Scientific Series

A superoscillatory function is a bandlimited function that, on some interval, oscillates faster than the highest frequency component shown in the function's Fourier transform. Superoscillations can be arbitrarily fast and of arbitrarily long duration but come at the expense of requiring a correspondingly large dynamic range. I will review how superoscillatory wave forms can be constructed and I will discuss the unusual behavior of wave functions that superoscillate. For example, they can describe particles that automatically strongly accelerate when passing through a slit. A postselected stream of them represents a ray that cools the slit walls, raising foundational and thermodynamic questions. Superoscillatory wave forms are already being used for practical applications such as spatial resolution beyond the diffraction limit. 

The LHC bear great potential in seeking for hidden sector particles, such as a high-quality QCD axion, glueballs, and heavy neutrinos. 

In this talk, I will present my recent studies on how to probe these hidden sector particles through the novel but challenging long-lived particle searches.

Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
Our main result is the construction of a mapping class group action on these models, formulated under weaker assumptions than the associated topological quantum field theories, namely for pivotal Hopf algebras in symmetric monoidal categories. This description also yields new structures for semisimple finite-dimensional Hopf algebras. The action of the mapping class group is defined in terms of simple graph transformations and allows one to compute quantum Dehn twists explicitly.

With the detection of GW170817 we have observed the first multi messenger signal from two merging neutron stars. This signal carried a multitude of information about the underlying equation of state (EOS) of nuclear matter, which so far is not known for densities above nuclear saturation. In particular it is not known if exotic states or even a phase transition to quark matter can occur at densities so extreme that they can't be probed by any current experiment.

I will show how the information carried in the gravitational wave signal of GW170817 can be used to constrain the EOS at densities above saturation and what we can learn about the possible existence of phase transitions. I will
also comment on how we can improve on those limits with upcoming observations of the NICER mission.In the second part of the talk I will focus on what we can learn about exotic states of matter from neutron star mergers.I will comment briefly on the impact of high spins in mergers and the importance of accurate numerical modelling in the context of these studies.Finally I will show how neutron star mergers can be used to study quark phase transitions and the phase diagram of QCD.

We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground state is a universal resource for measurement based quantum computation. Joint work with Cihan Okay, Dong-Sheng Wang, David T. Stephen, Hendrik Poulsen Nautrup; J-ref: Phys. Rev. Lett. 122, 090501

We consider a consistent theory of classical systems coupled to quantum ones. The dynamics is linear in the density matrix, completely positive and trace-preserving. We apply this to construct a theory of classical gravity coupled to quantum field theory. The theory doesn't suffer the pathologies of semi-classical gravity and reduces to Einstein's equations in the appropriate limit. The assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally information destroying involving finite sized and stochastic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. The theory can be regarded as fundamental, or as an effective theory of quantum field theory in curved space where backreaction is consistently accounted for.

The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry.  The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon.  From a modern point of view, topological defects generalize the notion of global symmetries.  We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry. The duality defect extends the Monster group to a larger category of topological defects that contains an Ising subcategory.  We introduce the defect McKay-Thompson series defined as the Monster partition function twisted by the duality defect, and find that it is invariant under the genus-zero congruence subgroup 16D0 of PSL(2,Z).

The central idea of the bootstrap philosophy is to constrain observables directly from consistency conditions alone, bypassing the intricacies of the Lagrangian formalism. In this talk, I will adopt this viewpoint and describe a boundary-centric approach to determine cosmological correlators, following a perspective familiar from the modern studies of scattering amplitudes. Specifically, I will describe the symmetries and singularities of three- and four-point functions in de Sitter space and inflation, and explain how these principles can be used to fully determine the final answer without reference to bulk time evolution. I will also highlight spectroscopic features encoded in these correlators, relevant for the search of primordial non-Gaussianity in future cosmological observations.

Maps of the mass density field can be used to predict peculiar velocities point-by-point. The comparison of these predictions to peculiar velocity data can be used to determine the cosmological parameter combination f sigma_8. I will briefly discuss the history of this field, present some of our recent results as well as other applications to calibrating the Hubble constant via SNe and gravitational waves, and discuss ongoing work to improving these measurements, through better modelling and, more importantly, acquiring more peculiar velocity data.

I will briefly review the pseudogap phenomenology in high Tc cuprate superconductor, especially the recent experiments, and propose a unified picture of the phenomenology under only one assumption: the fluctuating pair density wave. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

We derive general results relating revivals in the dynamics of quantum
many-body systems to the entanglement properties of energy eigenstates.
For a D-dimensional lattice system of N sites initialized in a
low-entangled and short-range correlated state, our results show that a
perfect revival of the state after a time at most poly(N) implies the
existence of "quantum many-body scars", whose number grows at least as
the square root of N up to poly-logarithmic factors. These are energy
eigenstates with energies placed in an equally-spaced ladder and with
Rényi entanglement entropy scaling as log(N) plus an area law term for
any region of the lattice. This shows that quantum many-body scars are a
necessary condition for revivals, independent of particularities of the
Hamiltonian leading to them. We also present results for approximate
revivals, for revivals of expectation values of observables and prove
that the duration of revivals of states has to become vanishingly short
with increasing system size.

Work in collaboration with Henrik Wilming (ETH)

I will describe how current and upcoming 21-cm measurements during cosmic dawn can probe a plethora of dark-matter and dark-energy models. This era saw the formation of the first stars, which coupled the spin temperature of hydrogen to its kinetic temperature---producing 21-cm absorption. The depth of this absorption acts as a thermostat, allowing us to constrain exotic cooling or heating due to dark matter. Additionally, the timing of the 21-cm signal strongly depends on the abundance of the small minihalos that hosted the first stars, allowing us to tightly constrain dark-matter models with suppressed power, such as warm or fuzzy dark matter. Finally, I will describe how in LCDM the acoustic physics of recombination are imprinted onto the 21-cm power spectrum during cosmic dawn, resulting in robust velocity-induced acoustic oscillations (VAOs). These act as a new standard ruler at z~20, opening up searches for early dark energy and perhaps resolving the H0 tension.