Scientific Series

For many optimal measurement problems of interest, the problem may be re-cast as a semi-definite program, for which efficient numerical techniques are available. Nevertheless, numerical solutions give limited insight into more general instances of the problem, and further, analytical solutions may be desirable when an optimised measurement appears as a sub-problem in a larger problem of interest. I will discuss analytical techniques for finding optimal measurements for state discrimination with minimum error and present applications to studying the gap between the theoretically optimal measurement and simpler, experimentally achievable schemes for bi-partite measurement problems.

Quantized lattices, or q-lattices, appear naturally through categorification constructions (for example from zigzag-algebras), but they haven't been studied from a lattice theory point of view. After establishing the necessary background, we'll explain the q-versions of various lattice theory concepts illustrated with examples from combinatorics and graph theory, and we'll list a number of open problems.

I will first outline an effective field theory for cosmology (EFTC) that is based on the Standard Model coupled to General Relativity and improved with Weyl symmetry. Any version of quantum gravity (QG), including string theory, must include the same improvement, otherwise QG will not be geodesically complete.  Based on arguments of an underlying QG theory, this effective field theory banishes higher curvature terms in the action,  thus making this EFTC  mathematically sufficiently well behaved to make unique predictions for the classical solutions and the quantum wavefunction at the singularity, as well as past the singularity, for a complete cosmology that includes the past, future and detailed quantitative solution at the big bang.
Using this EFTC, I will show its predictions of surprising behavior of the universe at the singularity that cosmologists usually "conveniently" ignore, but they should not, because this predicts the initial conditions. I will illustrate this behavior with detailed formulas and plots of the classical and quantum solutions. The solutions are given in the geodesically complete mini-superspace that has the flavor of the extended spacetime of a black hole or extended Rindler spacetime. The analytic continuation of the quantum wavefunction across the horizons describes the passage through the singularities. The mathematical solution of this analytic continuation solves a long-standing problem of the singular 1/r^2 potential in quantum mechanics that dates back to Von-Neumann. The analytic properties of the wavefunction  also reveals an infinite stack of universes sewn together at the horizons of the geodesically complete space. Remaining open questions and problems will be outlined.

The entanglement entropy, while being under the spotlight of theoretical physics for more than ten years now, remains very challenging to compute, even in free quantum field theories, and a number of issues are yet to be explored.

One such issues concerns boundary effects on entanglement entropy, which is important both for theoretical explorations of entanglement and for applications of entanglement entropy to lattice simulations, condensed matter systems, etc.. During this talk, I will show how the presence of spacetime boundaries affects the entanglement entropy, with emphasize on universal (boundary-induced) logarithmic terms, using field theoretic, lattice, and holographic methods.  

Burst phenomena are ubiquitous in astrophysics. Understanding the origin of bright and rapid bursts, like FRBs, is an important goal of contemporary astrophysics.  We apply Dicke's superradiance, a coherent quantum mechanical radiation mechanism, to explain these burst phenomena. We show that bursts lasting from a few milliseconds (FRBs) to a few years (e.g. OH masers) can be produced by very large groups of entangled atoms/molecules. This is in contrast with the common assumption that, in the interstellar medium, the atoms/molecules in a radiating gas act independently from each other. Superradiance, a well-known and intensely studied phenomenon in the physics community, was first discussed by R. H. Dicke in 1954. I will present our superradiance models developed to explain some maser flares and FRBs, and discuss our results for the 6.7-GHz methanol, 1612-MHz OH, and 22-GHz water spectral lines. Our analyses suggest that the aforementioned groups of entangled atoms/molecules, developing over distances of up to a few kilometers for maser flares and 1000 AU for FRBs, can reproduce the observed light curves

Recent quench experiments in a quantum simulator of interacting Rydberg atoms demonstrated surprising long-lived, periodic revivals from certain low entanglement states, while apparently quick thermalization from others. Motivated by these findings, I will in this talk analyze the dynamics of a family of kinetically constrained spin models related to the experiments. By introducing a manifold of locally entangled spins, representable by a low-bond dimension matrix product state (MPS), I will derive "semiclassical" equations of motion for them. I find that they host isolated, unstable periodic orbits, the presence of which captures the long-lived oscillations and gives rise to slow relaxation of local observables from certain initial configurations. This thus represents a form of weak breaking of ergodicity in dynamics. Our results are reminiscent of the phenomenon of quantum scarring in single-particle chaotic systems which is rooted in classical unstable periodic orbits, and complement the explanation of the recurrences given by [Nature Physics (2018), doi:10.1038/s41567-018-0137-5], in terms of motion over special nonergodic many-body eigenstates, suggestively dubbed `quantum many-body scars'. 

The recent detections of gravitational waves from compact object binary
lead to detailed investigations of the origin of these objects. In my talk
I will discuss the questions: What is the astrophysical origin of these objects?
What do these detections tell us about the formation of black holes and neutron stars?
What are the main problems that they pose?
What to expect in the coming gravitational observations?

Axions are attractive candidates for theories of large-field inflation that are capable of generating observable primordial gravitational wave backgrounds. These fields enjoy shift-symmetries that protect their role as inflatons from being spoiled by coupling to unknown UV physics. This symmetry also restricts the couplings of these axion fields to other matter fields. At lowest order, the only allowed interactions are derivative couplings to gauge fields and fermions. These derivative couplings lead to the biased production of fermion and gauge-boson helicity states during and after inflation. I will discuss preheating in axion-inflation models that are derivatively coupled to Abelian gauge-fields and fermion axial-currents.

For an axion coupled to U(1) gauge fields preheating is efficient for a wide range of parameters. In certain cases the inflaton is seen to transfer all its energy to the gauge fields within a few oscillations. Identifying the gauge field as the hypercharge sector of the Standard Model can lead to the generation of cosmologically relevant magnetic fields.

Coupling the inflaton-axion to Majorana fermions leads to the biased production of fermion helicity-states which can have interesting phenomenological implications for leptogenesis.

I will argue that in the context of string theory, the Big Bang singularity of standard and inflationary cosmology is automatically resolved. To see this at the level of an effective field theory, ideas from "Double Field Theory" are useful.

In this talk I will discuss several recent advances in loop quantum cosmology and its extension to inhomogeneous models. I will focus on spherically symmetric spacetimes and Gowdy cosmologies with local rotational symmetry in vacuum. I will discuss how to implement a quantum Hamiltonian evolution on these quantizations. Then, I will focus on how we can extract predictions from those quantum geometries, and finally analyze a concrete example: cosmological perturbations on Bianchi I spacetimes in LQC.

The power spectrum for fluctuations in the number density of galaxies can be very different in shape from the power spectrum for fluctuations in the mass density at very small wave vectors (i.e., large length scales) if the primordial density fluctuations are non-Gaussian. I review this phenomena. (It  is fairly well known in the more astrophysical part of the cosmology community but less so in the particle physics part of the field.) Then I show that primordial non-Gaussianities that arise from quantum loop diagrams in de-Sitter space can give rise to this phenomena. I also discuss if it is observable given constraints on primordial non-Gaussianity that arise from the Cosmic Microwave Background