Scientific Series

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular ℏ→0 limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits.

The structure of entanglement can yield new physical insights into strongly interacting quantum critical states. I’ll describe key properties of the entanglement entropy of conformal field theories (CFTs) in 2+1d. In particular, we’ll see that sharp corners in the entangling surface contribute a regulator-independent function that depends non-trivially on the corner angle. I’ll argue that in the smooth limit this function yields the 2-point function of the stress tensor. This sheds light on recent cutting edge simulations of the quantum critical Ising, XY and Heisenberg models. I’ll also present a new lower bound for this function. I will then generalize to Rényi entropies, which yields a simple procedure to extract the thermal entropy using corner entanglement of the groundstate alone. Connections will be made to CFTs in 1+1d and 3+1d, as well as to Lifshitz theories.

In effective field theory, causality fixes the signs of certain interactions.  I will describe how these Lorentzian constraints are encoded in the Euclidean theory, and use the conformal bootstrap to derive analogous causality constraints in CFT. Applied to spinning fields, these constraints include (some of) the Hofman-Maldacena bounds derived from conformal collider physics. I will also discuss applications to holographic theories.

We propose the discovery of the electroweak monopole as the final test of the standard model. Unlike the Dirac's monopole in electrodynamics which is optional, the electroweak monopole must exist within the framework of the standard model because the $U(1)_{em}$ becomes non-trivial. We estimate the mass of the monopole to be around 4 to 7 TeV, and expect the production rate to be relatively large, $(1/\alpha_{em})^2$ times bigger than the WW production rate. This implies that the MoEDAL detector at LHC could have a real chance to detect it.  

The global redshifted 21-cm radiation background is expected to be a powerful probe of the re-heating and re-ionization of the intergalactic medium. However, its measurement is technically challenging: one must extract the small, frequency-dependent signal from under much brighter and spectrally smooth foregrounds. Traditional approaches to study the global signal have used single-antenna systems, where one must calibrate out frequency-dependent structure in the overall system gain, as well as remove the noise bias from auto-correlating a single amplifier output. I will review these approaches, and critically examine several recent proposals to measure the global background using interferometric setups. In particular, using very general principles, I will show that the latters' sensitivity is directly related to two characteristics: the cross-talk between the readout channels (i.e. the signal picked up at one antenna when the other one is driven) and the correlated noise due to thermal fluctuations of lossy elements (e.g. absorbers or the ground) radiating into both channels. I will also briefly discuss the implications and future prospects for interferometric methods.

If the dark matter is made up of a bosonic particle, it can be ultralight, with a mass potentially much below 1 eV. Well-known DM candidates of this type include pseudoscalars like the QCD axion, and vectors such as hidden photons kinetically mixed with the Standard Model. Moduli, even-parity scalars with nonderivative couplings to the SM, can also be light dark matter. I will show that they cause tiny fractional oscillations of SM parameters, such as the electron mass and the fine-structure constant, in turn modulating length and time scales of atoms. Rods and clocks, used in gedanken experiments in relativity, have since transformed into actual precision instruments. The size of acoustic resonators and the frequency of optical clocks can now be measured to 1 part in 10^22 and 10^18, respectively, and thus constitute sensitive probes of moduli. 

In this talk, I will give an overview of the parameter space of modulus dark matter, and discuss the sensitivity of the proposed experiments compared to existing constraints from fifth-force tests.

Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions enforces and protects emergent gapless excitations, and symmetry is intrinsically tied to the topological protection in a certain class. Namely, unless the symmetry is broken, the topological nature is intact. We show novel interplay phenomena between symmetry and topology in topological phase transitions associated with line-nodal superconductors. The interplay may induce an exotic universality class in sharp contrast to that of the phenomenological Landau-Ginzburg theory. Hyper-scaling violation and emergent relativistic scaling are main characteristics, and the interplay even induces unusually large quantum critical region. We propose characteristic experimental signatures around the phase transitions in three spatial dimensions, for example, a linear phase boundary in a temperature-tuning parameter phase-diagram. 

Radio pulsars are Nature's most perfect clock and hence are useful for precision work on a wide variety of physical and astrophysical topics, ranging from sensitive tests of relativistic gravity to constraining the equation of state of ultradense matter. I will describe current ongoing surveys for radio pulsars using the two largest radio telescopes in the world, and how these surveys are also valuable for searching for Fast Radio Bursts, a newly recognized astrophysical phenomenon of unknown origin. 

Based on first-principle calculations, we show that a family of nonmagnetic materials including TaAs, TaP, NbAs, and NbP are Weyl semimetals (WSM) without inversion centers. We find twelve pairs of Weyl points in the whole Brillouin zone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), band inversions in mirror-invariant planes lead to gapless nodal rings in the energy-momentum dispersion. The strong SOC in these materials then opens full gaps in the mirror planes, generating nonzero mirror Chern numbers and Weyl points off the mirror planes. The transport properties obtained by the Boltzmann equation combined with the semiclassical treatments of the unique electronic structure in these materials will also be discussed in comparison with the most recent experimental data.

The discovery of postquantum nonlocality, i.e. the existence of nonlocal correlations stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that post-quantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.

 

For a CFT perturbed by a relevant operator, the entanglement entropy of a spherical region may be computed as a perturbative expansion in the coupling.  A similar perturbative expansion applies for excited states near the vacuum.  I will describe a method due to Faulkner for calculating these entanglement entropies, and apply it in the limit of small sphere size.  The motivation for these calculations is a recent proposal by Jacobson suggesting an equivalence between the Einstein equation and the "maximal vacuum entanglement hypothesis" for quantum gravity.  This proposal relies on a conjecture about the behavior of entanglement entropies for small spheres.  The calculations presented here suggest that this conjecture must be modified, but I will discuss how Jacobson's derivation still applies under the modified conjecture.