Scientific Series

Long-range quantum entanglement is now being recognized as a key characteristic of many novel states of quantum matter. The description of this entanglement requires the introduction of emergent “gauge fields”, much like those found in Maxwell’s theory of light. I will highlight some recent experiments on the copper-based high temperature superconductors, and interpret them using theories of emergent gauge fields.

Time in quantum mechanics has duly received a lot of attention over the years. Perfect clocks which can turn on/off a particular interaction at a precise time that have been proposed only exist in infinite dimensions and have unphysical Hamiltonians (their spectrum is unbounded from below). It was this observation which led many to conclude that an operator for time cannot exist in quantum mechanics. Here, we prove rigorous results about the accuracy of finite dimensional clocks and show that they can well approximate their infinite dimensional counterparts under the right conditions.

The LHCb detector was designed to be the dedicated heavy-flavor physics experiment at the LHC, and has been the world's premier lab for studying processes where the net quark content changes for several years. These studies permit observing virtual contributions from beyond the SM particles up to very high mass scales, potentially (greatly) exceeding the direct reach of the LHC.  I will summarize the constraints placed on high-mass BSM physics by such studies, and also highlight a few interesting anomalies.  I will also discuss direct searches for low-mass BSM physics, and a selection of novel SM studies.  Finally, future prospects will be presented. 

One possibility for studying reheating is to link the duration and final temperature after reheating, and its equation of state, to inflationary observables. By restricting the equation of state to lie within a broad physically allowed range, one can bracket an allowed range of $n_s$ and $r$ for models of inflation. The results are similar to, but do a little better, than requiring the length of inflation lie between 50 and 60 efolds. The added constraints can help break degeneracies between inflation models that otherwise overlap in their predictions.

According to the standard model of cosmology 96% of the matter and energy in the universe is invisible. The dark matter particles comprising the invisible material have so far not been detected in laboratory and astrophysical experiments.  The dark energy responsible for the acceleration of the universe is still a controversial issue. A modified gravity theory is presented that can potentially fit current cosmological and astrophysical data. The black holes and their shadows predicted by MOG can differ from the predictions of Einstein gravity.

Fast radio bursts (FRBs) are bright, broadband, non-repeating, millisecond flashes of unknown astronomical origin. The dispersion of these bursts by intervening plasma suggests that the sources of the 16 bursts reported to date= are at 0.2<z<1. I will discuss the possibility of using dispersion, instead of redshift, to study the large-scale structure of the Universe in three dimensions. Like redshift, which is distorted by peculiar velocities, dispersion is an imperfect proxy for distance as it is distorted by inhomogeneities in the electron density. These dispersion-space distortions are calculable and actually greatly enhance the signal. The clustering signal in dispersion space could be detected in a survey of 10 000 FRBs, as is expected to be produced by the CHIME telescope over three years.

The greatest uncertainty in whether this technique will be successful is the unknown nature of FRB sources. A new observation tells us more about the environment of a source than ever before through the polarization and scattering properties of a burst. More observations of this type, along with observations that identify host galaxies, will soon tell whether FRBs will provide a new probe of structure.

Let $S$ be a surface, $G$ a semi-simple group of type B, C or D. I will explain why the moduli space of framed local systems $A_{G,S}$ defined by Fock and Goncharov has the structure of a cluster variety, and fits inside a larger structure called a cluster ensemble. This was previously known only in type A. This gives a more direct proof of results of Fock and Goncharov for the symplectic and spin groups, and also allows one to quantize higher Teichmuller space in these cases. If time permits, I hope to talk about applications to counting tensor invariants of finite dimensional representations of these groups.

Quantum adiabatic optimization (QAO) slowly varies an initial Hamiltonian with an easy-to-prepare ground-state to a final Hamiltonian whose ground-state encodes the solution to some optimization problem. Currently, little is known about the performance of QAO relative to classical optimization algorithms as we still lack strong analytic tools for analyzing its performance. In this talk, I will unify the problem of bounding the runtime of one such class of Hamiltonians -- so-called stoquastic Hamiltonians -- with questions about functions on graphs, heat diffusion, and classical sub-stochastic processes. I will introduce new tools for bounding the spectral gap of stoquastic Hamiltonians and, by exploiting heat diffusion, show that one of these techniques also provides an optimal and previously unknown gap bound for particular classes of graphs. Using this intuition and combining heat diffusion with classical sub-stochastic processes, I will offer a classical adiabatic algorithm that exhibits behavior typically considered "quantum", such as tunneling.

In the rst part of this talk I will give a brief introduction to the variational class of continuous
matrix product states (cMPS). Then I will present a time evolution algorithm for cMPS with periodic
boundary conditions. In the second part, I will explain how to apply this method to simulate
atomtronic circuits. In particular, I will show results for persistent currents in an interacting bose
gas rotating in a ring shaped trap in the presence of an arti cial U(1) gauge potential.

The BPS spectrum of d=4 N=2 field theories in general contains not only hyper and vector-multipelts but also short multiplets of particles with arbitrarily high spin. These BPS states of higher spin reveal quite a peculiar behavior, so sometimes they are called "wild"

states. In this talk we would try to discuss a small refinement of the asymptotic study (spectral network technique) of tt* equations arising in an effective theory on 2d defects in N=2 4d SYM theory capturing spin information and apply it to study some properties of wild BPS spectra.

The vacuum energy changes when cosmological phase transitions take place, or in environments with high temperatures or chemical potentials.  The propagation of primordial gravity waves is affected through the trace anomaly, and eras where the vacuum energy dominates can lead tofeatures in the gravity wave spectrum.  High density phases of QCD in neutron stars, where the vacuum is rearranged, are also a novel probe:  The mass-radius relationships for neutron stars is sensitive to the equation of state appearing in the Einstein equations, which may depend on new dynamics associated with vacuum energy.  Such observations could potentially rule out large classes of explanations for the smallness of the currently observed cosmological constant.