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Non-normalizable quantum states are usually discarded as mathematical artefacts in quantum mechanics. However, such states naturally occur in quantum gravity as solutions to physical constraints. This suggests reconsidering the interpretation of such states. Some of the existing approaches to this question seek to redefine the inner product, but this arguably leads to further challenges. 

In this talk, I will propose an alternative interpretation of non-normalizable states using pilot-wave theory. First, I will argue that the basic conceptual structure of the theory contains a straightforward interpretation of these states. Second, to better understand such states, I will discuss non-normalizable states of the quantum harmonic oscillator from a pilot-wave perspective. I will show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the pilot-wave velocity field vy→0 at large ±y. Third, I will introduce a new notion of equilibrium, named pilot-wave equilibrium, and use it to define physically-meaningful equilibrium densities for such states. I will show, via an H-theorem, that an arbitrary initial density with compact support relaxes to pilot-wave equilibrium at a coarse-grained level, under assumptions similar to those for relaxation to quantum equilibrium. I will conclude by discussing the implications for pilot-wave theory, quantum gravity and quantum foundations in general. 

Based on:

I. Sen. "Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium" arXiv:2208.08945 (2022)

Zoom link:  https://pitp.zoom.us/j/93736627504?pwd=VGtxZE5rTFdnT1dqZlFRWTFvWlFQUT09

Experimental realizations of long-range entangled states such as quantum spin liquids are challenging due to numerous complications in solid state materials. Digital quantum simulators, on the other hand, have recently emerged as a promising platform to controllably simulate exotic phases. I will talk about a constructive design of long-range entangled states in this setting, and exploit competing measurements as a new source of frustration to generate spin liquid. Specifically, we consider random projective measurements of the anisotropic interactions in the Kitaev honeycomb model. The monitored trajectories can produce analogues of the two phases in the original Kitaev model: (i) a topologically-ordered phase with area-law entanglement and two protected logical qubits, and (ii) a “critical” phase with a logarithmic violation of area-law entanglement and long-range tripartite entanglement. A Majorana parton description permits an analytic understanding of these two phases through a classical loop model. Extensive numerical simulations of the  monitored dynamics confirm our analytic predictions. This talk is based on https://arxiv.org/abs/2207.02877.

Zoom link:  https://pitp.zoom.us/j/99600719755?pwd=a0pOWlliU0swVDdGYnhxaGFGNkJSdz09

Quantum correlations in general and quantum entanglement in particular embody both our continued struggle towards a foundational understanding of quantum theory as well as the latter’s advantage over classical physics in various information processing tasks. Consequently, the problems of classifying (i) quantum states from more general (non-signalling) correlations, and (ii) entangled states within the set of all quantum states, are at the heart of the subject of quantum information theory.

In this talk I will present two recent results (from https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.062420 and https://arxiv.org/abs/2207.00024) that shed new light on these problems, by exploiting a surprising connection with time in quantum theory:

First, I will sketch a solution to problem (i) for the bipartite case, which identifies a key physical principle obeyed by quantum theory: quantum states preserve local time orientations—roughly, the unitary evolution in local subsystems.

Second, I will show that time orientations are intimately connected with quantum entanglement: a bipartite quantum state is separable if and only if it preserves arbitrary local time orientations. As a variant of Peres's well-known entanglement criterion, this provides a solution to problem (ii).

Zoom link:  https://pitp.zoom.us/j/97607837999?pwd=cXBYUmFVaDRpeFJSZ0JzVmhSajdwQT09

Scientific programs involving joint analyses of different tracers of large-scale structure and CMB are increasingly gaining attention as they often increase the prospects to detect and characterise new signals by reducing systematics, cancelling cosmic variance and breaking degeneracies. In this talk, I will demonstrate how these programs will provide the most precise tests of fundamental physics by measuring galaxy peculiar velocity throughout cosmic time, opening new and unique windows into unexplored epochs of structure formation such as the epoch helium reionization, making pioneering first detections of multiple CMB signals and reducing the confusion effects from scattering and lensing on the CMB, while not requiring new experiments other than those being built or proposed.

Zoom link:  https://pitp.zoom.us/j/98508740176?pwd=a3BUc1lpZi82c0R0SkJyd1FPRFRUZz09

The observation of the Cosmic Microwave Background (CMB) is a powerful probe to unravel many mysteries of the late-time Universe. During the first half of the talk, I will discuss how future low-noise and high-resolution CMB experiments can be used to probe the detailed physics of reionization, constraining the morphology, shape, and temperature of ionized bubbles. Furthermore, I will talk about the prospects of LSS x CMB to understand the thermodynamic properties of gas in the halos. In the second part of my talk, I will also talk about "line intensity mapping", a novel technique that will provide us with new information from the star formation in galaxies to the expansion of our Universe. Mentioning the viable challenges, I will discuss the estimators to extract the signal in the presence of interlopers and instrumental noise. I will also describe how the MLIM could help us to perform cross-correlations with complementary probes such as CMB lensing and galaxy field. In the end, I will present the constraints on astrophysical and cosmological parameters that we hope to achieve from future intensity mapping observations.

Zoom link:  https://pitp.zoom.us/j/93308659447?pwd=VVM2czBWc0NTeTA5eTRWdzVFRUtndz09