As physicists pursue precision neutrino measurements, complementary experiments covering varied oscillation landscapes have become essential for resolving current tensions in global fits. This thesis presents projected sensitivities and forecasted performance of two next-generation long-baseline experiments: DUNE and T2HK, through detailed simulations addressing fundamental questions including neutrino mass ordering, leptonic CP violation, and the octant of $\theta_{23}$. We demonstrate through simulated analyses that while each experiment alone faces inherent degeneracies, their complementary features enable breakthrough projected sensitivities in both standard oscillation parameter measurements and forecasted searches for new physics beyond the Standard Model. The combined simulation results reveal that DUNE-T2HK synergy will be crucial for achieving a comprehensive understanding of neutrino properties in the coming decade.

We present a theoretical study of the magnetic field generated by a toroidal current loop situated in the equatorial plane of a non-rotating Schwarzschild black hole, based on the dynamics of charged particles. Using the exact general relativistic solution for the magnetic field, we analyze particle motion both analytically and numerically, identifying regions of stable and unstable orbits. In particular, we classify charged particle dynamics into attractive and repulsive Lorentz force configurations and show that in the attractive case, charged particles can accumulate near the current loop, forming collective currents that oppose the original current loop magnetic field. We demonstrate that charged particle accumulation can lead to the formation of toroidal structures analogous to radiation belts in the BH magnetosphere. We compare the curved spacetime solution to flat spacetime analogs and highlight general relativistic effects such as the existence of the innermost stable circular orbit for charged particles, which sets a lower bound for radiation belt formation. The divergence of the vector potential at the loop location in the idealized infinitesimal loop model is addressed, and we argue that a physically realistic model must consider a finite-width current distribution to avoid unphysical divergences in the effective potential.

We investigate the motion of test particles in quantum-gravitational backgrounds by introducing the concept of q--desics, quantum-corrected analogs of classical geodesics. Unlike standard approaches that rely solely on the expectation value of the spacetime metric, our formulation is based on the expectation value of quantum operators, such as the the affine connection-operator. This allows us to capture richer geometric information. We derive the q--desic equation using both Lagrangian and Hamiltonian methods and apply it to spherically symmetric static backgrounds obtained from canonical quantum gravity. Exemplary results include, light-like radial motion and circular motion with quantum gravitational corrections far above the Planck scale. This framework provides a refined description of motion in quantum spacetimes and opens new directions for probing the interface between quantum gravity and classical general relativity.

Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled $n=2$ Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous $U(1)$ symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.

It is well known that Kasner geometry with space-like singularity can be extended to bulk AdS-like geometry, furthermore one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including space-like geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

Determining crystal structures from X-ray diffraction data is fundamental across diverse scientific fields, yet remains a significant challenge when data is limited to low resolution. While recent deep learning models have made breakthroughs in solving the crystallographic phase problem, the resulting low-resolution electron density maps are often ambiguous and difficult to interpret. To overcome this critical bottleneck, we introduce XDXD, to our knowledge, the first end-to-end deep learning framework to determine a complete atomic model directly from low-resolution single-crystal X-ray diffraction data. Our diffusion-based generative model bypasses the need for manual map interpretation, producing chemically plausible crystal structures conditioned on the diffraction pattern. We demonstrate that XDXD achieves a 70.4\% match rate for structures with data limited to 2.0~Å resolution, with a root-mean-square error (RMSE) below 0.05. Evaluated on a benchmark of 24,000 experimental structures, our model proves to be robust and accurate. Furthermore, a case study on small peptides highlights the model's potential for extension to more complex systems, paving the way for automated structure solution in previously intractable cases.

Studies of entanglement dynamics in quantum many-body systems have focused largely on initial product states. Here, we investigate the far richer dynamics from initial entangled states, uncovering universal patterns across diverse systems ranging from many-body localization (MBL) to random quantum circuits. Our central finding is that the growth of entanglement entropy can exhibit a non-monotonic dependence on the initial entanglement in many non-ergodic systems, peaking for moderately entangled initial states. To understand this phenomenon, we introduce a conceptual framework that decomposes entanglement growth into two mechanisms: ``build'' and ``move''. The ``build'' mechanism creates new entanglement, while the ``move'' mechanism redistributes pre-existing entanglement throughout the system. We model a pure ``move'' dynamics with a random SWAP circuit, showing it uniformly distributes entanglement across all bipartitions. We find that MBL dynamics are ``move-dominated'', which naturally explains the observed non-monotonicity of the entanglement growth. This ``build-move'' framework offers a unified perspective for classifying diverse physical dynamics, deepening our understanding of entanglement propagation and information processing in quantum many-body systems.

Here we show that the phenomenon of arbitrarily long-lived quasinormal modes (called quasiresonances) of a massive scalar field in the vicinity of a black hole is not an artifact of the test field approximation, but takes place also when the (derivative) coupling of a scalar field with the Einstein tensor is taken into consideration. We observe that at large coupling and high multipole numbers, the growing modes appear in the spectrum, which are responsible for the eikonal instability of the field. For small coupling, when the configuration is stable, there appear the purely imaginary quasinormal modes which are nonperturbative in the coupling constant. At the sufficiently small coupling the nonminimal scalar field is stable and the asymptotic late-time tails are not affected by the coupling term. The accurate calculations of quasinormal frequencies for a massive scalar field with the derivative coupling in the Reissner-Nordström black-hole background are performed with the help of Frobenius method, time-domain integration and WKB expansion.

We present exact solutions to Cho-Maison magnetic monopole in a family of effective electroweak models that have a Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We find that the lower bound to the mass of the magnetic monopole is $M \geq 2\pi v/ g \approx 2.37\,\,\mathrm{TeV}$. We argue that this bound holds universally, not just in theories with a BPS limit.

In [J. Blazquez-Salcedo, C. Knoll, E. Radu, Phys. Rev. Lett. 126 (2021) no.10, 101102] asymptotically flat traversable wormhole solutions were obtained in the Einstein-Dirac-Maxwell theory without using phantom matter. The normalizable numerical solutions found therein require a peculiar behavior at the throat: the mirror symmetry relatively the throat leads to the nonsmoothness of gravitational and matter fields. In particular, one must postulate changing of the sign of the fermionic charge density at the throat, requiring coexistence of particle and antiparticles without annihilation and posing a membrane of matter at the throat with specific properties. Apparently this kind of configuration could not exist in nature. We show that there are wormhole solutions, which are asymmetric relative the throat and endowed by smooth gravitational and matter fields, thereby being free from all the above problems. This indicates that such wormhole configurations could also be supported in a realistic scenario.

Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's, have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern--Simons terms in the three-form field strength $H_{\mu\nu\rho}$ play a crucial role.

A false zero resistance behavior was observed during our study on the search of superconductivity in Ge-doped GaNb4Se8. This zero resistance was proved to be caused by open-circuit in multi-phase samples comprised of metals and insulators by measuring with four-probe method. The evidence strongly suggests that the reported superconductivity in hydrides should be carefully re-checked.

We extend recent discussions about the effect of nonzero temperature on the induced electric charge, due to CP violation, of a Dirac or an 't Hooft-Polyakov monopole. In particular, we determine the fractional electric charge of a very small 't Hooft-Polyakov monopole coupled to light fermions at nonzero temperature. If dyons with fractional electric charge exist in the Weinberg-Salam model, as recently suggested in the literature, then their charge too should be temperature dependent.

Core-collapse supernovae undergoing a first-order quantum chromodynamics (QCD) phase transition experience the collapse of the central proto-neutron star that leads to a second bounce. This event is accompanied by the release of a second neutrino burst. Unlike the first stellar core bounce neutrino burst which consists exclusively of electron neutrinos, the second burst is dominated by electron antineutrinos. Such a condition makes QCD supernovae an ideal site for the occurrence of fast neutrino flavor conversion (FFC), which can lead to rapid flavor equilibration and significantly impact the related neutrino signal. In this work, we perform a detailed analysis of the conditions for fast flavor instability (FFI) around and after the second neutrino burst in QCD phase transition supernova models launched from 25~$M_\odot$ and 40~$M_\odot$ progenitor models. We evaluate the relevant instability criteria and find two major phases of FFC. The first phase is closely associated with the collapse and the rapidly expanding shock wave, which is a direct consequence of the proto-neutron star collapse due to the phase transition. The second phase takes place a few milliseconds later when electron degeneracy is restored near the proto-neutron star surface. We also characterize the growth rate of FFI and estimate its impact on the evolution of the neutrino flavor content. The potential observational consequences on neutrino signals are evaluated by comparing a scenario assuming complete flavor equipartition with other scenarios without FFC. Finally, we investigate how FFC may influences $r$-process nucleosynthesis associated with QCD phase transition driven supernova explosions.

The aspect-based sentiment analysis (ABSA) is a standard NLP task with numerous approaches and benchmarks, where large language models (LLM) represent the current state-of-the-art. We focus on ABSA subtasks based on Twitter/X data in underrepresented languages. On such narrow tasks, small tuned language models can often outperform universal large ones, providing available and cheap solutions. We fine-tune several LLMs (BERT, BERTweet, Llama2, Llama3, Mistral) for classification of sentiment towards Russia and Ukraine in the context of the ongoing military conflict. The training/testing dataset was obtained from the academic API from Twitter/X during 2023, narrowed to the languages of the V4 countries (Czech Republic, Slovakia, Poland, Hungary). Then we measure their performance under a variety of settings including translations, sentiment targets, in-context learning and more, using GPT4 as a reference model. We document several interesting phenomena demonstrating, among others, that some models are much better fine-tunable on multilingual Twitter tasks than others, and that they can reach the SOTA level with a very small training set. Finally we identify combinations of settings providing the best results.

Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams, implementing systematic renormalization, and evaluating high-dimensional integrals. We present a unifying framework that integrates QFT computational workflows with an AI-powered technology stack. A cornerstone of this framework is representing Feynman diagrams as computational graphs, which structures the inherent mathematical complexity and facilitates the application of optimized algorithms developed for machine learning and high-performance computing. Consequently, automatic differentiation, native to these graph representations, delivers efficient, fully automated, high-order field-theoretic renormalization procedures. This graph-centric approach also enables sophisticated numerical integration; our neural-network-enhanced Monte Carlo method, accelerated via massively parallel GPU implementation, efficiently evaluates challenging high-dimensional diagrammatic integrals. Applying this framework to the uniform electron gas, we determine the quasiparticle effective mass to a precision significantly surpassing current state-of-the-art simulations. Our work demonstrates the transformative potential of integrating AI-driven computational advances with QFT, opening systematic pathways for solving complex quantum many-body problems across disciplines.