Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics

We study the $O(N_1)\times O(N_2)\times O(N_3)$ symmetric quantum mechanics of 3-index Majorana fermions. When the ranks $N_i$ are all equal, this model has a large $N$ limit which is dominated by the melonic Feynman diagrams. We derive an integral formula which computes the number of $SO(N_1)\times SO(N_2)\times SO(N_3)$ invariant states for any set of $N_i$. For equal ranks the number of singlets is non-vanishing only when $N$ is even, and it exhibits rapid growth: it jumps from $36$ in the $O(4)^3$ model to $595354780$ in the $O(6)^3$ model. We derive bounds on the values of energy, which show that they scale at most as $N^3$ in the large $N$ limit, in agreement with expectations. We also show that the splitting between the lowest singlet and non-singlet states is of order $1/N$. For $N_3=1$ the tensor model reduces to $O(N_1)\times O(N_2)$ fermionic matrix quantum mechanics, and we find a simple expression for the Hamiltonian in terms of the quadratic Casimir operators of the symmetry group. A similar expression is derived for the complex matrix model with $SU(N_1)\times SU(N_2)\times U(1)$ symmetry. Finally, we study the $N_3=2$ case of the tensor model, which gives a more intricate complex matrix model whose symmetry is only $O(N_1)\times O(N_2)\times U(1)$. All energies are again integers in appropriate units, and we derive a concise formula for the spectrum. The fermionic matrix models we studied possess standard 't Hooft large $N$ limits where the ground state energies are of order $N^2$, while the energy gaps are of order $1$.Comment: 42 pages, 1 figure. v2: minor improvements, references added. v3: minor corrections. v4: minor improvement

Magic Angles In Equal-Twist Trilayer Graphene

We consider a configuration of three stacked graphene monolayers with equal consecutive twist angles $\theta$. Remarkably, in the chiral limit when interlayer coupling terms between $\textrm{AA}$ sites of the moir\'{e} pattern are neglected we find four perfectly flat bands (for each valley) at a sequence of magic angles which are exactly equal to the twisted bilayer graphene (TBG) magic angles divided by $\sqrt{2}$. Therefore, the first magic angle for equal-twist trilayer graphene (eTTG) in the chiral limit is $\theta_{*} \approx 1.05^{\circ}/\sqrt{2} \approx 0.74^{\circ}$. We prove this relation analytically and show that the Bloch states of the eTTG's flat bands are non-linearly related to those of TBG's. Additionally, we show that at the magic angles, the upper and lower bands must touch the four exactly flat bands at the Dirac point of the middle graphene layer. Finally, we explore the eTTG's spectrum away from the chiral limit through numerical analysis.Comment: 4 pages, 4 figures, 1 tabl

Spectrum of Majorana Quantum Mechanics with O(4)3O(4)^3 Symmetry

We study the quantum mechanics of 3-index Majorana fermions $\psi^{abc}$ governed by a quartic Hamiltonian with $O(N)^3$ symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large $N$ limit dominated by the melonic diagrams. For $N=4$ the total number of states is $2^{32}$, but they naturally break up into distinct sectors according to the charges under the $U(1)\times U(1)$ Cartan subgroup of one of the $O(4)$ groups. The biggest sector has vanishing charges and contains over $165$ million states. Using a Lanczos algorithm, we determine the spectrum of the low-lying states in this and other sectors. We find that the absolute ground state is non-degenerate. If the $SO(4)^3$ symmetry is gauged, it is known from earlier work that the model has $36$ states and a residual discrete symmetry. We study the discrete symmetry group in detail; it gives rise to degeneracies of some of the gauge singlet energies. We find all the gauge singlet energies numerically and use the results to propose exact analytic expressions for them.Comment: 15 pages, 1 figure, 3 tables; v2: minor improvements, a reference added; v3: minor revisions, journal versio

Supplementary material for the article: Milenković, M.; Shcherbakov, I. N.; Popov, L. D.; Levchenkov, S. I.; Borodkin, S. A.; Alexandrov, G. G. Synthesis, Characterization and Crystal Structures of Ni(II) and Cu(I) Complexes with the Condensation Product of 2-(Diphenylphosphino)Benzaldehyde and 1-Hydrazinophthalazine. Polyhedron 2017, 121, 278–284. https://doi.org/10.1016/j.poly.2016.10.020

Supplementary material for: [https://doi.org/10.1016/j.poly.2016.10.020]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2368]Related to accepted version: [http://cherry.chem.bg.ac.rs/handle/123456789/3256

Insights from the preimaginal morphology of the constans species‑group, to reveal novel morphological patterns of the Merodon albifrons‑evolutionary lineage (Diptera, Syrphidae)

Merodon triangulum Vujić, Radenković & Hurkmans, 2020 is a European endemic hoverfly species belonging to Merodon constans species-group, inside albifrons-lineage. The distribution of this species is known to be mostly central Europe and Balkan peninsula and it has been categorized as Near Threatened in the European IUCN red list of hoverflies; this paper cites the species for the first time in Ukraine (western Ukraine, specifically). In the present study, the preimaginal stages of this species are described and figured using Scanning Electron Microscopy. The material used for the descriptions were larvae collected in Ukraine and Serbia feeding inside underground storage organs of the spring snowflake Leucojum vernum L., 1753. This morphological description constitutes the first one inside the constans species-group, and the sixth description of the albifrons-lineage, in which there is only one species-group left to have at least one species of the preimaginal stages described (i.e., ruficornis species-group). The descriptions were compared with the rest available of the genus, stating the diagnostical characters of the present species and the shared characters inside the lineage. The novel information provided on the trophic interaction between M. triangulum larvae and Leucojum bulbs is stated for the first time and further supports the association of the constans species-group with the underground storage organs of snowflakes and snowdrops (Galantheae) in their role as host plants.Partial financial support was received from the research department of the University of Alicante in the frame work of a predoctoral grant (UAFPU2019-03). In addition, the study has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grant No. 451-03-47/2023-01/200125 and Grant No. 451-03-47/2023-01/200358)

Supplementary material for the article: Milenković, M.; Shcherbakov, I. N.; Popov, L. D.; Levchenkov, S. I.; Borodkin, S. A.; Alexandrov, G. G. Synthesis, Characterization and Crystal Structures of Ni(II) and Cu(I) Complexes with the Condensation Product of 2-(Diphenylphosphino)Benzaldehyde and 1-Hydrazinophthalazine. Polyhedron 2017, 121, 278–284. https://doi.org/10.1016/j.poly.2016.10.020

Supplementary material for: [https://doi.org/10.1016/j.poly.2016.10.020]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2368]Related to accepted version: [http://cherry.chem.bg.ac.rs/handle/123456789/3256

Two-particle correlations in azimuthal angle and pseudorapidity in inelastic p + p interactions at the CERN Super Proton Synchrotron

Results on two-particle ΔηΔϕ correlations in inelastic p + p interactions at 20, 31, 40, 80, and 158 GeV/c are presented. The measurements were performed using the large acceptance NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. The data show structures which can be attributed mainly to effects of resonance decays, momentum conservation, and quantum statistics. The results are compared with the Epos and UrQMD models.ISSN:1434-6044ISSN:1434-605

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis