Integrability and action-angle variables of binary black holes at second post-Newtonian order

Accurate and efficient modeling of binary black holes (BBHs) is crucial for the detection of gravitational waves (GWs) emitted by them. Closed-form solutions to these systems when they are in the initial inspiral phase are highly sought after and have been worked out by many groups in the post-Newtonian (PN) approximation. Most of these worked-out solutions are valid only in certain limits (small eccentricity, no spins, equal mass, etc). Establishing the integrable nature of PN BBHs opens up the possibility of constructing closed-form solutions since integrability precludes chaos and guarantees the existence of action-angle variables. In this talk, against the backdrop of the PN Hamiltonian framework, I will discuss our series of efforts in establishing the integrable nature of the most general BBH system (arbitrary masses, spins, and eccentricity) as per the Liouville-Arnold theorem at 2PN order. I will also discuss our recently derived action-angle-based solution for these systems at 1.5PN order.

Quantum Computing, Quantum Teleportation and Time Crystals

Quantum Computing is parallel computing and is nonlocal in nature. Geometry, physics, and computing are triangularly interrelated. There exist four new fundamental nonlocal operator-state relations for an entangled atomic chain. Computation states are then cyclic. There exists a minimum focus distance for the entanglement between two atoms. Any addition of four times of that focus distance provides the foundation for quantum teleportation in a piece-wise Euclidean chain. Time crystals are the direct computation results that an entangled atomic chain is capable of computing. There are four interacting planar time crystals with the same Poincare cycle, but only half of them are observable as we predict, and quantum computing is irreversible. When the geometry changes, there exist “spherical time crystals” from the rotational symmetry breaking. Thus, we predict that “time” can be “curved” in Fourier space, the space we observe all the computation results. In a long chain, it is possible to have “birth-and-death” of time crystals elsewhere in the chain. Sierpinski triangle with self-similar features provides the foundation for true artificial intelligence and the larger-scale operator-state relations to emerge.

An introduction to the quantum vacuum

One of the most fascinating predictions of quantum field theory is that quantum fluctuations induce nonlinearities in the quantum vacuum. These nonlinearities lead to a number of surprising phenomena: the vacuum behaves like a polarising material, it acts to screen electric charge, and is even unstable to the application of electric fields, "decaying" via the Schwinger pair-creation mechanism.

This talk will provide a pedagogical introduction to the quantum vacuum in quantum electrodynamics. I will discuss vacuum polarisation and charge screening in standard QFT, and will then describe the richer structure of the vacuum in the presence of external electromagnetic fields. Finally I will describe some experimental facilities currently under construction that are aiming to probe the nonlinear structure of the vacuum for the first time. Comments and questions will be welcome throughout!

Classification of the universal dynamics in two-dimensional strongly ferromagnetic superfluids

Scale invariance and self-similarity in physics provide a unified framework to classify phases of matter and dynamical properties of near- and far-from-equilibrium many-body systems. To address universality, we monitor the non equilibrium dynamics of a two-dimensional ferromagnetic spinor gas subjected to quenches of the quadratic Zeeman coefficient. This allows to dynamically cross the underlying second-order magnetic phase transitions triggering spin-mixing. Within the short time-evolution we observe the spontaneous nucleation of topological defects (gauge or spin vortices) which annihilate through their interaction giving rise to magnetic domains for longer timescales where the gas enters the universal coarsening regime. This is characterized by the spatiotemporal scaling of the spin correlation functions and structure factor allowing to measure corresponding scaling exponents which depend crucially on the symmetry of the order parameter and belong to distinct universality classes. Our experimental observations are in excellent agreement with the predictions of the truncated Wigner method accounting both for quantum and thermal fluctuations in the initial state. These results represent a paradigmatic example of categorizing far-from-equilibrium dynamics in quantum many-body systems and reveal the interplay of topological defects for the emergent universality class.

An introduction to the quantum vacuum

One of the most fascinating predictions of quantum field theory is that quantum fluctuations induce nonlinearities in the quantum vacuum. These nonlinearities lead to a number of surprising phenomena: the vacuum behaves like a polarising material, it acts to screen electric charge, and is even unstable to the application of electric fields, "decaying" via the Schwinger pair-creation mechanism.

This talk will provide a pedagogical introduction to the quantum vacuum in quantum electrodynamics. I will discuss vacuum polarisation and charge screening in standard QFT, and will then describe the richer structure of the vacuum in the presence of external electromagnetic fields. Finally I will describe some experimental facilities currently under construction that are aiming to probe the nonlinear structure of the vacuum for the first time. Comments and questions will be welcome throughout!