Matthias C. Löbl, Stefano Paesani, Anders S. Sørensen
{"title":"Efficient percolation simulations for lossy photonic fusion networks","authors":"Matthias C. Löbl, Stefano Paesani, Anders S. Sørensen","doi":"10.1103/physrevresearch.6.033273","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033273","url":null,"abstract":"The study of percolation phenomena has various applications ranging from social networks or materials science to quantum information. The most common percolation models are bond or site percolation for which the Newman-Ziff algorithm enables an efficient simulation. Here, we consider several nonstandard percolation models that appear in the context of measurement-based photonic quantum computing with so-called graph states and fusion networks. The associated percolation thresholds determine the tolerance to photon loss in such systems and we develop modifications of the Newman-Ziff algorithm to efficiently perform the corresponding percolation simulations. We demonstrate our algorithms by using them to characterize exemplary fusion networks and graph states.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mikhail Maslov, Georgios M. Koutentakis, Mateja Hrast, Oliver H. Heckl, Mikhail Lemeshko
{"title":"Theory of angular momentum transfer from light to molecules","authors":"Mikhail Maslov, Georgios M. Koutentakis, Mateja Hrast, Oliver H. Heckl, Mikhail Lemeshko","doi":"10.1103/physrevresearch.6.033277","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033277","url":null,"abstract":"We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Madhur Mangalam, Henrik Seckler, Damian G. Kelty-Stephen
{"title":"Machine-learning classification with additivity and diverse multifractal pathways in multiplicativity","authors":"Madhur Mangalam, Henrik Seckler, Damian G. Kelty-Stephen","doi":"10.1103/physrevresearch.6.033276","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033276","url":null,"abstract":"Evidence of multifractal structures has spread to a wider set of physiological time series supporting the intricate interplay of biological and psychological functioning. These dynamics manifest as random multiplicative cascades, embodying nonlinear relationships characterized by recurring division, branching, and aggregation processes implicating noise across successive generations. This investigation focuses on how well the diversity of multifractal properties can be specific to the type of cascade relationship between generation (i.e., multiplicative, additive, or a mixture) as well as to the type of noise (i.e., including additive white Gaussian noise, fractional Gaussian noise, and various amalgamations) among 15 distinct types of binomial cascade processes. Cross-correlation analysis of multifractal spectral features confirms that these features capture nuanced aspects of cascading processes with minimal redundancy. Principal component analysis using 13 distinct multifractal spectral features shows that different cascade processes can manifest multifractal evidence of nonlinearity for distinct reasons. This transparency of multifractal spectral features to underlying cascade dynamics becomes less amenable to machine-learning strategies. Fully connected neural networks struggled to classify the 15 distinct types of cascade processes based on the respective multifractal spectral features (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>45.5</mn><mo>%</mo></mrow></math> accuracy) yet demonstrated improved accuracy when addressing single categories of cross-generation relationships, that is, additive (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>91.6</mn><mo>%</mo></mrow></math>), multiplicative (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>75.4</mn><mo>%</mo></mrow></math>), or additomultiplicative (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>70.6</mn><mo>%</mo></mrow></math>). While traditional principal component analysis reveals distinct loadings attributed to individual noise processes, multiplicative relationships between generations effectively make the constituent noise processes less discernible to neural networks. Neural networks may lack sufficient hierarchical depth required to effectively distinguish among nonadditive cascading processes, recommending either elaborating multifractal geometry or using alternate architectures for machine-learning classification of cascades with multiplicative relationships.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ground state magnetic structure and magnetic field effects in the layered honeycomb antiferromagnet YbOCl","authors":"Zheng Zhang, Yanzhen Cai, Jinlong Jiao, Jing Kang, Dehong Yu, Bertrand Roessli, Anmin Zhang, Jianting Ji, Feng Jin, Jie Ma, Qingming Zhang","doi":"10.1103/physrevresearch.6.033274","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033274","url":null,"abstract":"YbOCl is a representative member of the van der Waals layered honeycomb rare-earth chalcohalide <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi><mtext>Ch</mtext><mi>X</mi></math> (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math> = rare earth; Ch = O, S, Se, and Te; and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>X</mi></math> = F, Cl, Br, and I) family reported recently. Its spin ground state remains to be explored experimentally. We grew high-quality single crystals of YbOCl and conducted comprehensive thermodynamic, elastic, and inelastic neutron scattering experiments down to 50 mK. The experiments reveal an antiferromagnetic phase below 1.3 K which is identified as a spin ground state with an intralayer ferromagnetic and interlayer antiferromagnetic ordering. By applying sophisticated numerical techniques to a honeycomb (nearest-neighbor)–triangle (next-nearest-neighbor) model Hamiltonian which accurately describes the highly anisotropic spin system, we are able to simulate the experiments well and determine the diagonal and off-diagonal spin-exchange interactions. The simulations give an antiferromagnetic Kitaev term comparable to the Heisenberg one. The experiments under magnetic fields allow us to establish a magnetic field–temperature phase diagram around the spin ground state. Most interestingly, a relatively small magnetic field (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>∼</mo><mn>0.3</mn></math> to 3 T) can significantly suppress the antiferromagnetic order, suggesting an intriguing interplay of the Kitaev interaction and magnetic fields in the spin system. The present study provides fundamental insights into the highly anisotropic spin systems and opens a window to look into Kitaev spin physics in a rare-earth-based system.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Rossi, F. Šimkovic IV, M. Ferrero, A. Georges, A. M. Tsvelik, N. V. Prokof'ev, I. S. Tupitsyn
{"title":"Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models","authors":"R. Rossi, F. Šimkovic IV, M. Ferrero, A. Georges, A. M. Tsvelik, N. V. Prokof'ev, I. S. Tupitsyn","doi":"10.1103/physrevresearch.6.l032058","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032058","url":null,"abstract":"The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"bold\">Q</mi><mi>N</mi></msub></math>, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"bold\">Q</mi><mi>N</mi></msub></math> is given by <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mi>χ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>∝</mo><mrow><mo>|</mo><mi mathvariant=\"normal\">Δ</mi><mi>q</mi><mo>|</mo></mrow></mrow></math>. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mi>χ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>∝</mo><msup><mrow><mo>|</mo><mi mathvariant=\"normal\">Δ</mi><mi>q</mi><mo>|</mo></mrow><mn>2</mn></msup></mrow></math> dependence yields a robust finite-<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>(</mo><mi>t</mi><mo>−</mo><msup><mi>t</mi><mo>′</mo></msup><mo>)</mo></mrow></math> Hubbard model and found that at large <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>U</mi><mo>/</mo><mi>t</mi><mo>></mo><mn>5.5</mn></mrow></math> before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mi>χ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>∝</mo><msup><mrow><mo>|</mo><mi mathvariant=\"normal\">Δ</mi><mi>q</mi><mo>|</mo></mrow><mn>2</mn></msup></mrow></math>. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nathan Vani, Sacha Escudier, Deok-Hoon Jeong, Alban Sauret
{"title":"Role of the constriction angle on the clogging by bridging of suspensions of particles","authors":"Nathan Vani, Sacha Escudier, Deok-Hoon Jeong, Alban Sauret","doi":"10.1103/physrevresearch.6.l032060","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032060","url":null,"abstract":"Confined flows of particles can lead to clogging, and therefore failure, of various fluidic systems across many applications. As a result, design guidelines need to be developed to ensure that clogging is prevented or at least delayed. In this Letter, we investigate the influence of the angle of reduction in the cross section of the channel on the bridging of semidilute and dense non-Brownian suspensions of spherical particles. We observe a decrease of the clogging probability with the reduction of the constriction angle. This effect is more pronounced for dense suspensions close to the maximum packing fraction where particles are in contact in contrast to semidilute suspensions. We rationalize this difference in terms of arch selection. We describe the role of the constriction angle and the flow profile, providing insights into the distinct behavior of semidilute and dense suspensions.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Collective gradient sensing by dilute swimming bacteria without clustering","authors":"Tatsuro Kai, Takahiro Abe, Natsuhiko Yoshinaga, Shuichi Nakamura, Seishi Kudo, Shoichi Toyabe","doi":"10.1103/physrevresearch.6.l032061","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032061","url":null,"abstract":"We characterize the taxis enhancement of swimming bacteria by collective migration without apparent clustering. We confine a dilute <i>Salmonella</i> suspension in a shallow channel and evaluate the thermotaxis response to local heating and diffusion. By combining cell tracking analysis and numerical simulation based on simple modeling, we show that the alignment interaction suppresses orientation fluctuation, strengthens migration bias, and also prevents the dispersion of accumulated population. The results show a prominent example of how a collective motion of active matter implements a biological function.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prerelaxation in quantum, classical, and quantum-classical two-impurity models","authors":"Michael Elbracht, Michael Potthoff","doi":"10.1103/physrevresearch.6.033275","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033275","url":null,"abstract":"We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the nonequilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Lancellotti, S. Welte, M. Simoni, C. Mordini, T. Behrle, B. de Neeve, M. Marinelli, V. Negnevitsky, J. P. Home
{"title":"Low-excitation transport and separation of high-mass-ratio mixed-species ion chains","authors":"F. Lancellotti, S. Welte, M. Simoni, C. Mordini, T. Behrle, B. de Neeve, M. Marinelli, V. Negnevitsky, J. P. Home","doi":"10.1103/physrevresearch.6.l032059","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.l032059","url":null,"abstract":"We demonstrate low-excitation transport and separation of two-ion crystals consisting of one <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mmultiscripts><mi>Be</mi><none></none><mo>+</mo><mprescripts></mprescripts><none></none><mn>9</mn></mmultiscripts></math> and one <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mmultiscripts><mi>Ca</mi><none></none><mo>+</mo><mprescripts></mprescripts><none></none><mn>40</mn></mmultiscripts></math> ion, with a high mass ratio of 4.4. The full separation involves transport of the mixed-species chain, splitting each ion into separate potential wells, and then transport of each ion prior to detection. We find the high mass ratio makes the protocol sensitive to mode crossings between axial and radial modes, as well as to uncontrolled radial electric fields that induce mass-dependent twists of the ion chain, which initially gave excitations <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover accent=\"true\"><mi>n</mi><mo>¯</mo></mover><mo>≫</mo><mn>10</mn></mrow></math>. By controlling these stages, we achieve excitation as low as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover accent=\"true\"><mi>n</mi><mo>¯</mo></mover><mo>=</mo><mrow><mn>1.40</mn><mo>±</mo><mn>0.08</mn></mrow><mspace width=\"0.28em\"></mspace><mi>phonons</mi></mrow></math> for the calcium ion and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover accent=\"true\"><mi>n</mi><mo>¯</mo></mover><mo>=</mo><mrow><mn>1.44</mn><mo>±</mo><mn>0.09</mn></mrow><mspace width=\"0.28em\"></mspace><mi>phonons</mi></mrow></math> for the beryllium ion. Separation and transport of mixed-species chains are key elements of the quantum charge-coupled device architecture and may also be applicable to quantum-logic-based spectroscopy of exotic species.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andreu Puy, Elisabet Gimeno, David March-Pons, M. Carmen Miguel, Romualdo Pastor-Satorras
{"title":"Signatures of criticality in turning avalanches of schooling fish","authors":"Andreu Puy, Elisabet Gimeno, David March-Pons, M. Carmen Miguel, Romualdo Pastor-Satorras","doi":"10.1103/physrevresearch.6.033270","DOIUrl":"https://doi.org/10.1103/physrevresearch.6.033270","url":null,"abstract":"Moving animal groups transmit information through propagating waves or behavioral cascades, exhibiting characteristics akin to systems near a critical point from statistical physics. Using data from freely swimming schooling fish in an experimental tank, we investigate spontaneous behavioral cascades involving turning avalanches, where large directional shifts propagate across the group. We analyze several avalanche metrics and provide a detailed picture of the dynamics associated with turning avalanches, employing tools from avalanche behavior in condensed-matter physics and seismology. Our results identify power-law distributions and robust scale-free behavior through data collapses and scaling relationships, confirming a necessary condition for criticality in fish schools. We explore the biological function of turning avalanches and link them to collective decision-making processes in selecting a new movement direction for the school. We report relevant boundary effects arising from interactions with the tank walls and influential roles of boundary individuals. Finally, spatial and temporal correlations in avalanches are explored using the concept of aftershocks from seismology, revealing clustering of avalanche events below a designated timescale and an Omori law with a faster decay rate than observed in earthquakes.","PeriodicalId":20546,"journal":{"name":"Physical Review Research","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}