Abstract We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q . At sufficiently large t , diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t , we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t and L are large while the ratio between L and L Th ( t ), the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that the resulting scaling functions are universal in the scaling limit.
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Spectral statistics of a minimal quantum glass model
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.
more » « less- PAR ID:
- 10494500
- Publisher / Repository:
- SciPost
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 15
- Issue:
- 3
- ISSN:
- 2542-4653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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ABSTRACT We present results of recurrence analysis of the black hole X-ray binary Cygnus X-1 using combined observations from the Rossi X-ray Timing Explorer All-sky Monitor and the Japanese Monitor of All-sky X-ray Image aboard the International Space Station. From the time-dependent windowed recurrence plot (RP), we compute 10 recurrence quantities that describe the dynamical behaviour of the source and compare them to the spectral state at each point in time. We identify epochs of state changes corresponding to transitions into highly deterministic or highly stochastic dynamical regimes and their correlation to specific spectral states. We compare k-Nearest Neighbors and Random Forest models for various sizes of the time-dependent RP. The spectral state in Cygnus X-1 can be predicted with greater than 95 per cent accuracy for both types of models explored across a range of RP sizes based solely on the recurrence properties. The primary features from the RP that distinguish between spectral states are the determinism, Shannon entropy, and average line length, all of which are systematically higher in the hard state compared to the soft state. Our results suggest that the hard and soft states of Cygnus X-1 exhibit distinct dynamical variability and the time domain alone can be used for spectral state classification.
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A bstract It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p -spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.more » « less
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Understanding the biophysical basis of protein aggregation is important in biology because of the potential link to several misfolding diseases. Although experiments have shown that protein aggregates adopt a variety of morphologies, the dynamics of their formation are less well characterized. Here, we introduce a minimal model to explore the dependence of the aggregation dynamics on the structural and sequence features of the monomers. Using simulations, we demonstrate that sequence complexity (codified in terms of word entropy) and monomer rigidity profoundly influence the dynamics and morphology of the aggregates. Flexible monomers with low sequence complexity (corresponding to repeat sequences) form liquid-like droplets that exhibit ergodic behavior. Strikingly, these aggregates abruptly transition to more ordered structures, reminiscent of amyloid fibrils, when the monomer rigidity is increased. In contrast, aggregates resulting from monomers with high sequence complexity are amorphous and display nonergodic glassy dynamics. The heterogeneous dynamics of the low and high-complexity sequences follow stretched exponential kinetics, which is one of the characteristics of glassy dynamics. Importantly, at nonzero values of the bending rigidities, the aggregates age with the relaxation times that increase with the waiting time. Informed by these findings, we provide insights into aging dynamics in protein condensates and contrast the behavior with the dynamics expected in RNA repeat sequences. Our findings underscore the influence of the monomer characteristics in shaping the morphology and dynamics of protein aggregates, thus providing a foundation for deciphering the general rules governing the behavior of protein condensates.
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Abstract We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large- N limit. Using numerical large- N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large- N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.15.3.084
