Scientific Series

Abstract TBA

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Zoom link: https://pitp.zoom.us/j/97133792880?pwd=d1pxMThTd1R3YjZUVENiOWRLOUZpZz09

I will introduce a new picture of quantum dynamics that might be thought of as "gauging" Schrodinger's picture that results in many "local" Hilbert spaces [1]. Truncating the dimensions of the local Hilbert spaces in this new picture yields an exciting new kind of tensor network whose computational cost does not increase with increasing spatial dimension (for fixed bond dimension) [2]. More detail: Although quantum dynamics are local for local Hamiltonians, the locality is not explicit in the Schrodinger picture since the wavefunction amplitudes do not obey a local equation of motion. In the first part of this talk, I will introduce a new picture of quantum dynamics—the gauge picture—which is similar to Schrodinger's picture, but with the feature that spatial locality is explicit in the equations of motion. In a sense, the gauge picture might be thought of as the result of "gauging" the global unitary symmetry of quantum dynamics into a local symmetry[1]. In the second part of the talk, I discuss a new kind of tensor network ansatz that is inspired from the gauge picture. In the gauge picture, different regions of space are associated with different Hilbert spaces, which are related by gauge connections. By relaxing the unitary constraint on the gauge connections, we can truncate the Hilbert space dimensions associated with different regions to obtain an approximate description of quantum dynamics. This truncated gauge picture, which we dub "quantum gauge network", is intriguingly similar to a classical lattice gauge theory coupled to a Higgs field (which are "local" wavefunctions in the gauge picture), but with non-unitary connections. In one spatial dimension, a quantum gauge network can be easily mapped to a matrix product density operator, and a matrix product state can be mapped to a quantum gauge network. Unlike tensor networks such as PEPS, quantum gauge networks boast the advantage that for fixed bond dimension, the computational cost does not increase with the number of spatial dimensions! Encoding fermionic wavefunctions is also remarkably straightforward. We provide a simple algorithm for approximately simulating quantum dynamics of bosonic or fermionic Hamiltonians in any spatial dimension. We compare the new quantum dynamics algorithm to exact methods for fermion systems in up to three spatial dimensions [2]. [1] The Gauge Picture of Quantum Dynamics. arXiv:2210.09314 [2] Quantum Gauge Networks: A New Kind of Tensor Network. arXiv:2210.12151

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Zoom link: https://pitp.zoom.us/j/94596192271?pwd=MytzNUx4ZEZEemkvcEEzbllWM1J6QT09

The onset of the formation of structure in the early universe was marked by the monolithic collapse of smooth peaks in the initial density field. This process creates prompt rho ~ r^-1.5 density cusps of dark matter, which persist largely unaltered through the subsequent growth of dark matter halos around them. Consequently, in the standard collisionless dark matter paradigm, these prompt cusps are expected to be enormously abundant, and one resides at the center of every halo and subhalo. Prompt cusps present new opportunities to test the nature of dark matter. In annihilating dark matter models, the abundance of these features and the high density inside them greatly influence the intensity and morphology of the annihilation signal. For example, if the Galactic Center gamma-ray excess is due to annihilating dark matter, then a matching signal from unresolved prompt cusps should be detectable elsewhere. Moreover, the properties of prompt cusps are closely linked to details of the primordial density field. In warm dark matter models, prompt cusps are expected to be large enough to influence stellar motions within galaxies at detectable levels.

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Zoom link: https://pitp.zoom.us/j/98307421845?pwd=V3BqZmtyQ09XcjBwNEltTzFPTHJPUT09

In this informal talk, I shall give a short introduction to the field of higher-order quantum transformations, including its subfield of indefinite causal order. I shall discuss some of the motivations and important results in the field, current research directions and open problems, as well potential applications in quantum information processing.

In classical relativity we usually think of the metric signature as fixed, but quantum cosmology already forces us to consider more general situations such as transitions from Riemannian to Lorentzian signature. I will discuss the less studied phenomenon of an overall "flip" where all metric components change sign simultaneously (e.g., from "East Coast" to "West Coast" signature). Such an overall flip can represent saddle point solutions in quantum cosmology, or appear classically in the Plebański formalism or even a slight extension of Einstein--Hilbert gravity. Interestingly, at such a transition the cosmological constant can change both sign and magnitude, with a pure sign change being the most minimalistic proposal. Cosmological solutions transitioning classically between de Sitter and anti de Sitter can be found immediately, and the quantisation of a minisuperspace model turns out to be simpler than in the fixed signature case: in particular, the gravitational action reduces to a pure boundary term. Various other applications and the relation to unimodular gravity are also discussed.

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Zoom link: https://pitp.zoom.us/j/93255772501?pwd=bWhzZUVBOTM2a3QvTGlXVGJ5TlZnUT09

In quantum field theories, locality and unitarity are essential properties. For functorial field theories, locality is manifested through compatibility with cutting and gluing of manifolds, which can be fully encoded in the definition of fully extended functorial field theories. However, unitarity or reflection positivity (its Euclidean version) has so far only been defined for non-extended or invertible field theories. In this talk, I will address the challenge of defining reflection positivity for extended topological field theories, proposing a definition based on a version of higher dagger categories.

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Zoom link: https://pitp.zoom.us/j/93806769415?pwd=TVJFbWlJK0JyZCtjbHMvOWYxVUlRUT09

While Einstein's theory of gravity is formulated in a smooth setting, the singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature, there is a highly successful theory of metric and metric-measure geometry which includes Riemannian manifolds as a special case, but permits the extraction of nonsmooth limits under curvature and dimension bounds analogous to the energy conditions in relativity: here sectional curvature is reformulated through triangle comparison, while Ricci curvature is reformulated using entropic convexity along geodesics of probability measures.This lecture explores recent progress in the development of an analogous theory in Lorentzian signature, whose ultimate goal is to provide a nonsmooth theory of gravity. We highlight how the null energy condition of Penrose admits a nonsmooth formulation as a variable lower bound on timelike Ricci curvature. We discuss an example showing the null energy condition does not survive the same sort of limits that uniform bounds on the timelike Ricci curvature respect. 

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Zoom link: https://pitp.zoom.us/j/92777399316?pwd=QmNaM1J0elgyRGdmaGxCTTQxT2Y4QT09

I will begin by reviewing the general mathematical concept of representation. I will then show that representation theory is more generally applicable than one might expect, for example in quantum foundations, in quantum gravity and in machine learning. In those contexts, I will first talk about the notion of representation underlying phenomena of emergence in quantum gravity. I will then discuss how quantum reference frames might be viewed as representations. Finally, I will talk about how transformer models, such as GPT-4, construct representations of what they learn and, in that light, what it may take for machines to reach AGI or even consciousness.  

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Zoom link: https://pitp.zoom.us/j/99349397588?pwd=T056VjZXRWZWT28zY3VOZHFDcmQ3QT09

In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

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Zoom link: https://pitp.zoom.us/j/95550331572?pwd=OW1oYlBvUWVxaGNJRWl5aHVrS0pJZz09

In this colloquium, the communicative boundary between science and society in Africa will be explored, using physics as an illustration. Different types of contact zones and scenes will be discussed, as well as the societal impact of staging and narrative formats. Based on our ongoing engagement project Making Science the Star, an overview of the relationship between sender and receiver will be presented, and recipes for tuning this interaction to unlock untapped potential in predominantly non-scientific communities will be analyzed.

DISCLAIMER: This talk contains Season1 Episode2 from the show series Science In The City. This is used with permission from Dr. Stéphane Kenmoe, Producer of the series and Presenter of this talk.

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Bio: Stéphane Kenmoe got a Ph.D. in Physics from the Max Planck Institute for Iron Research in Germany in 2015. He is presently a habilitation candidate at the Faculty of Chemistry at the University of Duisburg-Essen, Germany. He is also a science popularizer on TV and on social media, a science writer and a novelist. In 2020, he produced the movie ‘’Science in the City’’ (Science dans la Cité) in Cameroon. He is very active in networking for the promotion of early career African scientists and for connecting science and society. He has won many awards for his engagement, among which the 2020 Diversity Prize for Academic Leadership at the University of Duisburg-Essen, the Falling Walls Award for Science Engagement in 2021 and the Award for Prototypes of Humanity of the Dubai Authority for arts and culture in 2022. Since 2022, he is the chief editor of the African Physics Newsletter, an electronic quarterly about physics in Africa published by the American Physical Society. 

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Zoom link: https://pitp.zoom.us/j/92725978684?pwd=Yys0ci9JdE0zS054SGxyaWoxZkdUUT09

In this talk, I will discuss the analyticity properties of 2d Ising field theories (IFTs). I will start with a short introduction to 2d Ising field theory, which is the continuous limit of the 2d Ising model on square lattice. Then the different spectrum scenarios for high-T and low-T domains will be introduced. Generally speaking, an IFT which sits not at the critical temperature and has a non-vanishing external field is neither solvable nor integrable. However, it's possible to look into the analytical properties of various quantities in the theory space, then further non-perturbative information can be extracted. I will focus on the analyticity properties for mass of the first excitation, and discuss its critical behaviours and dispersion relations in both ordered and disordered phase. Finally, if time allowed, I will switch to the analyticity properties of the analytical structure of S-matrices, and show various related interesting phenomenons together with unsolved problems

References:
[1], Ising field theory in a magnetic field: Analytic properties of the free energy, P. Fonseca and A. Zamolodchikov, hep-th/0112167 [hep-th].
[2], Ising Spectroscopy II: Particles and poles at T > Tc, A. Zamolodchikov, 1310.4821 [hep-th].
[3], 2D Ising Field Theory in a magnetic field: the Yang-Lee singularity, H. Xu and A. Zamolodchikov, 2203.11262 [hep-th].
[4], On the S-matrix of Ising field theory in two dimensions, B. Gabai and X. Yin, 1905.00710 [hep-th]
[5], Ising field theory in a magnetic field: phi^3 coupling at T > Tc, H. Xu and A. Zamolodchikov, 2304.07886 [hep-th]
[6], Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field, V.V.Mangazeev, B.Hagan and V.V.Bazhanov, 2308.15113 [hep-th]
[7], Ising Field Theory in a Magnetic Field: Extended analyticity properties of M1, H. Xu, in preparation.

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Zoom link: https://pitp.zoom.us/j/97062411964?pwd=TWFHU0I5UGw3eXZjZzRHUEFnbjlydz09

The Callan Rubakov Effect describes the interaction between (massless) fermions and a smooth monopole in 4d gauge theory. In this scenario, the fermions can probe the UV physics inside the monopole core which leads to interesting effects such as proton decay in GUT models. However, the monopole-fermion scattering appears to lead to out-states that are not in the perturbative Hilbert space. In this talk, we will review this issue and propose a new physical mechanism that resolves this long-standing confusion.

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Zoom link: https://pitp.zoom.us/j/93551249905?pwd=REJvOUtTMlh6RU0vRjZnRVdZckgyZz09