tools are used to construct device-independent dimension witnesses robust to unbounded shared entanglement and several resource inequalities for quantum communications.

I will consider the phase space at null-infinity from the r\rightarrow\infty limit of a quasi-local phase space for a finite box with a boundary that is null. This box will serve as a natural IR regulator. To remove the IR regulator, I will consider a double null foliation together with an adapted Newman--Penrose null tetrad. The limit to null infinity (on phase space) is obtained in the limit where the boundary is sent to infinity. I will introduce various charges and explain the role of the corresponding balance laws. The talk is based on the paper: arXiv:2012.01889.

The talk will be based on my latest two papers 2103.02616 and 2103.05700. 
In the first part, I will present my GRMHD simulation of a neutron-star post-merger disk with neutrino fast flavour conversion included dynamically. The fast conversion of neutrinos can lead to flavour space equipartition ubiquitously on the time scale as short as 1ns. Due to the reduction of the number density of electron and anti-electron neutrino, the ejecta becomes more neutron rich. The final r-process nucleosynthesis sees an enhanced abundance of heavy elements close to the solar values. A similar effect may allow for increased lanthanide production in collapsars.
In the second part, I will present fast magnetic energy dissipation through the collision of Alfven waves with anti-aligned magnetic fields. The collision produces a current sheet sustained by an electrical field breaking the MHD condition. Particles entering the current sheet are accelerated following a relativistic variation of Speiser orbit and escape with higher energy. This mechanism can dissipate a large fraction of wave energy, nearly 100% when the wave magnetic field equals the background magnetic field. The fast dissipation may occur in various objects, including magnetars, jets from accreting black holes, and pulsar wind nebulae.

Discriminating between quantum computing architectures that can provide quantum advantage from those that cannot is of crucial importance. From the fundamental point of view, establishing such a boundary is akin to pinpointing the resources for quantum advantage; from the technological point of view, it is essential for the design of non-trivial quantum computing architectures. Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures, including those based on continuous variables (CVs). However, it is not a sufficient resource, and it is an open question under which conditions CV circuits displaying Wigner negativity offer the potential for quantum advantage. In this work, we identify vast families of circuits that display large Wigner negativity, and yet are classically efficiently simulatable, although they are not recognized as such by previously available theorems. These families of circuits employ bosonic codes based on either translational or rotational symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include both Gaussian and non-Gaussian gates and measurements. Crucially, within these encodings, the computational basis states are described by intrinsically negative Wigner functions, even though they are stabilizer states if considered as codewords belonging to a finite-dimensional Hilbert space. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.

I describe recent progress on a program of research aimed at finding a simultaneous completion of quantum mechanics and general relativity, while also addressing the question of how the universe chose its effective laws out of a vast landscape of possible laws.    This is based on a few principles:   time in the sense of causation is fundamental, as are events, and the views  of events (their backward celestial spheres.) Further the view of every event must be distinct from that of every other.  This is enforced by a choice for potential energy that maximizes the diversity of views of events, called the variety.    Given these postulates, everything else emerges dynamically, including space, spacetime, and quantum dynamics; as the variety turns out to reduce appropriately to Bohm’s quantum potential, which in turn is responsible for quantum non-locality, entanglement etc.  

A consequence of these ideas is that the effective low energy laws, including the values of the dimensionless constants of the standard model,  should evolve dynamically.    I present three realizations of this idea: cosmological natural selection (1992), the principle of precedence (2005), and the hypothesis that the universe may learn how to choose its vacuum out of a landscape of possible vacua through a process formally analogous to machine learning (2021).   I discuss the prospects for observational tests of these ideas.

At the technical level,  some of these ideas are related through the use of matrix modes whose actions are cubic in the matrices, which are tied to topological and gravitational theories.  At a methodological level, issues involving an interplay of reductionist and functionalist reasoning may be discussed.  

Collaborators on recent work include Stephon Alexander, Marina Cortes, William Cunningham,  Stuart Kauffman, Jaron Lanier,  Andrew Liddle,  Joao Magueijo,   Stefan Stanojevic,  Michael W. Toomey, Clelia Verde and Dave Wecker.

I will discuss what happens when a black hole captures a much larger in
size cosmic string loop. In some cosmological scenarios, such encounters
are not unlikely for supermassive black holes in galactic nuclei, and
for primordial black holes. The talk will feature some fun physics and
geometry: non-flat quadrilaterals, black-hole superradiance,
one-dimensional geometric flows, and persistent ultra-relativistic
gravitational-wave whips.

Agency accounts of causation are often criticised as being unacceptably subjective: if there were no human agents there would be no causal relations, or, at the very least, if humans had been different then so too would causal relations. Here we describe a model of a causal agent that is not human, allowing us to explore the latter claim.   

Our causal agent is special kind of open, dissipative physical system, maintained far from equilibrium by a low entropy source of energy, with accurate sensors and actuators. It has a memory to record sensor measurements and actuator operations, and a learning system that can access the sensor and actuator records to learn and represent the causal relations. We claim that causal relations are relations between the internal sensor and actuator records and the causal concept inherent in these correlations is then inscribed in the physical dynamics of the internal learning machine. We use this model to examine the relationships between three familiar asymmetries aligned with causal asymmetry: time's arrow, the thermodynamic arrow and the arrow of deliberation and action. We consider both classical and quantum agent models and illustrate some differences between the two.