Talks

Building on the fact that quantum uncertainty is a dynamical degree of freedom in itself in quantum mechanics, I will start with the remark that its evolution can provide a notion of intrinsic clock. To illustrate the non-triviality of this idea, we’ll check the dynamics of the uncertainty if gravitizing quantum mechanics into a non-linear Schrödinger equation, and will see that it (surprisingly?) follows the same trajectories as planetary orbits. A third thread will come from the black hole mini-superspace in general relativity. We will see that, assuming that the quantization preserves all the symmetries of the theory, universal quantum gravity corrections can also be written as a non-linear Schrödinger equation, leading to a non-trivial evolution of the “classicality” of black hole wave-packets along the radial coordinate.

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Zoom link: https://pitp.zoom.us/j/95808416532?pwd=cHJnVXpzdDd3eXdFbUlMamFsMFV3UT09

Abstract TBA

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Zoom link: https://pitp.zoom.us/j/91816652867?pwd=bnQzYzA0SXBuL3BTTmNUMFBMcEFWdz09

Anticipating the launch of several next-generation gravitational wave (GW) detectors in the 2030s, we will be able to more precisely measure spacetime ripples from binary black hole (BH) mergers in a larger parameter space. The forthcoming data will require us to develop more accurate predictions of GWs not only in General Relativity (GR) but also in theories beyond GR and diverse astrophysical environments. Black hole perturbation theory is a cornerstone for making these predictions. In recent years, there have been extensive studies of perturbations of BHs in theories beyond GR, but only for non-rotating or slowly rotating BHs. In this talk, I will present a new formalism, based on Teukolsky's seminal work in the 1970s, to study perturbations of BHs with arbitrary spin in beyond-GR theories and in more complicated astrophysical environments. I will first discuss how to derive a modified Teukolsky equation for BHs deforming perturbatively from their counterparts in GR due to beyond-GR or environmental effects and the necessary techniques to evaluate this equation. Subsequently, I will discuss some applications of this formalism. Specifically, I will prescribe utilizing this formalism to investigate the isospectrality breaking of quasinormal modes (QNMs) in beyond-GR theories, compute the QNM frequency shifts in some specific theories, and efficiently extract these shifts from observation data. Furthermore, I will also show how to apply this formalism to study extreme mass-ratio inspirals beyond GR.

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Zoom link: https://pitp.zoom.us/j/99282316326?pwd=REtBSFUxdlgxUGVwZFFvVEVBVnFTUT09

We study the quantum connection in positive characteristic for conical symplectic resolutions. We conjecture the equivalence of the p-curvature of such connections with (equivariant generalizations of) quantum Steenrod operations of Fukaya and Wilkins, which are endomorphisms of mod p quantum cohomology deforming the Steenrod operations. The conjecture is verified in a wide range of examples, including the Springer resolution, thereby providing a geometric interpretation of the p-curvature and a full computation of quantum Steenrod operations. The key ingredients are a new compatibility relation between the quantum Steenrod operations and the shift operators, and structural results for the mod p quantum connection recently obtained by Etingof--Varchenko.

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Zoom link: https://pitp.zoom.us/j/91010341249?pwd=QXJuMlJrWWd0dHpPdUpDUGVqVmYvZz09

Supermaps are higher-order transformations taking maps as input.  We consider quantum algorithms implementing supermaps for the input given by unknown Hamiltonian dynamics, which can be regarded as infinitely divisible unitary operations.  We first show a quantum algorithm that approximately but universally transforms black-box Hamiltonian dynamics into controlled Hamiltonian dynamics utilizing a higher-order transformation called neutralization.  Then, we present another universal algorithm that efficiently simulates linear transformations of any Hamiltonian consisting of a polynomial number of terms in system size, using only controlled-Pauli gates and time-correlated randomness.  This algorithm for implementing Hamiltonian supermaps is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. As examples, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.

References:

Q. Dong, S. Nakayama, A. Soeda and M. Murao, arXiv:1911.01645v3
T. Odake, Hlér Kristjánsson, A. Soeda M. Murao, arXiv:2303.09788

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Zoom Link: https://pitp.zoom.us/j/94278362588?pwd=MGszYk9uN1A3K1RTOVhYSGpkL1FQdz09

I argue that the answer is yes, by reviewing the history and current status of such a theory.  Since 1982, I have been developing a series of such theories, beginning in 1982 with an N --> infinity limit of 2+1 dimensional matrix model (the IAS model), through another N --> infinity, T --> 0 limit of a BFSS model.  During this time our work was complemented by Adler's Trace model and others.   

Beginning in 2012, Cortes and I developed a different approach to an relational quantum cosmology by adding intrinsic energy momentum to Sorkin et al's causal set models.  The addition of energy- momentum as intrinsic variables opens up a new mechanism for the emergence of space, and spacetime, plus interacting relativistic particles.  Note that the warm phase is purely algebraic, you need no prior existence of any space to get other dimensions to emerge.   In 2021 I discovered how to derive quantum non-relativistic many body theory from what has since been called the Causal Theory of Views.  Finally in papers since we report progress on the construction of special and general relativistic  Causal Theory of Views.

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Zoom link: https://pitp.zoom.us/j/95891848248?pwd=TUpWK2RWbU9GTGxZS1lMeS81QWp1dz09

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spacetime region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We first derive a bound on the accessible information and demonstrate that the Bekenstein bound constrains the decoding instead of the encoding. Then we study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is therefore confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound. In contrast, the entanglement-assisted capacity is as large as the input size even at arbitrarily high Unruh temperatures. This reflects that the Bekenstein bound can be violated if we do not properly constrain the decoding operation in accordance with the bound. We further find that the Unruh channel can transmit a significant number of zero-bits, which are communication resources that can be used as minimal substitutes for the classical/quantum bits needed for many primitive information processing protocols, such as dense coding and teleportation. We show that the Unruh channel has a large zero-bit capacity even at high temperatures, which underpins the capacity boost with entanglement assistance and allows Alice and Bob to perform quantum identification. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are not constrained by the Bekenstein bound. (This talk is based on the recent work (https://arxiv.org/abs/2309.07436) with Patrick Hayden.)

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Zoom link: https://pitp.zoom.us/j/98778081764?pwd=WktjNU84R3NWRXNyVmt1eDVMK2JnUT09