5,230 research outputs found

    Complexity & wormholes in holography

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    Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory

    Symmetries of Riemann surfaces and magnetic monopoles

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    This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Mirror symmetry for Dubrovin-Zhang Frobenius manifolds

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    Frobenius manifolds were formally defined by Boris Dubrovin in the early 1990s, and serve as a bridge between a priori very different fields of mathematics such as integrable systems theory, enumerative geometry, singularity theory, and mathematical physics. This thesis concerns, in particular, a specific class of Frobenius manifolds constructed on the orbit space of an extension of the affine Weyl group defined by Dubrovin together with Youjin Zhang. Here, we find Landau-Ginzburg superpotentials, or B-model mirrors, for these Frobenius structures by considering the characteristic equation for Lax operators of relativistic Toda chains as proposed by Andrea Brini. As a bonus, the results open up various applications in topology, integrable hierarchies, and Gromov-Witten theory, making interesting research questions in these areas more accessible. Some such applications are considered in this thesis. The form of the determinant of the Saito metric on discriminant strata is investigated, applications to the combinatorics of Lyashko-Looijenga maps are given, and investigations into the integrable systems theoretic and enumerative geometric applications are commenced

    Understanding and controlling structural distortions underlying superconductivity in lanthanum cuprates

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    The suppression of superconductivity in layered lanthanum cuprates near x = 1/8 coincides with a structural phase transition from a low-temperature orthorhombic to a low-temperature tetragonal phase. The low-temperature phases are characterised by a static tilt of the CuO6 octahedra away from the layering axis in distinct directions. It remained an open question whether the orthorhombic-to-tetragonal phase transition would only occur in the context of competing electronic orders in the lanthanum cuprates. This thesis proposes a novel approach to studying the orthorhombic-to-tetragonal phase transition using the novel La2MgO4 system. La2MgO4 adopts the layered Ruddlesden-Pepper structure of the lanthanum cuprates but lacks the strong electron correlations and octahedral distortions associated with the Jahn-Teller active Cu site. Combining first-principles simula- tions using density-functional theory with experimental data on the novel La2MgO4 system, the context in which these structural phases can occur is detailed, outlining the key param- eters determining the stability of the phase which suppresses bulk superconductivity. The same sequence of structural phase transitions occurs in La2MgO4 as in La1.875Ba0.125CuO4, and the tetragonal phase is stabilised via steric effects beyond a critical octahedral tilt magnitude. Larger Jahn-Teller distortions favour the orthorhombic phase. The effect of isotropic and anisotropic pressure on La2MgO4 and La2CuO4 is explored. These form the basis for a structural mechanism to understand the experimental trends of the bulk superconducting transition temperature under uniaxial pressure. Finally, the justification for the methodology used throughout this thesis to simulate these systems is provided, highlighting that DFT+U accurately describes their atomic and electronic structure.Open Acces

    Matter relative to quantum hypersurfaces

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    We explore the canonical description of a scalar field as a parameterized field theory on an extended phase space that includes additional embedding fields that characterize spacetime hypersurfaces X\mathsf{X} relative to which the scalar field is described. This theory is quantized via the Dirac prescription and physical states of the theory are used to define conditional wave functionals âˆŁÏˆÏ•[X]⟩|\psi_\phi[\mathsf{X}]\rangle interpreted as the state of the field relative to the hypersurface X\mathsf{X}, thereby extending the Page-Wootters formalism to quantum field theory. It is shown that this conditional wave functional satisfies the Tomonaga-Schwinger equation, thus demonstrating the formal equivalence between this extended Page-Wootters formalism and standard quantum field theory. We also construct relational Dirac observables and define a quantum deparameterization of the physical Hilbert space leading to a relational Heisenberg picture, which are both shown to be unitarily equivalent to the Page-Wootters formalism. Moreover, by treating hypersurfaces as quantum reference frames, we extend recently developed quantum frame transformations to changes between classical and nonclassical hypersurfaces. This allows us to exhibit the transformation properties of a quantum field under a larger class of transformations, which leads to a frame-dependent particle creation effect.Comment: 21 pages, 3 figures. Comments welcom

    Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics

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    It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM “Schwingungen in rotierenden Maschinen”. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name “European Conference on Rotordynamics”. This new international profile has also been emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations

    Introduction to black hole thermodynamics

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    Questa tesi ha l’obiettivo di introdurre il lettore allo studio dei buchi neri, partendo dalle equazioni di campo di Einstein fino ad arrivare a discutere il paradosso dell’informazione di Hawking ed il Principio Olografico. Le principali caratteristiche matematiche e fisiche verrano esposte sulla base delle teorie della relatività generale e dei campi quantistici, facendo ampio uso di uno spazio-tempo a simmetria sferica e delle coordinate di Rindler. Particolare importanza verrà data alle proprietà termodinamiche dei buchi neri ed al loro processo di evaporazione. I primi tre capitoli contengono materiale di base, che verrà poi utilizzato per esporre la trattazione termodinamica a partire dal quarto capitolo

    R\'enyi entropies in the n→0n\to0 limit and entanglement temperatures

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    Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0n \to 0 limit of R\'enyi entropies SnS_n, can be computed from the ET. This establishes a formula for these R\'enyi entropies for any region in terms of solutions of the eikonal equations. In the n→0n\to 0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.Comment: 33 pages, 3 figure
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