Tootfinder

Was a bit frustrated and tired after work due to some false positives I couldn't figure out. Slept for two hours and then got up again to not loose a bike day in the Swiss #BikeToWork campaign and—more important 😉—to not break my #BikeStreak. It became yet another midnight ride, so in theory it …

2d Sinh-Gordon model on the infinite cylinder
Colin Guillarmou, Trishen S. Gunaratnam, Vincent Vargas
https://arxiv.org/abs/2405.04076 https://

2d Sinh-Gordon model on the infinite cylinder
For $R>0$, we give a rigorous probabilistic construction on the cylinder $\mathbb{R} \times (\mathbb{R}/(2πR\mathbb{Z}))$ of the (massless) Sinh-Gordon model. In particular we define the $n$-point correlation functions of the model and show that these exhibit a scaling relation with respect to $R$. The construction, which relies on the massless Gaussian Free Field, is based on the spectral analysis of a quantum operator associated to the model. Using the theory of Gaussian multiplicative chaos…

James Is Missing - complete series 👨‍👩‍👧‍👦🕵️📺
Dramatized sit-com series | Total listening time: 1h 30m
A group of ride-or-die friends is thrown into chaos when one of their members suddenly ghosts them all. Everyone has their theory. Only one of them can be true.
#AudioFiction #FictionPodcast

James Is Missing - complete series 👨‍👩‍👧‍👦🕵️📺
Dramatized sit-com series | Total listening time: 1h 30m A group of ride-or-die friends is thrown into chaos when one of their members suddenly ghosts them all. Everyone has their theory. Only one of them can be true. 1 seasons, 6 episodes as of Nov 24, 2023.

Spectral form factor in chaotic, localized, and integrable open quantum many-body systems
Jiachen Li, Stephen Yan, Toma\v{z} Prosen, Amos Chan
https://arxiv.org/abs/2405.01641

Spectral form factor in chaotic, localized, and integrable open quantum many-body systems
We numerically study the spectral statistics of open quantum many-body systems (OQMBS) as signatures of quantum chaos (or the lack thereof), using the dissipative spectral form factor (DSFF), a generalization of the spectral form factor to complex spectra. We show that the DSFF of chaotic OQMBS generically displays the $\textit{quadratic}$ ramp-plateau behaviour of the Ginibre ensemble from random matrix theory, in contrast to the linear ramp-plateau behaviour of the Gaussian ensemble in closed…

This https://arxiv.org/abs/2310.11355 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that the scaling predictions are matched by a privileged stochastic process, and serve as bound…

To what extent are multiple pendulum systems viable in pseudo-random number generation?
Matthew Sigit
https://arxiv.org/abs/2404.16860 https://

To what extent are multiple pendulum systems viable in pseudo-random number generation?
This paper explores the development and viability of an alternative pseudorandom number generator (PRNG) that leverages the chaotic dynamics of multiple pendulum systems. Some traditional PRNGs, notably the one implemented in the Java.Random class, suffer from predictability which gives rise to exploitability. This study identifies these vulnerabilities and proposes a novel PRNG designed using ordinary differential equations, physics modeling, and chaos theory. The performance of the new PRNG i…

Out of Time Order Correlation of the Hubbard Model with Random Local Disorder
Chakradhar Rangi, Juana Moreno, Ka-Ming Tam
https://arxiv.org/abs/2403.03214 …

Out of Time Order Correlation of the Hubbard Model with Random Local Disorder
The out of time order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory (DMFT) and coherent potential approximation (CPA) combined with diagrammatic perturbation on the Schwinger-Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electrons interaction. Our key finding is that random disorder en…

On the stochastics of human and artificial creativity
Solve S{\ae}b{\o}, Helge Brovold
https://arxiv.org/abs/2403.06996 https://arxiv…

On the stochastics of human and artificial creativity
What constitutes human creativity, and is it possible for computers to exhibit genuine creativity? We argue that achieving human-level intelligence in computers, or so-called Artificial General Intelligence, necessitates attaining also human-level creativity. We contribute to this discussion by developing a statistical representation of human creativity, incorporating prior insights from stochastic theory, psychology, philosophy, neuroscience, and chaos theory. This highlights the stochastic na…

Structural Stability Hypothesis of Dual Unitary Quantum Chaos
Jonathon Riddell, Curt von Keyserlingk, Toma\v{z} Prosen, Bruno Bertini
https://arxiv.org/abs/2402.19096

Structural Stability Hypothesis of Dual Unitary Quantum Chaos
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping …

This https://arxiv.org/abs/2311.09292 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Full range spectral correlations and their spectral form factors in chaotic and integrable models
Correlations between the eigenenergies of a system's spectrum can be a defining feature of quantum chaos. We characterize correlations between energies for all spectral distances by studying the distributions of $k$-th neighbor level spacings ($k$nLS) and compute their associated $k$-th neighbor spectral form factor ($k$nSFF). Specifically, we find analytical expressions for these signatures in paradigmatic models of quantum chaos, namely the three Gaussian ensembles of random matrix theory, an…

This https://arxiv.org/abs/2402.07980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Lanczos spectrum for random operator growth
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the context of Schrodinger evolution, this tridiagonalization has been carried out in Random Matrix Theory. We extend these developments to Heisenberg time evolution, describing how the Liouvillian can b…

On the stochastics of human and artificial creativity
Solve S{\ae}b{\o}, Helge Brovold
https://arxiv.org/abs/2403.06996 https://arxiv…

On the stochastics of human and artificial creativity
What constitutes human creativity, and is it possible for computers to exhibit genuine creativity? We argue that achieving human-level intelligence in computers, or so-called Artificial General Intelligence, necessitates attaining also human-level creativity. We contribute to this discussion by developing a statistical representation of human creativity, incorporating prior insights from stochastic theory, psychology, philosophy, neuroscience, and chaos theory. This highlights the stochastic na…

Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint
Yuzuru Kato
https://arxiv.org/abs/2403.19297 https://

Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint
We have recently proposed a fully quantum-mechanical definition of the asymptotic phase for quantum nonlinear oscillators, which is also applicable in the strong quantum regime [Kato and Nakao 2022 Chaos 32 063133]. In this study, we propose a definition of the quantum asymptotic amplitude for quantum oscillatory systems, which extends naturally the definition of the asymptotic amplitude for classical nonlinear oscillators on the basis of the Koopman operator theory. We introduce the asymptotic…

This https://arxiv.org/abs/2303.07348 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic evolution equations with Wick-analytic nonlinearities
We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher--KPP equations, stochastic Allen--Cahn, stochastic Newell--Whitehead--Segel, and stochastic Fujita--Gelfand equations. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this…

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo
https://arxiv.org/abs/2403.08503…

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can an…

This https://arxiv.org/abs/2403.14334 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New bounds for normal approximation on product spaces with applications to monochromatic edges, random sums and an infinite de Jong CLT
We extend the Malliavin theory for $L^2$-functionals on product probability spaces that has recently been developed by Decreusefond and Halconruy (2019) and by Duerinckx (2021), by characterizing the domains and investigating the actions of the three Malliavin operators in terms of the infinite Hoeffding decomposition in $L^2$, which we identify as the natural analogue of the famous Wiener-Itô chaos decomposition on Gaussian and Poisson spaces. We further combine this theory with Stein's metho…

New bounds for normal approximation on product spaces with applications to monochromatic edges, random sums and an infinite de Jong CLT
Christian D\"obler
https://arxiv.org/abs/2403.14334

New bounds for normal approximation on product spaces with applications to monochromatic edges, random sums and an infinite de Jong CLT
We extend the Malliavin theory for $L^2$-functionals on product probability spaces that has recently been developed by Decreusefond and Halconruy (2019) and by Duerinckx (2021), by characterizing the domains and investigating the actions of the three Malliavin operators in terms of the infinite Hoeffding decomposition in $L^2$, which we identify as the natural analogue of the famous Wiener-Itô chaos decomposition on Gaussian and Poisson spaces. We further combine this theory with Stein's metho…

This https://arxiv.org/abs/2403.08503 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can an…

This https://arxiv.org/abs/2303.09912 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Law of large numbers for the maximum of the two-dimensional Coulomb gas potential
We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of exponential moments, and the theory of Gaussian multiplicative chaos.

This https://arxiv.org/abs/2303.09912 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Law of large numbers for the maximum of the two-dimensional Coulomb gas potential
We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of exponential moments, and the theory of Gaussian multiplicative chaos.