Emergent spectral form factors in sonic systems

Winer, Michael; Swingle, Brian

doi:10.1103/physrevb.108.054523

Cited by 5 publications

(3 citation statements)

References 62 publications

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“…which, unlike the result for even dimensions, is exponentially decaying and therefore much less relevant at large timescales. These two results agrees with the hydrodynamic computation in [27], which is again to be expected from holography.…”

Section: Contributions From Diffusive and Hydrodynamic Modes To The O...supporting

confidence: 89%

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Comments on the double cone wormhole

Chen,

Ivo,

Maldacena

2024

J. High Energ. Phys.

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In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes Tr[e−iKT], a trace of the “evolution” operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution $$\widetilde{K}$$ which involves a slightly complex geometry, so that we are really computing $${\text{Tr}}\left[{e}^{-i\widetilde{K}T}\right]$$. We argue that, for general black holes, the spectrum of $$\widetilde{K}$$ is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of JT gravity, we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of $$\widetilde{K}$$.

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Section: Contributions From Diffusive and Hydrodynamic Modes To The O...supporting

confidence: 89%

“…We discussed some applications of the modified boost. One was the hydrodynamic contribution to the spectral form factor, reproducing [18,27]. The other was the exponential suppression to the spectral form factor when we slightly change the couplings, reproducing the discussion in [6].…”

Section: Jhep04(2024)124 8 Conclusionmentioning

confidence: 56%

Comments on the double cone wormhole

Chen,

Ivo,

Maldacena

2024

J. High Energ. Phys.

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“…For instance, if H is not a GUE matrix but the direct sum H 1 ⊕H 2 of two GUE matrices, the ramp will be enhanced by a factor of two. This enhancement shows up in realistic systems such as the Bunimovich stadium [58,59], which have different sectors of their Hamiltonian which behave differently under reflection symmetry. It has recently been shown [46] that at times sub-exponential in system size, all-to-all spin glasses exhibit an enhancement of the ramp equal to the number of effective "sectors", i.e., regions of configuration space rendered dynamically disconnected by large energy barriers.…”

Section: Review Of the Spectral Form Factormentioning

confidence: 99%

Spectral statistics of a minimal quantum glass model

Barney,

Winer,

Baldwin

et al. 2023

SciPost Phys.

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Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the “Block Rosenzweig-Porter” (BRP) model. We calculate the spectral form factors of both models at all timescales larger than the inverse spectral width. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the steepness of the ramp of the spectral form factor.

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