Scientific Series

In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply 

related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space, 

defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators. 

In this talk, we propose the general definition, i.e., many-body invariants, for electric multipoles in crystals, which are related with recently-discovererd higher-order topological insulators. 

Our invariants are designed to measure the distribution of electron charge in unit cells and thus can detect multipole moments purely from the bulk ground state wavefunctions. 

We provide analytic as well as numerical proofs for our invariants. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be briefly discussed.

I argue that we do not understand gauge theory as well as we think when boundaries are present. I will briefly explain the conceptual and technical issues that arise at the boundary.  I will then propose a tentative resolution, which requires us to think of theories not in spacetime, but in field-space. 

There is observational evidence that the X-ray continuum source that creates the broad fluorescent emission lines in some Seyfert Galaxies may be compact and located at a few gravitational radii above the black hole. We consider two scenarios for the X-ray emission. The first possibility is that the X-rays may be produced by particles accelerated in an electrostatic gap at the base of a putative jet. However, our detailed study of the gap kinetic physics and scaling suggests that the energetics is not enough in these environments. The second possibility is that the compact X-ray emitting source may be powered by small scale flux tubes near the black hole that are attached to the orbiting accretion disk. Our force-free simulations show that the field linking the black hole and the disk can get twisted up by the differential rotation to form a magnetic tower. When the confinement provided by the field from the outer disk is strong, the built-up magnetic tower can quickly become kink unstable, which leads to continuous reconnection and dissipates most of the energy extracted from the rotating black hole. This could in principle power a hot X-ray emitting region above the black hole.

Bernstein operators are vertex operators that create and annihilate Schur polynomials. These operators play a significant role in the mathematical formulation of the Boson-Fermion correspondence due to Kac and Frenkel. The role of this correspondence in mathematical physics has been widely studied as it bridges the actions of the infinite Heisenberg and Clifford algebras on Fock space. Cautis and Sussan conjectured a categorification of this correspondence within the framework of Khovanov's Heisenberg category. I will discuss how to categorify the Bernstein operators and settle the Cautis-Sussan conjecture, thus proving a categorical Boson-Fermion correspondence.

The elliptic quantum (toroidal) group U_{q,p}(g) is an elliptic and dynamical analogue of the Drinfeld realization 
of the affine quantum (toroidal) group U_q(g). I will discuss an interesting connection of its representations with 
a geometry such as an identification of the elliptic weight functions derived by using  the vertex operators with 
the elliptic stable envelopes in [Aganagic-  Okounkov ’16] and correspondence between the Gelfand-Tsetlin bases 
of a finite dimensional representation of U_{q,p} with the fixed point classes in the equivariant elliptic cohomology.

Cosmic Microwave Background (CMB) is a powerful probe to the Universe which carries signatures of cosmic secrets over a vast range of redshifts. Along with spatial fluctuations, spectral distortions of CMB blackbody are also a rich source of cosmological information. In my talk, I will introduce a new kind of spectral distortion of CMB which can arise due to the conversion of CMB photons into Axion-Like Particles (ALPs) in the presence of an external magnetic field. This effect leads to both polarized and unpolarized spatially varying spectral distortion signal with a unique spectral shape when CMB photons undergo resonant and non-resonant conversion into ALPs in the presence of the magnetic field of Milky Way, galaxy clusters and voids. I will discuss the spatial structure of this distortion which can arise from Milky Way and galaxy clusters and will show its uniqueness from other known cosmological and astrophysical signals. I will present the first all-sky map of this distortion which is obtained using the data of Planck satellite and will discuss the capability of this new cosmological window to probe ALPs from the upcoming ground-based and space-based CMB experiments such as CMB-S4, LiteBIRD, Simons Observatory, etc.

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a `fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. With the recent detection of gravitational waves, this idea has started to turn into reality.
Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves.
The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a non-invasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wave-current interactions and hence the effective field theories describing such systems.

The detection of gravitational waves from mergers of compact binaries in the first two runs of the Advanced LIGO-Virgo have brought in valuable insights into fundamental physics and astrophysics. The coalescence process sweeping the components through a range of frequencies at highly relativistic velocities, have enabled some of the first tests of general relativity in its highly dynamical and extremely strong field regime. The recent detection of the binary neutron star merger has shed first light on the elusive neutron star equation of state. Furthermore, with its coincident electromagnetic counterpart, a first "standard-siren" measurement of the Hubble parameter has been made independent of a cosmic distance ladder. Subsequent detections are expected to give us a more direct understanding of the nature of the black holes and the composition of neutron stars, as well as bring in a plethora of results in astrophysics and possibly new insights into cosmology. I will go over some of these exciting new results and talk about future prospects of fundamental physics and cosmology from gravitational-wave observations.

How does classical chaos affect the generation of quantum entanglement? What signatures of chaos exist at the quantum level and how can they be quantified? These questions have puzzled physicists for a couple of decades now. We answer these questions in spin systems by analytically establishing a connection between entanglement generation and a measure of delocalization of a quantum state in such systems. While delocalization is a generic feature of quantum chaotic systems, it is more nuanced in regular systems. We explore when the quantum dynamics mimics a localized classical trajectory, and find criteria to quantify Bohr's correspondence principle in periodically driven spin systems. These criteria are typically violated in a deep quantum regime due to delocalized evolution. Using our criteria, we establish that entanglement is a signature of chaos only in a semiclassical regime. Our work provides a new approach to analyzing quantum chaos and designing systems that can efficiently generate entanglement. This work has been done in collaboration with Prof. Shohini Ghose.

References: arXiv:1806.10545 (2018) and PRE 97, 052209 (2018).

While it’s undeniably sexy to work with infinite-dimensional categories “model-independently,” we contend there is a categorical imperative to familiarize oneself with at least one concrete model in order to check that proposed model-independent constructions interpret correctly. With this aim in mind, we recount the n-complicial sets model of (∞,n)-categories for 0 ≤ n ≤ ∞, the combinatorics of which are quite similar to its low-dimensional special cases: quasi-categories (n=1) and Kan complexes (n=0). We conclude by reporting on an encounter with 2-complicial sets in the wild, where a suitably-defined fibration of 2-complicial sets enables the comprehension construction introduced in joint work with Verity. Special cases of the comprehension construction can be used to “straighten” a co/cartesian fibration of (∞,1)-categories into a homotopy coherent functor, exhibit a quasi-categorical version of the “unstraightening” construction, and define an internal model of the Yoneda embedding for (∞,1)-categories.

Recent advances in scaling photonics for universal quantum computation spotlight the need for a thorough understanding of practicalities such as distinguishability in multimode quantum interference.  Rather than the usual second quantized approach, we can bring quantum information concepts to bear in first quantization.  Distinguishability can then be modelled as entanglement between photonic degrees of freedom, where loss of interference is caused by decoherence due to correlations with an environment carried by the particles themselves.  This shows that multiparticle, multimode Fock states can have natural Schmidt decompositions, corresponding to what has been called unitary-unitary duality in the representation theory of many-body physics.  
We present results along two lines: 
(i) Generalised Hong-Ou-Mandel interference as unambiguous state discrimination (arXiv:1806.01236, with S. Stanisic); we find optimised interferometers that discriminate between indistinguishable and interesting distinguishable states by projecting onto non-symmetric irreps of the unitary group of interferometers.  We give analytic and numerical results for up to nine photons in nine modes.
(ii) Quantum simulation of noisy boson sampling (arXiv:1803.03657, with A. Moylett); we provide quantum circuits that simulate bosonic sampling with arbitrarily distinguishable particles, based on the quantum Schur-Weyl transform.  This makes clear how particle distinguishabililty leads to decoherence in the standard quantum circuit model.  We show how ideal samples can be postselected, how photon loss can also be modelled, and how standard results in the classical simulation of noisy quantum computations fail to apply to the boson sampling case.

Infrared sensitivity of the de Sitter decay rate due to particle creation requires that gravitational backreaction be taken into account on the horizon scale. At lowest order, backreaction can be studied by Linear Response of the geometry to quantum matter perturbations around the Bunch-Davies state. In Linear Response the scalar degree of freedom derived from the conformal anomaly gives rise to scalar gravitational waves that grow without bound on the de Sitter horizon scale,  which implies substantial non-linear quantum backreaction effects in cosmology. Fluctuations in the conformalon scalar are potentially responsible for the primordial density fluctuations observed in the CMB anisotropy without an inflaton, and can also lead to dynamical, spacetime dependent dark energy. Possible observational tests of the conformal origin of primordial density fluctuations is suggested by the prediction of equality of scalar and tensor weight spectral indices, and the bispectral shape function of non-Gaussian correlations in the CMB predicted by conformal invariance.