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Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs., Comment: 9 pages, 5 figures

Large language models (LLMs) have taken centre stage in debates on Artificial Intelligence. Yet there remains a gap in how to assess LLMs' conformity to important human values. In this paper, we investigate whether state-of-the-art LLMs, GPT-4 and Claude 2.1 (Gemini Pro and LLAMA 2 did not generate valid results) are moral hypocrites. We employ two research instruments based on the Moral Foundations Theory: (i) the Moral Foundations Questionnaire (MFQ), which investigates which values are considered morally relevant in abstract moral judgements; and (ii) the Moral Foundations Vignettes (MFVs), which evaluate moral cognition in concrete scenarios related to each moral foundation. We characterise conflicts in values between these different abstractions of moral evaluation as hypocrisy. We found that both models displayed reasonable consistency within each instrument compared to humans, but they displayed contradictory and hypocritical behaviour when we compared the abstract values present in the MFQ to the evaluation of concrete moral violations of the MFV., Comment: Final version available at: https://ojs.aaai.org/index.php/AIES/article/view/31704 13 pages, 4 figures, 2 tables

We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in [Phys. Rev. E \textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process allows the clustering coefficient to vary from $C=0.828$ to $C=0$ while maintaining the behavior of average path length and other relevant quantities as in the deterministic Apollonian network. Robustness against the random deletion of nodes is also reported on spectral quantities such as the ground-state localization degree and its energy gap to the first excited state. The loss of the $2\pi / 3$ rotation symmetry as a tree-like network emerges is investigated in the light of the hub wavefunction amplitude. Our findings expose the interplay between the small-world property and other distinctive traits exhibited by Apollonian networks, as well as their resilience against random attacks., Comment: 6 pages, 7 figures

Using the inverse period map of the Gauss-Manin connection associated with $QH^{*}(\mathbb{CP}^2)$ and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of $\mathbb{CP}^2$. In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the j-invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of $QH^{*}(\mathbb{CP}^2)$ in closed form as the composition of the Weierstrass $\wp$-function and the universal coverings of $\mathbb{C} \setminus (\mathbb{Z} \oplus e^{\frac{\pi i}{3}}\mathbb{Z})$ and $\mathbb{C} \setminus (\mathbb{Z} \oplus z\mathbb{Z})$ respectively.

The time evolution of a topological Su-Schrieffer-Heeger chain is analyzed through the statistics of speckle patterns. The emergence of topological edge states dramatically affects the dynamical fluctuations of the wavefunction. The intensity statistics is found to be described by a family of noncentral chi-squared distributions, with the noncentrality parameter reflecting on the degree of edge-state localization. The response of the speckle contrast with respect to the dimerization of the chain is explored in detail as well as the role of chiral symmetry-breaking disorder, number of edge states, their energy gap, and the locations between which the transport occurs. In addition to providing a venue for speckle customization, our results appeal to the use of speckle patterns for characterization of nontrivial topological properties., Comment: 6 pages, 4 figures

Large language models (LLMs) exhibit expert-level performance in tasks across a wide range of different domains. Ethical issues raised by LLMs and the need to align future versions makes it important to know how state of the art models reason about moral and legal issues. In this paper, we employ the methods of experimental psychology to probe into this question. We replicate eight studies from the experimental literature with instances of Google's Gemini Pro, Anthropic's Claude 2.1, OpenAI's GPT-4, and Meta's Llama 2 Chat 70b. We find that alignment with human responses shifts from one experiment to another, and that models differ amongst themselves as to their overall alignment, with GPT-4 taking a clear lead over all other models we tested. Nonetheless, even when LLM-generated responses are highly correlated to human responses, there are still systematic differences, with a tendency for models to exaggerate effects that are present among humans, in part by reducing variance. This recommends caution with regards to proposals of replacing human participants with current state-of-the-art LLMs in psychological research and highlights the need for further research about the distinctive aspects of machine psychology.

There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary Apollonian network and obtain two structures featuring a kind of dendritic growth. They are found to inherit the small-world and scale-free property from the original network but display no clustering. Other key network properties are explored as well. Our results reveal that the structure contained in the Apollonian network may be employed to model an even wider class of real-world systems.

We define certain extensions of Jacobi groups of $A_n$, prove an analogue of Chevalley Theorem for their invariants, and construct a Dubrovin Frobenius structure on it orbit space., Comment: arXiv admin note: text overlap with arXiv:1907.01436

In cold core of dark molecular clouds, where the UV radiation from external sources is strongly attenuated, cosmic rays can induce chemical reactions on the surface of ice-covered grains promoting the ejection of the processed material to the gas phase. We report the positive and negative secondary ion emission from pure CH3CN, C2H3CN and i-C3H7CN ices due to the bombardment of heavy ions (252Cf fission fragments), simulating the incidence of cosmic rays onto icy surfaces. The secondary ions emitted from each sample were analysed by time-of-flight mass spectrometry (TOF-MS), using Plasma Desorption Mass Spectrometry (PDMS) technique. Several ionic species were identified, indicating strong fragmentation on the frozen surface. Proton-transfer processes are suggested to play a role for positive ion desorption, as evidenced by the protonated RCNH+ parent molecules and (RCN)nH+ ionic clusters. The high electron affinity of the cyano radical seems to contribute to the strong emission of CN-, as well as anions attributed to the CHmCN- fragment and (RCN)nCN- cluster series. Sputtering and desorption of ion clusters (positive and negative) induced by heavy ion bombardment are suggested to constitute a route by which new neutral or ionised molecular species may be delivered to the gas phase where thermal desorption is negligible.

We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how the latter responds to it. We find that moderate hopping pushes down the critical disorder strength for the disordered channel throughout the entire spectrum compared to the usual phase diagram for the 3D Anderson model. In that case, the ordered channel begins to feature an effective disorder also leading to the emergence of mobility edges but with higher associated critical disorder values. Both channels become pretty much alike as their hopping strength is further increased, as expected. We also consider the case of two disordered components and show that in the presence of certain correlations among the parameters of both lattices, one obtains a disorder-free channel decoupled from the rest of the system., Comment: 6 pages, 4 figures

We define certain extensions of Jacobi groups of $A_1$, prove an analogue of Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.

Generating high-quality multi-particle entanglement between communicating parties is the primary resource in quantum teleportation protocols. To this aim, we show that the natural dynamics of a single spin chain is able to sustain the generation of two pairs of Bell states - possibly shared between a sender and a distant receiver - which can in turn enable two-qubit teleportation. In particular, we address a spin-1/2 chain with XX interactions, connecting two pairs of spins located at its boundaries, playing the roles of sender and receiver. In the regime where both end pairs are weakly coupled to the spin chain, it is possible to generate at predefinite times a state that has vanishing infidelity with the product state of two Bell pairs, thereby providing nearly unit fidelity of teleportation. We also derive an effective Hamiltonian via a second-order perturbation approach that faithfully reproduces the dynamics of the full system., Comment: 11 pages, 4 figures. Comments welcome

We study an entanglement transfer protocol in a two-leg ladder spin-1/2 chain in the presence of disorder. In the regime where on-site energies and the intrachain couplings follow aproximately constant proportions locally, we set up a scheme for high-fidelity state transfer via a disorder-protected subspace wherein fluctuations in the parameters do not depend on the global disorder of the system, accounted by $W$. Moreover, we find that the leakage of information from that subspace is actually suppressed upon increasing $W$ and thus the transfer fidelity, evaluated through the entanglement concurrence at the other end of the chain, builds up with the disorder strength., Comment: 6 pages, 2 figures; comments welcome

An arbitrary qubit can be transmitted through a spin chain by perturbatively coupling both communicating parties to it. Those so-called weak-coupling models rely on effective Rabi oscillations between them, yielding nearly maximum fidelity while offering great resilience against disorder with the cost of having long transfer times. Considering this framework, here we address a 1D non-symmetric channel connecting two spins, one placed at each end of it. Given any pattern of nearest-neighbor coupling strengths, we obtain an analytical expression that accounts for the effective long-range interaction between them and study the interplay between transfer time and fidelity. Furthermore, we show that homogeneous channels provide the best speed-fidelity tradeoff., Comment: 5 pages, 3 figures. Appendix added

We discuss the quantum Hall effect on a single-layer graphene in the framework of noncommutative (NC) phase space. We find it induces a shift in the Hall resistivity. Furthermore, comparison with experimental data reveals an upper bound on the magnitude of the momentum NC parameter $\eta$ in about $\sqrt{\eta}\leq 2.5 \, \mathrm{eV}/c$., Comment: 7 pages

We investigate a tight-binding electronic chain featuring diagonal and off-diagonal disorder, these being modelled through the long-range-correlated fractional Brownian motion. Particularly, by employing exact diagonalization methods, we evaluate how the eigenstate spectrum of the system and its related single-particle dynamics respond to both competing sources of disorder. Moreover, we report the possibility of carrying out efficient end-to-end quantum-state transfer protocols even in the presence of such generalized disorder due to the appearance of extended states around the middle of the band in the limit of strong correlations., Comment: 15 pages, 5 figures

We study the emergence of bipartite entanglement between a pair of spins weakly connected to the ends of a linear disordered $XY$ spin-1/2 channel. We analyze how their concurrence responds to structural and on-site fluctuations embodied by long-range spatially-correlated sequences. We show that the end-to-end entanglement is very robust against disorder and asymmetries in the channel provided that the degree of correlations are strong enough and both entangling parties are tuned accordingly. Our results offer further alternatives in the design of stable quantum communication protocols via imperfect channels., Comment: 6 pages, 4 figures

We study quantum-state transfer in $XX$ spin-$1/2$ chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modelled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform an almost perfect quantum-state transfer in most of the samples even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough. In that case, we also show that the lack of mirror symmetry does not affect much the likelihood of having high-quality outcomes. Our results advance a further step in designing robust devices for quantum communication protocols., Comment: 8 pages, 5 figures

We study the creation and distribution of entanglement in disordered $XY$-type spin-$1/2$ chains for the paradigmatic case of a single flipped spin prepared on a fully polarized background. The local magnetic field is set to follow a disordered long-range-correlated sequence with power-law spectrum. Depending on the degree of correlations of the disorder, a set of extended modes emerge in the middle of the band yielding an interplay between localization and delocalization. As a consequence, a rich variety of entanglement distribution patterns arises, which we evaluate here through the concurrence between two spins. We show that, even in the presence of disorder, the entanglement wave can be pushed to spread out reaching distant sites and also enhance pairwise entanglement between the initial site and the rest of the chain. We also study the propagation of an initial maximally-entangled state through the chain and show that correlated disorder improves the transmission quite significantly when compared with the uncorrelated counterpart. Our work contributes in designing solid-state devices for quantum information processing in the realistic setting of correlated static disorder., Comment: 11 pages, 7 figures

We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing correlation between both coordinates at different times. The effect stands out as a signature of spatial noncommutativity and thus could offer a way to experimentally detect the phenomena. We further discuss some limiting scenarios and the trade-off between the scale imposed by the NC structure and the parameters of the Brownian motion itself., Comment: 9 pages

We consider a coupled-cavity array, where each cavity interacts with an atom under the rotating-wave approximation. For a staggered pattern of inter-cavity couplings, a pair of field normal modes each bi-localized at the two array ends arise. A rich structure of dynamical regimes can hence be addressed depending on which resonance condition between the atom and field modes is set. We show that this can be harnessed to carry out high-fidelity quantum-state transfer (QST) of photonic, atomic or polaritonic states. Moreover, by partitioning the array into coupled modules of smaller length, the QST time can be substantially shortened without significantly affecting the fidelity., Comment: 12 pages, 8 figures