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We extend the theory of quantum time loops introduced by Greenberger and Szovil [1] from the scalar situation (where paths have just an associated complex amplitude) to the general situation where the time traveling system has multi-dimensional underlying Hilbert space. The main mathematical tool which emerges is the noncommutative M\{o}bius Transformation and this affords a formalism similar to the modular structure well known to feedback control problems. We argue that a sum-over-all-paths approach may be carried out in the scalar case, but quickly becomes unwieldy in the general case. It is natural to replace the beamsplitters of [1] with more general components having their own quantum structure, in which case the theory starts to resemble the quantum feedback networks theory for open quantum optical models and indeed we exploit this to look at more realistic physical models of time loops. We analyze some Grandfather paradoxes in the new setting, Comment: 9 pages, 11 Figures

We give a simple argument to derive the transformation of quantum stochastic calculus formalism between inertial observers, and derive the quantum open system dynamics for a system moving in a vacuum (more generally coherent) quantum field under the usual Markov approximation. We argue that for uniformly accelerated open systems, however, the formalism must breakdown as we move from a Fock representation of the quantum noise to a unitarily inequivalent non-Fock representation - in particular, the latter is a thermal representation at the Unruh temperature. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes., Comment: 4 pages, no figures

A significant limitation of current smartphone-based eye-tracking algorithms is their low accuracy when applied to video-type visual stimuli, as they are typically trained on static images. Also, the increasing demand for real-time interactive applications like games, VR, and AR on smartphones requires overcoming the limitations posed by resource constraints such as limited computational power, battery life, and network bandwidth. Therefore, we developed two new smartphone eye-tracking techniques for video-type visuals by combining Convolutional Neural Networks (CNN) with two different Recurrent Neural Networks (RNN), namely Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU). Our CNN+LSTM and CNN+GRU models achieved an average Root Mean Square Error of 0.955cm and 1.091cm, respectively. To address the computational constraints of smartphones, we developed an edge intelligence architecture to enhance the performance of smartphone-based eye tracking. We applied various optimisation methods like quantisation and pruning to deep learning models for better energy, CPU, and memory usage on edge devices, focusing on real-time processing. Using model quantisation, the model inference time in the CNN+LSTM and CNN+GRU models was reduced by 21.72% and 19.50%, respectively, on edge devices.

In this paper, we study both open-loop control and closed-loop measurement feedback control of non-Markovian quantum dynamics resulting from the interaction between a quantum system and its environment. We use the widely studied cavity quantum electrodynamics (cavity-QED) system as an example, where an atom interacts with the environment composed of a collection of oscillators. In this scenario, the stochastic interactions between the atom and the environment can introduce non-Markovian characteristics into the evolution of quantum states, differing from the conventional Markovian dynamics observed in open quantum systems. As a result, the atom's decay rate to the environment varies with time and can be described by nonlinear equations. The solutions to these nonlinear equations can be analyzed in terms of the stability of a nonlinear control system. Consequently, the evolution of quantum state amplitudes follows linear time-varying equations as a result of the non-Markovian quantum transient process. Additionally, by using measurement feedback through homodyne detection of the cavity output, we can modulate the steady atomic and photonic states in the non-Markovian process. When multiple coupled cavity-QED systems are involved, measurement-based feedback control can influence the dynamics of high-dimensional quantum states, as well as the resulting stable and unstable subspaces.

We give a derivation of the non-Markovian quantum state diffusion equation of Di{\'o}si and Strunz starting from a model of a quantum mechanical system coupled to a bosonic bath. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal (complex wave) representation of the bath. In particular, we construct a reproducing kernel Hilbert space for the bath auto-correlation and realize the space of complex trajectories as a Hilbert subspace. The reproducing kernel naturally arises from a feature space where the underlying feature space is the one-particle Hilbert space of the bath quanta. We exploit this to derive the unravelling of the open quantum system dynamics and show equivalence to the equation of Di{\'o}si and Strunz. We also give an explicit expression for the reduced dynamics of a two-level system coupled to the bath via a Jaynes-Cummings interaction and show that this does indeed correspond to an exact solution of the Di{\'o}si-Strunz equation. Finally, we discuss the physical interpretation of the complex trajectories and show that they are intrinsically unobservable., Comment: 16 pages

We give an exact formula for the rate of change of the von Neumann entropy for the conditional state of a quantum system undergoing continuous measurement. Here we employ Paycha's Formula \cite{Paycha} which gives the noncommutative Taylor series development., Comment: 9 pages, 0 figures

Nancy Grace Roman Space Telescope will revolutionize our understanding of the Galactic Bulge with its Galactic Bulge Time Domain survey. At the same time, Rubin Observatories's Legacy Survey of Space and Time (LSST) will monitor billions of stars in the Milky Way. The proposed Roman survey of the Galactic Plane, with its NIR passbands and exquisite spacial resolution, promises groundbreaking insights for a wide range of time-domain galactic astrophysics. In this white paper, we describe the scientific returns possible from the combination of the Roman Galactic Plane Survey with the data from LSST., Comment: 8 pages, 1 figure, submitted to the 2024 Call for Community Input into the Definition of a Roman Galactic Plane Survey

Ultralight candidates for dark matter can present wavelike features on astrophysical scales. Full wave based simulations of such candidates are currently limited to box sizes of 1--10 Mpc/$h$ on a side, limiting our understanding of the impact of wave dynamics on the scale of the cosmic web. We present a statistical analysis of density fields produced by perturbative forward models in boxes of 128 Mpc/$h$ side length. Our wave-based perturbation theory maintains interference on all scales, and is compared to fluid dynamics of Lagrangian perturbation theory. The impact of suppressed power in the initial conditions and interference effects caused by wave dynamics can then be disentangled. We find that changing the initial conditions captures most of the change in one-point statistics such as the skewness of the density field. However, different environments of the cosmic web, quantified by critical points of the smoothed density, appear to be more sensitive to interference effects sourced by the quantum potential. This suggests that certain large-scale summary statistics may need additional care when studying cosmologies with wavelike dark matter., Comment: Accepted in Open Journal of Astrophysics, 15 pages + appendices, 16 figures

Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that that radius is more- or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ nonhomologously from those of the standard solar model., Comment: 19 pages, 5 figures, accepted for publication in MNRAS

In this paper, we show that quantum feedback control may be applied to generate desired states for atomic and photonic systems based on a semi-infinite waveguide coupled with multiple two-level atoms. In this set-up, an initially excited atom can emit one photon into the waveguide, which can be reflected by the terminal mirror or other atoms to establish different feedback loops via the coherent interactions between the atom and photon. When there are at most two excitations in the waveguide quantum electrodynamics (waveguide QED) system, the evolution of quantum states can be interpreted using random graph theory. While this process is influenced by the environment, and we clarify that the environment-induced dynamics can be eliminated by measurement-based feedback control or coherent drives. Thus, in the open system atom-waveguide interactions, measurement-based feedback can modulate the final steady quantum state, while simultaneously, the homodyne detection noise in the measurement process can induce oscillations, which is treated by the coherent feedback designs., Comment: 25 pages, 5 figures

[Abridged] The Nancy Grace Roman Space Telescope will be one of several flagship survey facilities operating over the next decade starting $\sim$2025. The deep near-IR imaging that Roman will deliver will be highly complementary to the capabilities of other survey telescopes that will operate contemporaneously, particularly those that can provide data at different wavelengths and messengers, or different time intervals. Combining data from multiple facilities can provide important astrophysical insights, provided the data acquisition is carefully scheduled, and careful plans are made for appropriate joint data analyses. In this White Paper, we discuss the broad range of science that would be enabled by coordinating Roman observations of the Galactic Bulge with those of the Vera C. Rubin Observatory. Specifically, we discuss how Roman's characterization of lensing events caused by exoplanets, stellar systems and stellar remnants can be enhanced by data from Rubin. The same data will also be highly advantageous for the determination of stellar properties, and for distinguishing exoplanetary transits. It will enable more accurate period-color-luminosity relationships to be measured for RR~Lyrae throughout the Milky Way Bulge and Bar, probing galactic structure and dynamics. But we stress that this is only a sample of the full potential and advocate for a more complete study to be made as a joint effort between these major projects. We note that we do not suggest any changes beyond the established Science Requirements for the RGBTDS, in terms of survey footprint or filter selection., Comment: Submitted to the 2023 call for White Papers regarding the Roman Mission Core Community Surveys