Search

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, $N$ Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For $t \lesssim \sqrt{N}$, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At $t \sim \sqrt{N}$, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading $1/N$ effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at $t \sim 2N$, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. The oscillations at $t \lesssim \sqrt{N}$ indicate lack of thermalization -- a desired feature for a better performance of quantum information devices., Comment: main manuscript: 5 pages, 2 figures, appendix: two pages, 1 figure. Added references

We identify a time crystal phase characterized by a frequency half of the driving frequency in disordered superconductors by employing the time dependent Bogoliubov-de Gennes formalism at zero temperature with a periodically driven coupling constant. After a period of exponential increase of spatial inhomogeneities and exponential suppression of the order parameter amplitude, the time crystal develops islands of different sizes. Each of these islands is a time crystal with the same frequency albeit with a phase shift $\pi$ with respect to the homogeneous time crystal. After its emergence, the island gradually becomes smaller, though the phase shift persists, until it is abruptly synchronized at a time that it depends on its initial size. We find a critical disorder strength, still deep in the metallic phase, at which the time crystal phase terminates. For even stronger disorder, the order parameter oscillates with the driving frequency in regions where localization effects are not important., Comment: 30 pages, 23 figures

Objectives: Metabolic Bariatric Surgery (MBS) is a critical intervention for patients living with obesity and related health issues. Accurate classification and prediction of patient outcomes are vital for optimizing treatment strategies. This study presents a novel machine learning approach to classify patients in the context of metabolic bariatric surgery, providing insights into the efficacy of different models and variable types. Methods: Various machine learning models, including GaussianNB, ComplementNB, KNN, Decision Tree, KNN with RandomOverSampler, and KNN with SMOTE, were applied to a dataset of 73 patients. The dataset, comprising psychometric, socioeconomic, and analytical variables, was analyzed to determine the most efficient predictive model. The study also explored the impact of different variable groupings and oversampling techniques. Results: Experimental results indicate average accuracy values as high as 66.7% for the best model. Enhanced versions of KNN and Decision Tree, along with variations of KNN such as RandomOverSampler and SMOTE, yielded the best results. Conclusions: The study unveils a promising avenue for classifying patients in the realm of metabolic bariatric surgery. The results underscore the importance of selecting appropriate variables and employing diverse approaches to achieve optimal performance. The developed system holds potential as a tool to assist healthcare professionals in decision-making, thereby enhancing metabolic bariatric surgery outcomes. These findings lay the groundwork for future collaboration between hospitals and healthcare entities to improve patient care through the utilization of machine learning algorithms. Moreover, the findings suggest room for improvement, potentially achievable with a larger dataset and careful parameter tuning.

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order-correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large $q$-limit of a $q$-body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of $q \geq 4$ based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment., Comment: 32 pages, 4 figures, we have added references and made minor corrections

We study the quench dynamics of a two dimensional superconductor in a lattice of size up to $200\times 200$ employing the self-consistent time dependent Bogoliubov-de Gennes (BdG) formalism. In the clean limit, the dynamics of the order parameter for short times, characterized by a fast exponential growth and an oscillatory pattern, agrees with the Bardeen-Cooper-Schrieffer (BCS) prediction. However, unlike BCS, we observe for longer times an universal exponential decay of these time oscillations that we show explicitly to be induced by the full emergence of spatial inhomogeneities of the order parameter, even in the clean limit, characterized by the exponential growth of its variance. The addition of a weak disorder does not alter these results qualitatively. In this region, the spatial inhomogeneities rapidly develops into an intricate spatial structure consisting of ordered fragmented stripes in perpendicular directions where the order parameter is heavily suppressed especially in the central region. As the disorder strength increases, the fragmented stripes gradually turn into a square lattice of approximately circular spatial regions where the condensate is heavily suppressed. A further increase of disorder leads to the deformation and ultimate destruction of this lattice. We explore suitable settings for the experimental confirmation of these findings., Comment: 27 pages and 16 figures. References added

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII$_\nu$, BDI$^\dagger_\nu$, BDI$_{++\nu}$, and CI$_{--\nu}$, we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with $\nu \in \mathbb{N}$ the difference between the number of rows and columns. We show analytically that this feature leads to the existence of $\nu$ robust purely \emph{real} eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this $\nu$ is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries., Comment: 66 pages, 9 figures, 19 tables. v2: expanded Sec. IIC and minor corrections, as published

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern insulators in condensed matter, to protected states in complex photonic lattices in optics, and the structure of the QCD vacuum. Here, we introduce another playground for topology: the dissipative dynamics of pseudo-Hermitian many-body quantum systems. For that purpose, we study two different systems, the dissipative Sachdev-Ye-Kitaev (SYK) model, and a quantum chaotic dephasing spin chain. For the two different many-body models, we find the same topological features for a wide range of parameters suggesting that they are universal. In the SYK model, we identify four universality classes, related to pseudo-Hermiticity, characterized by a rectangular block representation of the vectorized Liouvillian that is directly related to the existence of an anomalous trace of the unitary operator implementing fermionic exchange. As a consequence of this rectangularization, we identify a topological index $\nu$ that only depends on symmetry. Another distinct consequence of the rectangularization is the observation, for any coupling to the bath, of purely real topological modes in the Liouvillian. The level statistics of these real modes agree with that of the corresponding random matrix ensemble and therefore can be employed to characterize the four topological symmetry classes. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium, which may enable a direct path for experimental confirmation of topology in dissipative many-body quantum chaotic systems., Comment: 15 pages, 9 figures. v2: references added. v3: expanded discussion of universality, plus minor corrections. v4: as published

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions with $q$-body ($q>2$) infinite-range interactions. We calculate certain Out of Time Order Correlators (OTOC) for $N\le 64$ fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This suggests that in the sparse case, the Lyapunov exponent also saturates the low-temperature bound. A key ingredient to reaching $N = 64$ is the development of a novel quantum spin model simulation library that implements highly-optimized matrix-free Krylov subspace methods on Graphical Processing Units (GPUs). This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a vastly larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. Our results potentially broadens the landscape of theories that may have a gravity analogue., Comment: 8 pages, 6 figures

Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox and establishing the unitarity of black hole evaporation. In this letter, we propose the dissipative Sachdev-Ye-Kitaev model (SYK) as a minimal quantum model that exhibits entanglement dynamics with features qualitatively similar to replica wormholes. As a demonstration, we investigate the entanglement growth of a pair of dissipative SYK models initialized in a thermofield double state (TFD). In the regime of large $N$ with weak dissipation, we observe a first-order entanglement transition characterized by a switch of the dominant saddle point: from replica diagonal solutions for short times to replica wormhole-like off-diagonal solutions for long times. Furthermore, we show that signature of replica wormholes persists even at moderate $N \lesssim 30$ by using the Monte Carlo quantum trajectory method. Our work paves the way for explorations of replica wormhole physics in quantum simulators., Comment: 7 pages, 4 figures. Supplemental Material 8 pages, 2 figures

In the infrared limit, a nearly anti-de Sitter spacetime in two dimensions (AdS$_2$) perturbed by a weak double trace deformation and a two-site $(q>2)$-body Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas and a weak $2r$-body intersite coupling share the same near-conformal dynamics described by a traversable wormhole. We exploit this relation to propose a symmetry classification of traversable wormholes depending on $N$, $q$, and $r$, with $q>2r$, and confirm it by a level statistics analysis using exact diagonalization techniques. Intriguingly, a time-reversed state never results in a new state, so only six universality classes occur: A, AI, BDI, CI, C, and D., Comment: 7 pages, 3 figures + Supplemental Material. v2: as published

The proposal "no boundary" of physicists Hartle and Hawking seeks to build a satisfactory model of the early Universe, in a way that avoids the singularity "Big Bang" of the beginning of the Universe. As a consequence of this proposal, the concept of metric signature change arises, which is approached in different ways in the literature. Here, we reinterpret the Mansouri-Nozari approach, which modifies the FLRW metric, and uses the formalism of Colombeau's Algebras, to develop its equations. In addition, we write the function that changes the sign in terms of redshift. Finally, we developed Friedmann's equations, of the modified metric, as well as the equation of state and other relevant equations in Cosmology.