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Generation and statistical analysis of chaos-based pseudorandom sequences
Published 2019Subjects: “…Quantum chaos…”
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Multifractal eigenfunctions for a singular quantum billiard
Published 2021“…Whereas much work in the mathematical literature on quantum chaos has focused on phenomena such as quantum ergodicity and scarring, relatively little is known at the rigorous level about the existence of eigenfunctions whose morphology is more complex. …”
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Vibrating quantum billiards on Riemannian manifolds
Published 2001“…Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of quantum chaos that does not require the semiclassical (h → 0) or high quantum-number limits. …”
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Thermal diffusivity and chaos in metals without quasiparticles
Published 2018“…We study the thermal diffusivity D[subscript T] in models of metals without quasiparticle excitations (“strange metals”). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. …”
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Many-body chaos and energy dynamics in holography
Published 2018“…Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. …”
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Many-body chaos and energy dynamics in holography
Published 2018“…Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. …”
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Around quantum ergodicity
Published 2022“…Abstract We discuss Shnirelman’s Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.…”
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An introduction to fractal uncertainty principle
Published 2021“…This article provides a review of recent developments on the fractal uncertainty principle and of their applications to quantum chaos, including lower bounds on mass of eigenfunctions on negatively curved surfaces and spectral gaps on convex cocompact hyperbolic surfaces.…”
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Quantifying information scrambling via classical shadow tomography on programmable quantum simulators
Published 2022“…We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators. …”
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Chaos and ergodicity in extended quantum systems with noisy driving
Published 2021“…We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes e�ectively a random matrix in the many-body Hilbert space. …”
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Topics in sieve theory
Published 2022“…This set-up has a geometric interpretation which arises naturally in the field of quantum chaos. We tackle this problem using a modified half-dimensional Maynard-Tao sieve, and present details of the argument in Chapter 2.…”
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Horizon constraints on holographic Green’s functions
Published 2021“…We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.…”
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Semiclassical Measures for Higher-Dimensional Quantum Cat Maps
Published 2023“…Abstract Consider a quantum cat map M associated with a matrix $$A\in {{\,\textrm{Sp}\,}}(2n,{\mathbb {Z}})$$ A ∈ Sp ( 2 n , Z ) , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue of A of largest absolute value and (2) the characteristic polynomial of A is irreducible over the rationals. …”
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Impact of quantum-classical correspondence on entanglement enhancement by single-mode squeezing
Published 2015“…In particular, the entanglement generated through quantum chaos is found to be hardly enhanced by prior squeezing, since it is bounded by the saturation value of the maximally entangled Schmidt state with fixed energy. …”
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Cryptographic Censorship
Published 2025“…This result provides a sufficient condition guaranteeing that seminal holographic results on quantum chaos and thermalization, whose general applicability relies on typicality of horizons, will not be invalidated by the formation of naked singularities in AdS/CFT.…”
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