Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

Evnin, Oleg

doi:10.1088/1361-6382/ac1b46

Cited by 21 publications

(13 citation statements)

References 144 publications

(442 reference statements)

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“…Once P and Φ are specified, the metric function ω comes from integrating (25) directly, with ω(t, 0) = 0, (28) to fix the time-reparametrization freedom. One can integrate (26) to obtain…”

Section: Acknowledgmentsmentioning

confidence: 99%

De Sitter bubbles from anti-de Sitter fluctuations

Biasi¹,

Evnin²,

Sypsas³

2022

Preprint

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Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which is possible in theories admitting regular black holes with de Sitter-like interiors. We point out that, given a global anti-de Sitter background, the formation of such 'de Sitter bubbles' will be enhanced by mechanisms analogous to the Bizoń-Rostworowski instability in general relativity. This opens an arena for discussing the production of multiple accelerating universes from anti-de Sitter fluctuations. We demonstrate such collapse enhancement by explicit numerical work in the context of a simple two-dimensional dilaton-gravity model that mimics the spherically symmetric sector of higher-dimensional gravities.

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Section: Acknowledgmentsmentioning

confidence: 99%

De Sitter bubbles from anti-de Sitter fluctuations

Biasi¹,

Evnin²,

Sypsas³

2022

Preprint

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“…Quantum resonant systems (and their classical limits) arise as consistent weakly nonlinear approximations to a variety of physical problems featuring weak nonlinearities in strongly resonant domains. A recent review can be found in [80]. While their Hilbert spaces are infinite-dimensional, the Hamiltonians are block-diagonal in the Fock basis, with all blocks of finite sizes (although there is no bound on the size).…”

Section: Quantum Resonant Systemsmentioning

confidence: 99%

“…These classical systems display, for different choices of C nmkl , a wide range of analytic and dynamical patterns ranging from full solvability [71][72][73][74] to Lax-integrability [71][72][73][74][75][76][77], partial solvability [54-58, 64-66, 78, 79], turbulent cascades [47,[71][72][73][74][75][76][77], as well as generic chaotic dynamics expected from a nonlinear system with an infinite number of degrees of freedom when the mode couplings C nmkl are chosen randomly. A recent review can be found in [80]. In contrast to the rich array of classical dynamical behaviors, the corresponding quantum theory is very economical in its structure and can be explored via an operation as simple as diagonalizing finite-sized numerical matrices [41].…”

Section: Introductionmentioning

confidence: 99%

Bounds on quantum evolution complexity via lattice cryptography

et al. 2022

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We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal’ operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to \sim 10^4∼104.

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“…Due to the nonlinearity of the field equations, they interact with each other and may form black holes even if the perturbations are arbitrarily small. Despite many works on the turbulent instability [22][23][24][25][26][27][28][29][30][31][32][33][34][35], the final fate has not been clarified yet because the time evolution and final states are dependent on symmetries, dimensions and boundary conditions of the spacetime [36,37]. In addition to the case of matter fields, the stability of the asymptotically AdS Einstein-Vlasov system is also investigated in Ref.…”

Section: Introductionmentioning

confidence: 99%

Gravothermal catastrophe and critical dimension in a $D$-dimensional asymptotically AdS spacetime

Asami¹,

Yoo²

2022

Preprint

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We investigate the structure and stability of the thermal equilibrium states of a spherically symmetric self-gravitating system in a D-dimensional asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the Einstein-Vlasov equations with a negative cosmological constant. Due to the confined structure of the AdS potential, we can construct thermal equilibrium states without any artificial wall in the asymptotically AdS spacetime. Accordingly, the AdS radius can be regarded as the typical size of the system. Then the system can be characterized by the gravothermal energy and AdS radius normalized by the total particle number. We investigate the catastrophic instability of the system in a D-dimensional spacetime by using the turning point method. As a result, we find that the curve has a double spiral structure for 4 ≤ D ≤ 10 while it does not have any spiral structures for D ≥ 11 as in the asymptotically flat case confined by an adiabatic wall. Irrespective of the existence of the spiral structure, there exist upper and lower bounds for the value of the gravothermal energy. This fact indicates that there is no thermal equilibrium solution outside the allowed region of the gravothermal energy. This property is also similar to the asymptotically flat case.

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Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

Cited by 21 publications

References 144 publications

De Sitter bubbles from anti-de Sitter fluctuations

De Sitter bubbles from anti-de Sitter fluctuations

Bounds on quantum evolution complexity via lattice cryptography

Gravothermal catastrophe and critical dimension in a $D$-dimensional asymptotically AdS spacetime

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