@article{13118, abstract = {Under high pressures and temperatures, molecular systems with substantial polarization charges, such as ammonia and water, are predicted to form superionic phases and dense fluid states with dissociating molecules and high electrical conductivity. This behaviour potentially plays a role in explaining the origin of the multipolar magnetic fields of Uranus and Neptune, whose mantles are thought to result from a mixture of H2O, NH3 and CH4 ices. Determining the stability domain, melting curve and electrical conductivity of these superionic phases is therefore crucial for modelling planetary interiors and dynamos. Here we report the melting curve of superionic ammonia up to 300 GPa from laser-driven shock compression of pre-compressed samples and atomistic calculations. We show that ammonia melts at lower temperatures than water above 100 GPa and that fluid ammonia’s electrical conductivity exceeds that of water at conditions predicted by hot, super-adiabatic models for Uranus and Neptune, and enhances the conductivity in their fluid water-rich dynamo layers.}, author = {Hernandez, J.-A. and Bethkenhagen, Mandy and Ninet, S. and French, M. and Benuzzi-Mounaix, A. and Datchi, F. and Guarguaglini, M. and Lefevre, F. and Occelli, F. and Redmer, R. and Vinci, T. and Ravasio, A.}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1280--1285}, publisher = {Springer Nature}, title = {{Melting curve of superionic ammonia at planetary interior conditions}}, doi = {10.1038/s41567-023-02074-8}, volume = {19}, year = {2023}, } @article{13119, abstract = {A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.}, author = {Helson, Victor and Zwettler, Timo and Mivehvar, Farokh and Colella, Elvia and Roux, Kevin Etienne Robert and Konishi, Hideki and Ritsch, Helmut and Brantut, Jean Philippe}, issn = {1476-4687}, journal = {Nature}, pages = {716--720}, publisher = {Springer Nature}, title = {{Density-wave ordering in a unitary Fermi gas with photon-mediated interactions}}, doi = {10.1038/s41586-023-06018-3}, volume = {618}, year = {2023}, } @article{12911, abstract = {This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.}, author = {Feliciangeli, Dario and Gerolin, Augusto and Portinale, Lorenzo}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {4}, publisher = {Elsevier}, title = {{A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature}}, doi = {10.1016/j.jfa.2023.109963}, volume = {285}, year = {2023}, } @article{13177, abstract = {In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.}, author = {Hua, Bobo and Keller, Matthias and Schwarz, Michael and Wirth, Melchior}, issn = {1088-6826}, journal = {Proceedings of the American Mathematical Society}, number = {8}, pages = {3401--3414}, publisher = {American Mathematical Society}, title = {{Sobolev-type inequalities and eigenvalue growth on graphs with finite measure}}, doi = {10.1090/proc/14361}, volume = {151}, year = {2023}, } @article{14558, abstract = {n the dynamic minimum set cover problem, the challenge is to minimize the update time while guaranteeing a close-to-optimal min{O(log n), f} approximation factor. (Throughout, n, m, f , and C are parameters denoting the maximum number of elements, the number of sets, the frequency, and the cost range.) In the high-frequency range, when f = Ω(log n) , this was achieved by a deterministic O(log n) -approximation algorithm with O(f log n) amortized update time by Gupta et al. [Online and dynamic algorithms for set cover, in Proceedings STOC 2017, ACM, pp. 537–550]. In this paper we consider the low-frequency range, when f = O(log n) , and obtain deterministic algorithms with a (1 + ∈)f -approximation ratio and the following guarantees on the update time. (1) O ((f/∈)-log(Cn)) amortized update time: Prior to our work, the best approximation ratio guaranteed by deterministic algorithms was O(f2) of Bhattacharya, Henzinger, and Italiano [Design of dynamic algorithms via primal-dual method, in Proceedings ICALP 2015, Springer, pp. 206–218]. In contrast, the only result with O(f) -approximation was that of Abboud et al. [Dynamic set cover: Improved algorithms and lower bounds, in Proceedings STOC 2019, ACM, pp. 114–125], who designed a randomized (1+∈)f -approximation algorithm with amortized update time. (2) O(f2/∈3 + (f/∈2).logC) amortized update time: This result improves the above update time bound for most values of f in the low-frequency range, i.e., f=o(log n) . It is also the first result that is independent of m and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [Deterministically maintaining a (2 + ∈) -approximate minimum vertex cover in O(1/∈2) amortized update time, in Proceedings SODA 2019, SIAM, pp. 1872–1885] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). (3) O((f/∈3).log2(Cn)) worst-case update time: No nontrivial worst-case update time was previously known for the dynamic set cover problem. Our bound subsumes and improves by a logarithmic factor the O(log3n/poly (∈)) worst-case update time for the unweighted dynamic vertex cover problem (i.e., when f = 2 and C =1) of Bhattacharya, Henzinger, and Nanongkai [Fully dynamic approximate maximum matching and minimum vertex cover in O(log3)n worst case update time, in Proceedings SODA 2017, SIAM, pp. 470–489]. We achieve our results via the primal-dual approach, by maintaining a fractional packing solution as a dual certificate. Prior work in dynamic algorithms that employs the primal-dual approach uses a local update scheme that maintains relaxed complementary slackness conditions for every set. For our first result we use instead a global update scheme that does not always maintain complementary slackness conditions. For our second result we combine the global and the local update schema. To achieve our third result we use a hierarchy of background schedulers. It is an interesting open question whether this background scheduler technique can also be used to transform algorithms with amortized running time bounds into algorithms with worst-case running time bounds.}, author = {Bhattacharya, Sayan and Henzinger, Monika H and Nanongkai, Danupon and Wu, Xiaowei}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {5}, pages = {1132--1192}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Deterministic near-optimal approximation algorithms for dynamic set cover}}, doi = {10.1137/21M1428649}, volume = {52}, year = {2023}, }