1. Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMsMartin Bies, Mirjam Cvetič, Mingqiang Liu, 2021, original scientific article Abstract: In the largest, currently known, class of one quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vectorlike spectra are counted by cohomologies of root bundles. In this work, we apply a previously proposed method to identify toric base threefolds, which are promising to establish F-theory Standard Models with exactly three quark doublets and no vectorlike exotics in this representation. The base spaces in question are obtained from triangulations of 708 polytopes. By studying root bundles on the quark-doublet curve Cð3;2Þ1=6 and employing well-known results about desingularizations of toric K3 surfaces, we derive a triangulation independent lower bound Nˇ ð3Þ P for the number Nð3Þ P of root bundles on Cð3;2Þ1=6 with exactly three sections. The ratio Nˇ ð3Þ P =NP, where NP is the total number of roots on Cð3;2Þ1=6 , is largest for base spaces associated with triangulations of the eighth three-dimensional polytope Δ∘ 8 in the Kreuzer-Skarke list. For each of these Oð1015Þ threefolds, we expect that many root bundles on Cð3;2Þ1=6 are induced from F-theory gauge potentials and that at least every 3000th root on Cð3;2Þ1=6 has exactly three global sections and thus no exotic vectorlike quark-doublet modes.
Keywords: astrophysics, compactification, string theory models, geometry, higher-dimensional field theories, mathematical physics, quantum fields in curved spacetime, string phenomenology, supersymmetric models, topology
Published in DKUM: 16.10.2023; Views: 317; Downloads: 25
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2. Phenomenology of quantum eigenstates in mixed-type systems: Lemon billiards with complex phase space structureČrt Lozej, Dragan Lukman, Marko Robnik, 2022, original scientific article Abstract: The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between their centers, as introduced by Heller and Tomsovic [E. J. Heller and S. Tomsovic, Phys. Today 46, 38 (1993)]. This paper is a continuation of our recent papers on a classical and quantum ergodic lemon billiard (B = 0.5) with strong stickiness effects [C. Lozej ˇ et al., Phys. Rev. E 103, 012204 (2021)], as well as on the three billiards with a simple mixed-type phase space and no stickiness [C. Lozej ˇ et al., Nonlin. Phenom. Complex Syst. 24, 1 (2021)]. Here we study two classical and quantum lemon billiards, for the cases B = 0.1953, 0.083, which are mixed-type billiards with a complex structure of phase space, without significant stickiness regions. A preliminary study of their spectra was published recently [ C. Lozej, D. Lukman, and M. ˇ Robnik, Physics 3, 888 (2021)]. We calculate a very large number (106) of consecutive eigenstates and their Poincaré-Husimi (PH) functions, and analyze their localization properties by studying the entropy localization measure and the normalized inverse participation ratio. We introduce an overlap index, which measures the degree of the overlap of PH functions with classically regular and chaotic regions. We observe the existence of regular states associated with invariant tori and chaotic states associated with the classically chaotic regions, and also the mixed-type states. We show that in accordance with the Berry-Robnik picture and the principle of uniform semiclassical condensation of PH functions, the relative fraction of mixed-type states decreases as a power law with increasing energy, thus, in the strict semiclassical limit, leaving only purely regular and chaotic states. Our approach offers a general phenomenological overview of the structural and localization properties of PH functions in quantum mixed-type Hamiltonian systems.
Keywords: quantum physics, energy, localization, quantum chaos, billiards, chaotic systems
Published in DKUM: 12.10.2023; Views: 288; Downloads: 19
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3. Quantum chaos in triangular billiardsČrt Lozej, Giulio Casati, Tomaž Prosen, 2022, original scientific article Abstract: We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic angles with irrational ratios with π, whose classical dynamics is presumably mixing, and three with exactly one angle rational with π, which are presumably only weakly mixing or even nonergodic in case of right triangles. We find excellent agreement of short- and long-range spectral statistics with the Gaussian orthogonal ensemble of random matrix theory for the most irrational generic triangle, while the other cases show small but significant deviations which are attributed either to a scarring or superscarring mechanism. This result, which extends the quantum chaos conjecture to systems with dynamical mixing in the absence of hard (Lyapunov) chaos, has been corroborated by analyzing distributions of phase-space localization measures of eigenstates and inspecting the structure of characteristic typical and atypical eigenfunctions.
Keywords: quantum physics, quantum chaos, quantum scars, wave chaos, billiards, chaos and nonlinear dynamics, ergodic theory
Published in DKUM: 12.10.2023; Views: 294; Downloads: 35
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4. High-statistics study of $K^0_S K^0_S$ pair production in two-photon collisionsS. Uehara, Marko Bračko, Boštjan Golob, Jure Klučar, Samo Korpar, Peter Križan, Rok Pestotnik, Marko Petrič, Marko Starič, Luka Šantelj, Anže Zupanc, 2013, original scientific article Abstract: We report a high-statistics measurement of the differential cross section of the process $\gamma \gamma \to K^0_S K^0_S$ in the range $1.05\,{\mathrm {GeV}} \leq W \leq 4.00$ , where W is the center-of-mass energy of the colliding photons, using 972 $^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy e+e− collider operated at and near the $\Upsilon$-resonance region. The differential cross section is fitted by parameterized S-, $D_0$, $D_2$-, $G_0$-, and $G_2$-wave amplitudes. In the $D_2$ wave, the $f_2$(1270), $a_2$(1320), and $f′_2$(1525) are dominant and a resonance, the $f_2$(2200), is also present. The $f_0$(1710) and possibly the $f_0$(2500) are seen in the S wave. The mass, total width, and product of the two-photon partial decay width and decay branching fraction to the $K \bar {K}$ state $\Gamma _{\gamma \gamma }\mathcal {B}(K \bar {K})$ are extracted for the $f′_2$(1525), $f_0$(1710), $f_2$(2200), and $f_0$(2500). The destructive interference between the $f_2$(1270) and $a_2$(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states $\chi _{c0}$ and $\chi _{c2}$ are updated. Possible contributions from the $\chi _{c0}(2P)$ and $\chi _{c2}(2P)$ states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel $\eta _c \to K^0_S K^0_S$ is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.
Keywords: C00, C05, C07, C21, quantum chromodynamics, quark model, particle properties, lepton collider experiments, experimental particle physics
Published in DKUM: 21.07.2017; Views: 1578; Downloads: 238
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5. Effects of adaptive degrees of trust on coevolution of quantum strategies on scale-free networksQiang Li, Minyou Chen, Matjaž Perc, Azhar Iqbal, Derek Abbott, 2013, original scientific article Abstract: We study the impact of adaptive degrees of trust on the evolution of cooperation in the quantum prisoner's dilemma game. In addition to the strategies, links between players are also subject to evolution. Starting with a scale-free interaction network, players adjust trust towards their neighbors based on received payoffs. The latter governs the strategy adoption process, while trust governs the rewiring of links. As soon as the degree of trust towards a neighbor drops to zero, the link is rewired to another randomly chosen player within the network. We find that for small temptations to defect cooperators always dominate, while for intermediate and strong temptations a single quantum strategy is able to outperform all other strategies. In general, reciprocal trust remains within close relationships and favors the dominance of a single strategy. Due to coevolution, the power-law degree distributions transform to Poisson distributions.
Keywords: evolutionary games, quantum strategies, coevolution, random networks, cooperation, statistical physics of social systems
Published in DKUM: 23.06.2017; Views: 1021; Downloads: 365
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6. Influence of vacuum energy on scatteringMilan Marčič, 1997, original scientific article Abstract: We deal with photon-electron scattering which occurs between two uncharged conducting parallel plates moving away from each other at a constant velocity. The electromagnetic vacuum field between the two plates is defined by the configuration of space and also interacts with the electrons. We show the relevant operators for both the photon and the electron fields and the computation of the corresponding Feynman propagator, S-matrix and scattering cross section, taking into account the influence of the changeable vacuum field. Correction terms in the computed S-matrix and scattering cross section manifest the influence of the changeable vacuum field. We analyze an example for low-energy scattering of the influence of the changeable vacuum field uponthe scattering cross section.
Keywords: physics, quantum electrodynamics, statistical thermodynamics
Published in DKUM: 01.06.2012; Views: 2572; Downloads: 90
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