Search Talks

Quantum systems typically reach thermal equilibrium rather quickly when coupled to an external thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However, the gap, by itself, does not always yield a reasonable estimate for the thermalization time in many-body systems: without further structure, a uniform lower bound on it only constraints the thermalization time to be polynomially growing with system size. In this talk, we will discuss that for all 2-local models with commuting Hamiltonians, the thermalization time that one can estimate from the gap is in fact much smaller than direct estimates suggest: at most logarithmic in the system size. This yields the so-called rapid mixing of dissipative dynamics. We will show this result by proving that a finite gap directly implies a lower bound on the modified logarithmic Sobolev inequality (MLSI) for the class of models we consider. The result is particularly relevant for 1D systems, for which we can prove rapid thermalization with a constant decay rate, giving a qualitative improvement over all previous results. It also applies to hypercubic lattices, graphs with exponential growth rate, and trees with sufficiently fast decaying correlations in the Gibbs state. This has consequences for the rate of thermalization towards Gibbs states, and also for their relevant Wasserstein distances and transportation cost inequalities.

---

Zoom link https://pitp.zoom.us/j/91315419731?pwd=TGpFTjlHWEJZVWZkdTh6bDFKMjhQZz09

Standard model of cosmology is based on the cosmological principle. The cosmological principle states that the Universe is statistically homogeneous and isotropic on large scales. Is this hypothesis supported by the observations ? After a historical survey of the field, I shall use the high redshift data from radio galaxies and quasars to show that the early Universe does not seem to be isotropic and the rest frame of cosmic microwave background radiation does not coincide with the rest frame of distant sources. I shall also demonstrate that the cosmological principle is violated at a statistical significance of over 5-sigma.

---

Zoom link: https://pitp.zoom.us/j/94290315794?pwd=STFpalNNb1NNUHNPNWcvZlkreWNpZz09

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.

---

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

Abstract TBA

---

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.

--

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.

---

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