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Parameter space for a dissipative Fermi-Ulam model
Diego F. M. Oliveira, Edson D. Leonel, 2011, izvirni znanstveni članek

Opis: The parameter space for a dissipative bouncing ball model under the effect of inelastic collisions is studied. The system is described using a two-dimensional nonlinear area-contracting map. The introduction of dissipation destroys the mixed structure of phase space of the non-dissipative case, leading to the existence of a chaotic attractor and attracting fixed points, which may coexist for certain ranges of control parameters. We have computed the average velocity for the parameter space and made a connection with the parameter space based on the maximum Lyapunov exponent. For both cases, we found an infinite family of self-similar structures of shrimp shape, which correspond to the periodic attractors embedded in a large region that corresponds to the chaotic motion.
Ključne besede: parameter space, Fermi-Ulam model, inelastic collision
Objavljeno: 03.07.2017; Ogledov: 24; Prenosov: 2
.pdf Polno besedilo (2,84 MB)

Expanded boundary integral method and chaotic time-reversal in quatum billiards
Gregor Veble, Tomaž Prosen, Marko Robnik, 2007, izvirni znanstveni članek

Opis: We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.
Ključne besede: 2D Helmholtz equation, energy spectrum, quantum billiard
Objavljeno: 03.07.2017; Ogledov: 23; Prenosov: 0
.pdf Polno besedilo (2,90 MB)

Wave equation for the Wu black hole
Tolga Birkandan, Mirjam Cvetič, 2014, izvirni znanstveni članek

Opis: Wu black hole is the most general solution of maximally supersymmetric gauged supergravity in D=5, containing U(1)(3) gauge symmetry. We study the separability of the massless Klein-Gordon equation and probe its singularities for a general stationary, axisymmetric metric with orthogonal transitivity, and apply the results to the Wu black hole solution. We start with the zero azimuthal-angle eigenvalues in the scalar field Ansatz and find that the residuum of a pole in the radial equation is associated with the surface gravity calculated at this horizon. We then generalize our calculations to nonzero azimuthal eigenvalues and probing each horizon singularity, we show that the residua of the singularities for each horizon are in general associated with a specific combination of the surface gravity and the angular velocities at the associated horizon. It turns out that for the Wu black hole both the radial and angular equations are general Heun's equations with four regular singularities.
Ključne besede: black holes, string theory, conformal field models, string duality
Objavljeno: 27.06.2017; Ogledov: 46; Prenosov: 0
.pdf Polno besedilo (424,79 KB)

Vacuum polarization of STU black holes and their subtracted geometry limit
Mirjam Cvetič, G. W. Gibbons, Zain H. Saleem, Alejandro Satz, 2015, izvirni znanstveni članek

Opis: We study the vacuum polarization of a massless minimally coupled scalar field at the horizon of four-charge STU black holes. We compare the results for the standard asymptotically flat black holes and for the black holes obtained in the "subtracted limit", both in the general static case and at the horizon pole for the general rotating case. The original and the subtracted results are identical only in the BPS limit, and have opposite sign in the extremal Kerr limit. We also compute the vacuum polarization on the static solutions that interpolate between both the original and the subtracted case through a solution-generating transformation and show that the vacuum polarization stays positive throughout the interpolating solution. In the appendix we provide a closed-form solution for the Green's function on general (static or rotating) subtracted black hole geometries.
Ključne besede: black holes, supergravity, string theory, conformal field models, string duality
Objavljeno: 27.06.2017; Ogledov: 32; Prenosov: 0
.pdf Polno besedilo (372,93 KB)

Three-family particle physics models from global F-theory compactifications
Mirjam Cvetič, Denis Klevers, Damian Kaloni Mayorga Pena, Paul Oehlmann, Jonas Reuter, 2015, izvirni znanstveni članek

Opis: We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations X with the choice of base P-3. We observe that the F-theory conditions on the G(4)-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent G(4)-flux. For this purpose we compute the vertical cohomology H-V((2,2)) (X) in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the G(4)-flux allow for a cancellation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our G(4)-flux solutions are adequately quantized.
Ključne besede: black holes, supergravity, string theory, conformal field models, string duality
Objavljeno: 27.06.2017; Ogledov: 30; Prenosov: 0
.pdf Polno besedilo (890,06 KB)

Origin of Abelian gauge symmetries in heterotic/F-theory duality
Mirjam Cvetič, Antonella Grassi, Denis Klevers, Peng Song, Maximilian Poretschkin, 2016, izvirni znanstveni članek

Opis: We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) X Z(k) structure group and bundles with purely non-Abelian structure groups having a centralizer in E-8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stiickelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
Ključne besede: F-theory, string duality, superstrings, heterotic strings, M-theory
Objavljeno: 27.06.2017; Ogledov: 39; Prenosov: 0
.pdf Polno besedilo (1,15 MB)

On finiteness of type IIB compactifications
Mirjam Cvetič, James Halverson, Denis Klevers, Peng Song, 2014, izvirni znanstveni članek

Opis: The string landscape satisfies interesting finiteness properties imposed by supersymmetry and string-theoretical consistency conditions. We study N = 1 supersymmetric compactifications of Type IIB string theory on smooth elliptically fibered Calabi-Yau threefolds at large volume with magnetized D9-branes and D5-branes. We prove that supersymmetry and tadpole cancellation conditions imply that there is a finite number of such configurations. In particular, we derive an explicitly computable bound on the number of magnetic flux quanta, as well as the number of D5-branes, which is independent of the continuous moduli of the setup. The proof applies if a number of easy to check geometric conditions of the twofold base are met. We show that these geometric conditions are satisfied for the almost Fano twofold bases given by each toric variety associated to a reflexive two-dimensional polytope as well as by the generic del Pezzo surfaces dP(n) with n = 0, ..., 8. Physically, this finiteness proof shows that there exist a finite collection of four-dimensional gauge groups and chiral matter spectra in the 4D supergravity theories realized by these compactifications. As a by-product we explicitly construct all generators of the Kaahler cones of dP(n) and work out their relation to representation theory.
Ključne besede: black holes, supergravity, string theory, conformal field models, string duality
Objavljeno: 27.06.2017; Ogledov: 21; Prenosov: 0
.pdf Polno besedilo (1,01 MB)

Elliptic fibrations with rank three Mordell-Weilgroup
Mirjam Cvetič, Denis Klevers, Hernan Piragua, Peng Song, 2014, izvirni znanstveni članek

Opis: We analyze general F-theory compactifications with U(1)xU(1)xU(1) Abelian gauge symmetry by constructing the general elliptically fibered Calabi-Yau manifolds with a rank three Mordell-Weil group of rational sections. The general elliptic fiber is shown to be a complete intersection of two non-generic quadrics in P-3 and resolved elliptic fibrations are obtained by embedding the fiber as the generic Calabi-Yau complete intersection into Bl(3)P(3), the blow-up of P-3 at three points. For a fixed base B, there are finitely many Calabi-Yau elliptic fibrations. Thus, F-theory compactifications on these Calabi-Yau manifolds are shown to be labeled by integral points in reflexive polytopes constructed from the nef-partition of Bl(3)P(3). We determine all 14 massless matter representations to six and four dimensions by an explicit study of the codimension two singularities of the elliptic fibration. We obtain three matter representations charged under all three U(1)-factors, most notably a tri-fundamental representation. The existence of these representations, which are not present in generic perturbative Type II compactifications, signifies an intriguing universal structure of codimension two singularities of the elliptic fibrations with higher rank Mordell-Weil groups. We also compute explicitly the corresponding 14 multiplicities of massless hypermultiplets of a six-dimensional F-theory compactification for a general base B.
Ključne besede: flux compactifications, F-theory, superstring vacua, D-branes
Objavljeno: 27.06.2017; Ogledov: 18; Prenosov: 0
.pdf Polno besedilo (840,88 KB)

Electrodynamics of black holes in STU supergravity
Mirjam Cvetič, G. W. Gibbons, Christopher N. Pope, Zain H. Saleem, 2014, izvirni znanstveni članek

Opis: External magnetic fields can probe the composite structure of black holes in string theory. With this motivation we study magnetised four-charge black holes in the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. We employ solution generating techniques to obtain Melvin backgrounds, and black holes in these backgrounds. For an initially electrically charged static black hole immersed in magnetic fields, we calculate the resultant angular momenta and analyse their global structure. Examples are given for which the ergoregion does not extend to infinity. We calculate magnetic moments and gyromagnetic ratios via Larmor's formula. Our results are consistent with earlier special cases. A scaling limit and associated subtracted geometry in a single surviving magnetic field is shown to lift to AdS(3) x S-2. Magnetizing magnetically charged black holes give static solutions with conical singularities representing strings or struts holding the black holes against magnetic forces. In some cases it is possible to balance these magnetic forces.
Ključne besede: black holes, supergravity, string theory, conformal field models, string duality
Objavljeno: 27.06.2017; Ogledov: 24; Prenosov: 0
.pdf Polno besedilo (563,26 KB)

Compactifications of deformed conifolds, branes and the geometry of qubits
Mirjam Cvetič, G. W. Gibbons, Christopher N. Pope, 2016, izvirni znanstveni članek

Opis: We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CPn+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V-2(Rn+2) = SO(n+2)/SO(n) divided by Z(2). The second family are also Einstein-Kahler metrics, now on the Grassmannian manifolds G(2)(Rn+3) = SO(n+3)/((SO(n+1)xSO(2)), whose principal orbits are the Stiefel manifolds V-2(Rn+2) (with no Z(2) factoring in this case). The third family are Einstein metrics on the product manifolds Sn+1 x Sn+1, and are Kahler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kahler geometry of Fubini-Study metrics on CPn+1, and we apply the formalism to study the quantum entanglement of qubits.
Ključne besede: conformal field models, string theory, models of quantum gravity, differential geometry, algebraic geometry
Objavljeno: 27.06.2017; Ogledov: 26; Prenosov: 0
.pdf Polno besedilo (586,14 KB)

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