Search

We introduce a new approach for describing nonstationary quantum systems with a discrete energy spectrum. The essence of this approach is that we describe the evolution of a quantum system in a time-dependent basis. In a sense, this approach is similar to the description of the system in the interaction representation. However, the time dependence of the basic states of the representation is determined not by the evolution operator with a time-independent Hamiltonian but by the eigenstates of the time-dependent Hamiltonian defined at the current time. The time dependence of the basic states of the representation leads to the appearance of an additional term in the Schrödinger equation, which in the case of slowly changing parameters of the Hamiltonian can be considered as a small perturbation. The adiabatic representation is suitable in cases where it is impossible to apply the standard interaction representation. The application of the adiabatic representation is illustrated by the example of two spins connected by a magnetic dipole–dipole interaction in a slowly varying external magnetic field.

This work explores the generation of James Webb Space Telescope (JWSP) imagery via image-to-image translation from the available Hubble Space Telescope (HST) data. Comparative analysis encompasses the Pix2Pix, CycleGAN, TURBO, and DDPM-based Palette methodologies, assessing the criticality of image registration in astronomy. While the focus of this study is not on the scientific evaluation of model fairness, we note that the techniques employed may bear some limitations and the translated images could include elements that are not present in actual astronomical phenomena. To mitigate this, uncertainty estimation is integrated into our methodology, enhancing the translation’s integrity and assisting astronomers in distinguishing between reliable predictions and those of questionable certainty. The evaluation was performed using metrics including MSE, SSIM, PSNR, LPIPS, and FID. The paper introduces a novel approach to quantifying uncertainty within image translation, leveraging the stochastic nature of DDPMs. This innovation not only bolsters our confidence in the translated images but also provides a valuable tool for future astronomical experiment planning. By offering predictive insights when JWST data are unavailable, our approach allows for informed preparatory strategies for making observations with the upcoming JWST, potentially optimizing its precious observational resources. To the best of our knowledge, this work is the first attempt to apply image-to-image translation for astronomical sensor-to-sensor translation.

We present a novel information-theoretic framework, termed as TURBO, designed to systematically analyse and generalise auto-encoding methods. We start by examining the principles of information bottleneck and bottleneck-based networks in the auto-encoding setting and identifying their inherent limitations, which become more prominent for data with multiple relevant, physics-related representations. The TURBO framework is then introduced, providing a comprehensive derivation of its core concept consisting of the maximisation of mutual information between various data representations expressed in two directions reflecting the information flows. We illustrate that numerous prevalent neural network models are encompassed within this framework. The paper underscores the insufficiency of the information bottleneck concept in elucidating all such models, thereby establishing TURBO as a preferable theoretical reference. The introduction of TURBO contributes to a richer understanding of data representation and the structure of neural network models, enabling more efficient and versatile applications.

Six new complexes of the ligand HQcy (-4-(cyclohexanecarbonyl)-5-methyl-2-phenyl-2,4-dihydro-3H-pyrazol-3-one) and Ln3+ ions with emission in the near-infrared (Nd3+) or visible and near-infrared (Sm3+, Pr3+) spectral regions were synthesized and characterized using various methods, including single crystal X-ray diffraction. The study demonstrated that both tris complexes [LnQcy3(H2O)(EtOH)] and tetrakis-acids [H3O][LnQcy4] can be synthesized by varying the synthetic conditions. The photochemical properties of the complexes were investigated experimentally and theoretically using various molecular spectroscopy techniques and Judd–Ofelt theory. The objective was to quantitatively and qualitatively disclose the influence of complex stoichiometry on its luminescence properties. The study showed that the addition of an extra ligand molecule (in the tetrakis species) increased molar extinction by up to 2 times, affected the shape of photoluminescence spectra, especially of the Pr3+ complex, and increased the quantum yield of the Sm3+ complex by up to 2 times. The results obtained from this study provide insights into the luminescent properties of lanthanide coordination compounds, which are crucial for the design and development of novel photonic materials with tailored photophysical properties.

An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole–dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau–Majorana–Stuckelberg–Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.

We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.