Scientific Series

The hydrodynamic approximation is an extremely powerful tool to describe the behavior of many-body systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large space-time scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitely-many conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitely-many conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized one-dimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived, its relation to quantum and classical integrable systems, and some geometry that lies at its core. I will then explain how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and non-equilibrium currents.

This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, Jean-Sébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm.

The study of super-Eddington accretion is essential to our understanding of the growth of super-massive black holes in the early universe, the accretion of tidally disrupted stars, and the nature of ultraluminous X-ray sources.  Unfortunately, this mode of accretion is particularly difficult to model because of the multidimensionality of the flow, the importance magnetohydrodynamic turbulence, and the dominant dynamical role played by radiation forces.  However, recent increases in computing power and advances in algorithms are facilitating major improvements in our ability to model radiation in numerical simulations of astrophysical plasmas.  I will briefly describe our new radiation transfer modules and discuss our efforts to model super-Eddington accretion flows around stellar mass and supermassive black holes.  I will focus on applications to ultraluminous X-ray sources, which must be radiating well above their Eddington luminosity unless they harbour intermediate mass black holes. I will argue that most of these sources can be (and likely are) "normal" ~10 solar mass black holes accreting and radiating with luminosities well above their Eddington "limit”.

Causal set quantum gravity, computational methods Series

The Cactus High Performance Computing (HPC) Framework was designed to
facilitate the development of software to simulate astrophysically realistic
inspiral and merger of binary black holes and neutron stars.  A major part of the motivation for
its design was the US Binary Black Hole Grand Challenge in the 1990s, which
was an alliance of hundreds of scientists, all attempting to collaborate on
the same code base.  In order to handle such a large, diverse collaboration,
the design ended up being extremely general and versatile, able to support
virtually any sort of scientific computation.

I have developed an extensive software suite within the Cactus Framework for
doing large scale computations in discrete quantum gravity, using Causal Sets,
and also spin networks in Loop Quantum Gravity.  Recently, evidence is
emerging that ideas from discrete quantum gravity, and consequently this
software, may have much broader application in areas of Data Science,
including social science, computational neuroscience, and drug design.

The 21cm transition of atomic hydrogen is rapidly becoming one of our most powerful tools for probing the evolution of the universe.  The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a planned 1,024-element array to be built in South Africa that will study the (possible) evolution of dark energy from z=0.8 to 2.5. Its design also makes it an excellent pulsar and fast radio burst (FRB) search machine.  While the FRB rates in the HIRAX band are uncertain, we expect it will discover dozen(s) per day.  HIRAX will use inexpensive 6m satellite television-class dishes.  The same dishes can be used to build relatively inexpensive outrigger stations in southern Africa to localize a large fraction of the FRBs discovered by HIRAX to ~0.1 arcseconds, potentially transforming them into probes of the universe.

The era of gravitational wave detection is upon us.  Advanced LIGO (aLIGO) is now in full operation.  It has successfully detected the gravitational waves emitted from distant pairs of black holes (BHs) as they spiral together and merge.  And we have many more detections to look forward to.  But where are these BH-BH mergers happening, in the vast wilderness of the cosmos?  

One of the preferred candidates are globular clusters, massive systems of very old stars densely packed together and bound together by gravity.  Globular clusters are factories for black hole binary mergers. But we are only able to observe these factories in operation now. In order to understand how they were built and the treasures they should be expected to produce at present, we must somehow rewind their evolution over billions of years to say something about the initial conditions. Only then will we be able to understand how these beasts birth BH binaries, and are contributing to the gravitational waves currently being observed by aLIGO. After a brief overview of the concept of chaos, I will discuss recent progress in advancing our understanding of the origins of BH-BH mergers.

The theory of alphabits is a natural generalisation of approximate quantum error correction that proves fundamental to the study of asymptotic quantum resources. In particular, it leads to an asymptotically reversible variation on quantum teleportation, called zerobit teleportation, which decomposes qubits of communication into correlation and transmission components. They also naturally arise in the study of black holes with significant consequences for the nature of quantum error correction in AdS/CFT.

After reviewing the three things in the title I will argue that they represent the same physical phenomenon. In details, Jackiw–Teitelboim (JT) gravity coupled to an arbitrary quantum field theory results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed S-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the T\barT deformation of the initial quantum field theory compactified on a circle. The same dressed S-matrix is also obtained as a flat space limit of the near AdS2 holography based on (JT) gravity. In order to preserve the flat space unitarity, however, the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. As an intermediate result I will present a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT’s. 

Primordial black holes (PBHs) can appear from early Universe dynamics. We show that some or all of heavy element abundance from r-process nucleosynthesis can be produced in interactions of tiny primordial black holes with neutron stars (NSs), if PBHs make up a few percent or more of the dark matter. A PBH captured by a NS will eventually consume it. For a rapidly rotating pulsar, the resulting star spin-up will eject significant amount of cold neutron rich material. The ejection, decompression and decay of nuclear matter can produce electromagnetic transients, like kilonovae and fast radio bursts. Beta decay of ejected material yields positron emission consistent with the observed 511 keV-line from the Galactic Center. Lack of accompanying gravity wave (GW) signal and neutrino emission allows to distinguish these events from supernovae and compact object mergers. Finally, if the consumed star was part of a binary system, long after the event a distinct detectable GW signal from the binary merger with an atypically small solar mass BH will carry information about star's destruction.

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most hidden-variable models, this model does not violate the locality assumption in Bell's argument. Rather, it violates measurement independence, albeit in a decidedly non-conspiratorial way.

In quantum theory, there can exist correlations between subsystems of a new kind that are absent in classical systems. These correlations are nowadays called "entanglement".

An entanglement measure is a functional on states quantifying the amount of entanglement across two subsystems (i.e. causally disjoint regions in the context of quantum field theory). A reasonable measure should satisfy certain general properties: for example, it should assign zero entanglement to separable states, and be monotonic under separable, completely positive maps ("LOCC-operations"). The v. Neumann entropy of the "reduced state" (to one of the subsystems) is one such measure if the state for the total system is pure. But for mixed states, it is not, and one has to consider other measures. In particular, one has to consider other measures if the subsystems have a finite non-zero distance.

In this talk I will present several good measures, and in particular analyze the « relative entanglement entropy", $E_R$, defined as the "distance" of the given state to the set of separable states, where "distance" is defined using Araki's relative entropy. I will show several features of this measure for instance: (i) charged states, where the relative entanglement entropy is related to the quantum dimension of the charge, (ii) vacuum states in 1+1 dimensional integrable models, (iii) general upper bounds for certain special regions in general CFTs in d dimensions, (iv) area law type bounds. I will also explain the relationship between $E_R$ and other entanglement measures, such as distillable entropy.

[Based on joint work with Jacobus Sanders.]