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Published: Apr 16, 2021

Authors: Wimmer-Schweingruber, R., et al

Published: Apr 16, 2021

Authors: Wimmer-Schweingruber, R., et al

In review of the White Papers from the Voyage 2050 process and after the public presentation of a number of these papers in October 2019 in Madrid, we as White Paper lead authors have identified a coherent science theme that transcends the divisions around which the Topical Teams are structured. This note aims to highlight this synergistic science theme and to make the Topical Teams and the Voyage 2050 Senior Committee aware of the wide importance of these topics and the broad support that they have across the worldwide science community.

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Published: Apr 17, 2021

Authors: Christoph Riedl, Michael Foley, Rory Smead, Patrick Forber, Christoph Riedl

Published: Apr 17, 2021

Authors: Christoph Riedl, Michael Foley, Rory Smead, Patrick Forber, Christoph Riedl

Can egalitarian norms or conventions survive the presence of dominant individuals who are ensured of victory in conflicts? We investigate the interaction of power asymmetry and partner choice in games of conflict over a contested resource. We introduce three models to study the emergence and resilience of cooperation among unequals when interaction is random, when individuals can choose their partners, and where power asymmetries dynamically depend on accumulated payoffs. We find that the ability to avoid bullies with higher competitive ability afforded by partner choice mostly restores cooperative conventions and that the competitive hierarchy never forms. Partner choice counteracts the hyper dominance of bullies who are isolated in the network and eliminates the need for others to coordinate in a coalition. When competitive ability dynamically depends on cumulative payoffs, complex cycles of coupled network-strategy-rank changes emerge. Effective collaborators gain popularity (and thus power), adopt aggressive behavior, get isolated, and ultimately lose power. Neither the network nor behavior converge to a stable equilibrium. Despite the instability of power dynamics, the cooperative convention in the population remains stable overall and long-term inequality is completely eliminated. The interaction between partner choice and dynamic power asymmetry is crucial for these results: without partner choice, bullies cannot be isolated, and without dynamic power asymmetry, bullies do not lose their power even when isolated. We analytically identify a single critical point that marks a phase transition in all three iterations of our models. This critical point is where the first individual breaks from the convention and cycles start to emerge.

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Published: Apr 14, 2021

Authors: Gigliola Staffilani, Matthew Rosenzweig, Gigliola Staffilani

Published: Apr 14, 2021

Authors: Gigliola Staffilani, Matthew Rosenzweig, Gigliola Staffilani

In arXiv:1201.4067 and arXiv:1611.08030, Eyink and Shi and Chibbaro et al., respectively, formally derived an infinite, coupled hierarchy of equations for the spectral correlation functions of a system of weakly interacting nonlinear dispersive waves with random phases in the standard kinetic limit. Analogously to the relationship between the Boltzmann hierarchy and Boltzmann equation, this spectral hierarchy admits a special class of factorized solutions, where each factor is a solution to the wave kinetic equation (WKE). A question left open by these works and highly relevant for the mathematical derivation of the WKE is whether solutions of the spectral hierarchy are unique, in particular whether factorized initial data necessarily lead to factorized solutions. In this article, we affirmatively answer this question in the case of 4-wave interactions by showing, for the first time, that this spectral hierarchy is well-posed in an appropriate function space. Our proof draws on work of Chen and Pavlovi\'{c} for the Gross-Pitaevskii hierarchy in quantum many-body theory and of Germain et al. for the well-posedness of the WKE.

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Published: Apr 14, 2021

Authors: Atul Sharma, Atul Sharma

Published: Apr 14, 2021

Authors: Atul Sharma, Atul Sharma

We reformulate Euclidean general relativity without cosmological constant as an action governing the complex structure of twistor space. Extending Penrose's non-linear graviton construction, we find a correspondence between twistor spaces with partially integrable almost complex structures and four-dimensional space-times with off-shell metrics. Using this, we prove that our twistor action reduces to Plebanski's action for general relativity via the Penrose transform. This should lead to new insights into the geometry of graviton scattering as well as to the derivation of computational tools like gravitational MHV rules.

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Published: Apr 14, 2021

Authors: Joseph Subotnik, Vishikh Athavale, Hung-Hsuan Teh, Joseph Subotnik

Published: Apr 14, 2021

Authors: Joseph Subotnik, Vishikh Athavale, Hung-Hsuan Teh, Joseph Subotnik

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a CIS or TD-DFT configuration interaction Hamiltonian for a set of test cases. We find that, although we cannot achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

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Published: Apr 15, 2021

Authors: Vázquez, Saulo, et al

Published: Apr 15, 2021

Authors: Vázquez, Saulo, et al

A new approach is presented to improve the performance of semiempirical quantum mechanical (SQM) methods in the description of noncovalent interactions. To show the strategy, the PM6 Hamiltonian was selected, although, in general, the procedure can be applied to other semiempirical Hamiltonians and to different methodologies. In this way, analytical corrections to PM6 were derived from fits to CCSD(T) - PM6 interaction energy differences. A set of small molecules was selected as representative of the common functional groups, and intermolecular potential energy curves were evaluated for the most relevant orientations of interacting molecular pairs. The resulting method, called PM6-FGC (from Functional Group Corrections), significantly improves the performance of PM6 and previous corrected SQM methods, and shows the importance of including a sufficient number of orientations of the interacting molecules in the reference data set in order to obtain well-balanced descriptions.

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Published: Apr 15, 2021

Authors: V. Obukhov, V. Obukhov

Published: Apr 15, 2021

Authors: V. Obukhov, V. Obukhov

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time $V_4$ a group of motion $G_3$ acts simply transitively on a non-null subspace of transitivity $V_3$. It is shown that in the case of a Riemannian space $V_n$, in which the group $G_r$ acts simply transitively, the algebra of symmetry operators of the $n$-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group $G_r$.

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Published: Apr 19, 2021

Authors: Vito Latora, Iacopo Iacopini, Vito Latora

Published: Apr 19, 2021

Authors: Vito Latora, Iacopo Iacopini, Vito Latora

Adoption processes in socio-technological systems have been widely studied both empirically and theoretically. The way in which social norms, behaviors, and even items such as books, music, or other commercial or technological product spread in a population is usually modeled as a process of social contagion, in which the agents of a social system can infect their neighbors on the underlying network of social contacts. More recently, various models have also been proposed to reproduce the typical dynamics of a process of discovery, in which an agent explores a space of relations between ideas or items in search for novelties. In both types of processes, the structure of the underlying networks, respectively, the network of social contacts in the first case, and the network of relations among items in the second one, plays a fundamental role. However, the two processes have been traditionally seen and studied independently. Here, we provide a brief overview of the existing models of social spreading and exploration and of the latest advancements in both directions. We propose to look at them as two complementary aspects of the same adoption process: on the one hand, there are items spreading over a social network of individuals influencing each other, and on the other hand, individuals explore a network of similarities among items to adopt. The two-fold nature of the approach proposed opens up new stimulating challenges for the scientific community of network and data scientists. We conclude by outlining some possible directions that we believe may be relevant to be explored in the coming years.

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Published: Apr 13, 2021

Authors: Shing-Tung Yau, Cody Long, Artan Sheshmani, Cumrun Vafa, Shing-Tung Yau

Published: Apr 13, 2021

Authors: Shing-Tung Yau, Cody Long, Artan Sheshmani, Cumrun Vafa, Shing-Tung Yau

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).

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Published: Apr 13, 2021

Authors: Mitchell Luskin, Alexander Watson, Mitchell Luskin

Published: Apr 13, 2021

Authors: Mitchell Luskin, Alexander Watson, Mitchell Luskin

We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky-Kruchkov-Vishwanath (TKV). TKV have proved that for inverse twist angles $\alpha$ such that the effective Fermi velocity at the moir\'e $K$ point vanishes, the chiral model has a perfectly flat band at zero energy over the whole Brillouin zone. By a formal expansion, TKV found that the Fermi velocity vanishes at $\alpha \approx .586$. In this work we prove the Fermi velocity vanishes at $\alpha \approx .586$, and put rigorous minimum and maximum bounds on the location of this zero, by rigorously justifying TKV's formal expansion of the Fermi velocity over a sufficiently large interval of $\alpha$ values. The idea of the proof is to project the TKV Hamiltonian onto a finite dimensional subspace, and then expand the Fermi velocity in terms of explicitly computable linear combinations of modes in the subspace, while controlling the error. The proof relies on two assumptions which can be checked numerically: a bound below on the smallest eigenvalue of a positive semi-definite, Hermitian $81 \times 81$ matrix which is essentially the square of the projected Hamiltonian, and an assumption on the validity of the negative value of a real 18th order polynomial approximating the numerator of the Fermi velocity when evaluated at a specific value of $\alpha$. Since these assumptions can be verified up to high precision using standard numerical methods, together with TKV's work our result proves existence of at least one perfectly flat band of the chiral model.

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