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Out-of-time-ordered correlators (OTOCs), defined via the squared commutator of a time-evolving and a stationary operator, represent observables that provide useful indicators for chaos and the scrambling of information in complex quantum systems. Here we present a quasiclassical formalism of OTOCs, which is obtained from the semiclassical van Vleck-Gutzwiller propagator through the application of the diagonal approximation. For short evolution times, this quasiclassical approach yields the same result as the Wigner-Moyal formalism, i.e., OTOCs are classically described via the square of the Poisson bracket between the two involved observables, thus giving rise to an exponential growth in a chaotic regime. For long times, for which the semiclassical framework is, in principle, still valid, the diagonal approximation yields an asymptotic saturation value for the quasiclassical OTOC under the assumption of fully developed classical chaos. However, numerical simulations, carried out within chaotic few-site Bose-Hubbard systems in the absence and presence of periodic driving, demonstrate that this saturation value strongly underestimates the actual threshold value of the quantum OTOC, which is normally attained after the Ehrenfest time. This indicates that nondiagonal and hence genuinely quantum contributions, thus exceeding the framework of the quasiclassical description, are primarily responsible for describing OTOCs beyond the short-time regime.

We present VLT/MUSE integral-field spectroscopy ($R\approx 1\,800$) of four giant gravitational arcs exhibiting strong C IV absorption at 8 intervening redshifts, $z_{abs}\approx 2.0$--$2.5$. We detect C IV absorption in a total of 222 adjacent and seeing-uncorrelated sightlines, whose spectra sample beams of ("de-lensed") linear size $\approx 1$ kpc. Our data show that (1) absorption velocities cluster at all probed transverse scales, $\Delta r_\perp\approx0$--$15$ kpc, depending on system; (2) the (transverse) velocity dispersion never exceeds the mean (line-of-sight) absorption spread; and (3) the (transverse) velocity autocorrelation function does not resolve kinematic patterns at the above spatial scales, but its velocity projection, $\xi^{arc}(\Delta v)$, exhibits a similar shape to the known two-point correlation function toward quasars, $\xi^{QSO}(\Delta v)$. An empirical kinematic model suggests that these results are a natural consequence of wide-beam observations of an unresolved clumpy medium. Our model recovers both the underlying velocity dispersion of the clumps ($70$--$170$ \kms) and the mean number of clumps per unit area ($2$--$13$ kpc$^{-2}$). The latter constrains the projected mean inter-clump distance to within $\approx0.3$--$0.8$ kpc, which we argue is a measure of clump size for near-unity covering fraction. The model is also able to predict $\xi^{arc}(\Delta v)$ from $\xi^{QSO}(\Delta v)$, suggesting that the strong systems that shape the former and the line-of-sight velocity components that define the latter trace the same kinematic population. Consequently, the clumps must possess an internal density structure that generates both weak and strong components. We discuss how our interpretation is consistent with previous observations using background galaxies and multiple quasars., Comment: Accepted for publication in A&A

Based on periodic orbit theory we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic manifolds, described by the Selberg trace formula, displays a Schwarzian ($\sinh 2\pi\sqrt{E}$) mean level density. Due to its chaotic classical limit, this quantum system also shows all universal signatures of quantum chaos. These two properties imply a possible duality to Jackiw-Teitelboim-type quantum gravity at the level of a single system instead of an ensemble of systems like matrix theories and SYK models. Beyond the universal regime we show how the full wormhole geometry on the gravity side emerges from the discreteness of the set of periodic orbits. Thereby, we take initial steps towards a duality between gravitational and mesoscopic chaotic quantum systems through the topological, respectively, periodic orbit expansions of their correlators., Comment: 5 pages, 1 figure

We use a combinatorial approach to obtain exact expressions for the many-body density of states of fermionic and bosonic gases with equally spaced single-particle spectra. We identify a mapping that reveals a remarkable property, namely, fermionic and bosonic gases have the same many-body density of states, up to a shift corresponding to ground state energy. Additionally, we show that there is a regime, comprising the validity range of the Bethe approximation, where the many-body density of states becomes independent of the number of particles.

Linear methods are ubiquitous for control and estimation problems. In this work, we present a number of tensor operator norms as a means to approximately bound the error associated with linear methods and determine the situations in which that maximum error is encountered. An emphasis is placed on induced norms that can be computed in terms of matrix or tensor eigenvalues associated with coefficient tensors from higher-order Taylor series. These operator norms can be used to understand the performance and range of applicability of an algorithm exploiting linear approximations in different sets of coordinates. We examine uses of tensor operator norms in the context of linear and higher-order rendezvous guidance, coordinate selection for a filtering measurement model, and to present a unified treatment of nonlinearity indices for dynamical systems. Tensor norm computations can offer insights into these problems in one to two orders of magnitude less time than similarly accurate sampling methods while providing more general understanding of the error performance of linear or higher-order approximations.

We present an exhaustive analytical exploration of a variation of the eigenvector ensemble initially proposed by Deutsch for the foundations of the Eigenstate Thermalization Hypothesis (ETH) that drastically (but not fully) increases system-dependent information, and therefore serves as a model for the study of complex quantum systems beyond the universal Random Matrix Theory (RMT) regime. We especially focus on the remnants of system-specific information that modify the late-time behavior of correlation functions like the spectral form factor, or the inclusion of explicit system-dependent Hamiltonian corrections not captured by the RMT regime. The consistency of the predictions in the new ensemble with respect to the universal (Haar) one is made explicit by showing how that for arbitrary systems it defines an unitary 1-design and for strongly chaotic systems it becomes an approximated 2-design. While we are able to provide universal expressions for two- and four-point ensemble-averaged correlation functions and show how system-dependent information is spectrally decoupled, we also show that for small energy windows correlation functions defined by the new ensemble reduce to the predictions of the ETH., Comment: 50 pages + appendices

We present the first VLT/MUSE observations of a quasar featuring a proximate molecular absorption system, SDSS J125917.31+030922.5. The proximate damped Ly$\alpha$ absorption acts as a natural coronagraph, removing the quasar emission over $\sim$40 {\AA} in wavelength, and allows us to detect extended Ly$\alpha$ emission without the necessity of subtracting the quasar emission. This natural coronagraph permits the investigation of the quasar environment down to its inner regions ($r < 20$ kpc), where galaxy interactions or feedback processes should have the most noticeable effects. Our observations reveal a dense environment, with a highly asymmetric Ly$\alpha$ emission within $2"$ ($\sim 15$ kpc), possibly shaped by a companion galaxy, and a southern extension of the nebulae at about 50~kpc, with rotation-like kinematic signature. The width of the Ly$\alpha$ emission is broadest closer to the quasar, indicating perturbed kinematics as expected if interactions and significant gas flows are present. The foreground absorbing system itself is redshifted by $\approx $400 km/s relative to the background quasar, and therefore is likely arising from gas moving towards the quasar. Finally two additional Ly$\alpha$ emitters are detected with $>10\,\sigma$ significance at 96 and 223 kpc from the quasar, making this field overdense relative to other similar observations of quasars at $z\sim 3$. Our results support the hypothesis that quasars with proximate neutral/molecular absorption trace rich environments where galaxy interactions are at play and motivates further studies of H$_2$-selected quasars to shed light on feeding and feedback processes., Comment: Accepted for publication in A&A

The Model-X knockoffs is a practical methodology for variable selection, which stands out from other selection strategies since it allows for the control of the false discovery rate (FDR), relying on finite-sample guarantees. In this article, we propose a Truncated D-vine Copula Knockoffs (TDCK) algorithm for sampling approximate knockoffs from complex multivariate distributions. Our algorithm enhances and improves features of previous attempts to sample knockoffs under the multivariate setting, with the three main contributions being: 1) the truncation of the D-vine copula, which reduces the dependence between the original variables and their corresponding knockoffs, improving the statistical power; 2) the employment of a straightforward non-parametric formulation for marginal transformations, eliminating the need for a specific parametric family or a kernel density estimator; 3) the use of the "rvinecopulib'' R package offers better flexibility than the existing fitting vine copula knockoff methods. To eliminate the randomness in distinct realizations resulting in different sets of selected variables, we wrap the TDCK method with an existing derandomizing procedure for knockoffs, leading to a Derandomized Truncated D-vine Copula Knockoffs with e-values (DTDCKe) procedure. We demonstrate the robustness of the DTDCKe procedure under various scenarios with extensive simulation studies. We further illustrate its efficacy using a gene expression dataset, showing it achieves a more reliable gene selection than other competing methods, when the findings are compared with those of a meta-analysis. The results indicate that our Truncated D-vine copula approach is robust and has superior power, representing an appealing approach for variable selection in different multivariate applications, particularly in gene expression analysis., Comment: 31 pages, 9 figures, 1 table

The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called $\tau-$scaled limit of large times, $t \to \infty$, and fixed temperature in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the $\tau-$scaled SFF on the gravity side acquires both logarithmic and power law contributions in $t$, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity., Comment: version accepted for publication in JHEP, minor changes of text and references to the previous version, 34 pages+appendices

A bit catastrophe, loosely defined, is when a change in just one character of a string causes a significant change in the size of the compressed string. We study this phenomenon for the Burrows-Wheeler Transform (BWT), a string transform at the heart of several of the most popular compressors and aligners today. The parameter determining the size of the compressed data is the number of equal-letter runs of the BWT, commonly denoted $r$. We exhibit infinite families of strings in which insertion, deletion, resp. substitution of one character increases $r$ from constant to $\Theta(\log n)$, where $n$ is the length of the string. These strings can be interpreted both as examples for an increase by a multiplicative or an additive $\Theta(\log n)$-factor. As regards multiplicative factor, they attain the upper bound given by Akagi, Funakoshi, and Inenaga [Inf & Comput. 2023] of $O(\log n \log r)$, since here $r=O(1)$. We then give examples of strings in which insertion, deletion, resp. substitution of a character increases $r$ by a $\Theta(\sqrt{n})$ additive factor. These strings significantly improve the best known lower bound for an additive factor of $\Omega(\log n)$ [Giuliani et al., SOFSEM 2021]., Comment: This work is an extended version of our conference article with the same title, published in the proceedings of DLT 2023

It was recently proved that any Straight-Line Program (SLP) generating a given string can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We generalize this proof to a general class of grammars we call Generalized SLPs (GSLPs), which allow rules of the form $A \rightarrow x$ where $x$ is any Turing-complete representation (of size $|x|$) of a sequence of symbols (potentially much longer than $|x|$). We then specialize GSLPs to so-called Iterated SLPs (ISLPs), which allow rules of the form $A \rightarrow \Pi_{i=k_1}^{k_2} B_1^{i^{c_1}}\cdots B_t^{i^{c_t}}$ of size $2t+2$. We prove that ISLPs break, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness. Further, ISLPs can extract any substring of length $\lambda$, from the represented text $T[1.. n]$, in time $O(\lambda + \log^2 n\log\log n)$. This is the first compressed representation for repetitive texts breaking $\delta$ while, at the same time, supporting direct access to arbitrary text symbols in polylogarithmic time. We also show how to compute some substring queries, like range minima and next/previous smaller value, in time $O(\log^2 n \log\log n)$. Finally, we further specialize the grammars to Run-Length SLPs (RLSLPs), which restrict the rules allowed by ISLPs to the form $A \rightarrow B^t$. Apart from inheriting all the previous results with the term $\log^2 n \log\log n$ reduced to the near-optimal $\log n$, we show that RLSLPs can exploit balance to efficiently compute a wide class of substring queries we call ``composable'' -- i.e., $f(X \cdot Y)$ can be obtained from $f(X)$ and $f(Y)$..., Comment: This work is an extended version of articles published in SPIRE 2022 and LATIN 2024, which are now integrated into a coherent framework where specialized results are derived from more general ones, new operations are supported, and proofs are complete. arXiv admin note: substantial text overlap with arXiv:2402.09232

Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. However, when the data are structured in a non-linear way, like in the context of two-dimensional strings, inherent redundancy offers a rich source for compression, yet systematic studies on repetitiveness measures are still lacking. In the paper we introduce extensions of repetitiveness measures to general two-dimensional strings. In particular, we propose a new extension of the measures $\delta$ and $\gamma$, diverging from previous square based definitions proposed in [Carfagna and Manzini, SPIRE 2023]. We further consider generalizations of macro schemes and straight line programs for the 2D setting and show that, in contrast to what happens on strings, 2D macro schemes and 2D SLPs can be both asymptotically smaller than $\delta$ and $\gamma$. The results of the paper can be easily extended to $d$-dimensional strings with $d > 2$.

The following laboratory procedure provides students with a hands-on experience in nanomaterials chemistry and characterization. This three-day protocol is easy to follow for undergraduates with basic chemistry or materials science backgrounds and is suitable for inclusion in upper division courses in inorganic chemistry or materials science. Students use air-free chemistry procedures to synthesize and separate iron oxide magnetic nanoparticles and subsequently modify the nanoparticle surface using a chemical stripping agent. The morphology and chemical composition of the nanoparticles are characterized using electron microscopy and dynamic light scattering measurements. Additionally, magnetic characterization of the particles is performed using an open-source (3D-printed), inexpensive magnetophotometer. Possible modifications to the synthesis procedure including the incorporation of dopants to modify the magnetic response and alternative characterization techniques are discussed. The three-day synthesis, purification, and characterization laboratory will prepare students with crucial skills for advanced technology industries such as semiconductor manufacturing, nanomedicine, and green chemistry.

The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions in single-particle systems is lifted into many-body space. We achieve this by a many-body semiclassics analysis, appropriate for the mesoscopic regime of large but finite number of particles. We then identify the universality of both the cross-correlations and the Gaussian distribution of expansion coefficients as the signatures of chaotic eigenstates. Combined, these two aspects imprint a distinctive backbone to the morphology of eigenstates that we check against extensive quantum simulations. The universality of eigenstate correlations for fixed energy density is then a further signature of many-body quantum chaos that, while consistent with the eigenstate thermalization hypothesis, lies beyond random matrix theory.

In protoplanetary disks, atomic carbon is expected to originate from the PDR at the disk surface where CO is dissociated by UV photons coming from the stellar, or external interstellar, radiation field. Even though atomic carbon has been detected in several protoplanetary disks, there is a lack of spatially resolved observations of it. For HD 163296 protoplanetary disk, we aim to obtain both radial and vertical structure of [CI]$={^3}{P_1} - {^3}{P_0}$ line emission and perform the first direct comparison of this tracer with optically thick line emission $^{12}$CO $J=2-1$. We used archival ALMA data for [CI]$={^3}{P_1} - {^3}{P_0}$ and previously published ${^{12}}$ CO $J=2-1$ data in HD 163296. Through the software of disksurf we extracted the vertical structure, meanwhile radial profiles were obtained directly from imaging. Brand new DALI modelling was employed to perform direct comparison to the data. We found that these tracers are collocated radially but not vertically, where $^{12}$CO $J=2-1$ emission is, on average, located at higher altitudes, as it is also the case for other tracers in the same disk. Due to this difference in vertical height of the emission, the optically thick $^{12}$CO $J=2-1$ emission line appears to trace the highest altitudes, despite the expected formation mechanism of [CI] in the disk. The latter phenomena may be due to efficient mixing of the upper layers of the disk, or UV photons penetrating deeper than we expected.

We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are crucial in areas like Bioinformatics). The extension, called iterated SLPs (ISLPs), allows rules of the form $A \rightarrow \Pi_{i=k_1}^{k_2} B_1^{i^{c_1}}\cdots B_t^{i^{c_t}}$, for which we show how to extract any substring of length $\lambda$, from the represented text $T[1.. n]$, in time $O(\lambda + \log^2 n\log\log n)$. This is the first compressed representation for repetitive texts breaking $\delta$ while, at the same time, supporting direct access to arbitrary text symbols in polylogarithmic time. As a byproduct, we extend Ganardi et al.'s technique to balance any SLP (so it has a derivation tree of logarithmic height) to a wide generalization of SLPs, including ISLPs., Comment: This version of the article includes the proofs omitted from LATIN24

Inspired by animals that co-adapt their brain and body to interact with the environment, we present a tendon-driven and over-actuated (i.e., n joint, n+1 actuators) bipedal robot that (i) exploits its backdrivable mechanical properties to manage body-environment interactions without explicit control, and (ii) uses a simple 3-layer neural network to learn to walk after only 2 minutes of 'natural' motor babbling (i.e., an exploration strategy that is compatible with leg and task dynamics; akin to childsplay). This brain-body collaboration first learns to produce feet cyclical movements 'in air' and, without further tuning, can produce locomotion when the biped is lowered to be in slight contact with the ground. In contrast, training with 2 minutes of 'naive' motor babbling (i.e., an exploration strategy that ignores leg task dynamics), does not produce consistent cyclical movements 'in air', and produces erratic movements and no locomotion when in slight contact with the ground. When further lowering the biped and making the desired leg trajectories reach 1cm below ground (causing the desired-vs-obtained trajectories error to be unavoidable), cyclical movements based on either natural or naive babbling presented almost equally persistent trends, and locomotion emerged with naive babbling. Therefore, we show how continual learning of walking in unforeseen circumstances can be driven by continual physical adaptation rooted in the backdrivable properties of the plant and enhanced by exploration strategies that exploit plant dynamics. Our studies also demonstrate that the bio-inspired codesign and co-adaptations of limbs and control strategies can produce locomotion without explicit control of trajectory errors.

One of the fundamental results of semiclassical theory is the existence of trace formulae showing how spectra of quantum mechanical systems emerge from massive interference among amplitudes related with time-periodic structures of the corresponding classical limit. If it displays the properties of Hamiltonian integrability, this connection is given by the celebrated Berry-Tabor trace formula, and the periodic structures it is built on are KAM tori supporting closed trajectories in phase space. Here we show how to extend this connection into the domain of quantum many-body systems displaying integrability in the sense of the Bethe ansatz, where a classical limit cannot be rigorously defined due to the presence of singular potentials. Formally following the original derivation of Berry and Tabor [1, 2], but applied to the Bethe equations without underlying classical structure, we obtain a many-particle trace formula for the density of states of N interacting bosons on a ring, the Lieb-Liniger model. Our semiclassical expressions are in excellent agreement with quantum mechanical results for $N$ = 2, 3 and 4 particles. For N = 2 we relate our results to the quantization of billiards with mixed boundary conditions. Our work paves the way towards the treatment of the important class of integrable many-body systems by means of semiclassical trace formulae pioneered by Michael Berry in the single-particle context., Comment: 9 pages, 3 figures, contribution to the special issue honoring the scientific life of Michael Berry

This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e., it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose-Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed quite rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible)., Comment: 40 pages, 16 figures

We probed a gate-tunable InAs nanowire Josephson weak link by coupling it to a microwave resonator. Tracking the resonator frequency shift when the weak link is close to pinch-off, we observe that the ground state of the latter alternates between a singlet and a doublet when varying either the gate voltage or the superconducting phase difference across it. The corresponding microwave absorption spectra display lines that approach zero energy close to the singlet-doublet boundaries, suggesting parity flipping transitions, which are in principle forbidden in microwave spectroscopy and expected to arise only in tunnel spectroscopy. We tentatively interpret them by means of an ancillary state isolated in the junction acting as a reservoir for individual electrons.

This paper presents the results of 475 hours of interferometric observations with the Australia Telescope Compact Array towards the Spiderweb protocluster at \(z=2.16\). We search for large, extended molecular gas reservoirs among 46 previously detected CO(1-0) emitters, employing a customised method we developed. Based on the CO emission images and position-velocity diagrams, as well as the ranking of sources using a binary weighting of six different criteria, we have identified 14 robust and 7 tentative candidates that exhibit large extended molecular gas reservoirs. These extended reservoirs are defined as having sizes greater than 40 kpc or super-galactic scale. This result suggests a high frequency of extended gas reservoirs, comprising at least \(30 \%\) of our CO-selected sample. An environmental study of the candidates is carried out based on N-th nearest neighbour and we find that the large molecular gas reservoirs tend to exist in denser regions. The spatial distribution of our candidates is mainly centred on the core region of the Spiderweb protocluster. The performance and adaptability of our method are discussed. We found 13 (potentially) extended gas reservoirs located in nine galaxy (proto)clusters from the literature. We noticed that large extended molecular gas reservoirs surrounding (normal) star-forming galaxies in protoclusters are rare. This may be attributable to the lack of observations low-J CO transitions and the lack of quantitative analyses of molecular gas morphologies. The large gas reservoirs in the Spiderweb protocluster are a potential source of the intracluster medium seen in low redshift Virgo- or Coma-like galaxy clusters., Comment: 25 pages, 16 figures. Accepted for publication in MNRAS

We explore the effects of driving a cavity at a large photon number in a circuit-QED experiment where the ``matter-like'' part corresponds to an unique Andreev level in a superconducting weak link. The three many-body states of the weak link, corresponding to the occupation of the Andreev level by 0, 1 or 2 quasiparticles, lead to different cavity frequency shifts. We show how the non-linearity inherited by the cavity from its coupling to the weak link affects the state discrimination and the photon number calibration. Both effects require treating the evolution of the driven system beyond the dispersive limit. In addition, we observe how transition rates between the circuit states (quantum and parity jumps) are affected by the microwave power, and compare the measurements with a theory accounting for the ``dressing'' of the Andreev states by the cavity., Comment: Following remarks from referees, we have improved and simplified the presentation

Accuracy measures such as Recall, Precision, and Hit Rate have been a standard way of evaluating Recommendation Systems. The assumption is to use a fixed Top-N to represent them. We propose that median impressions viewed from historical sessions per diner be used as a personalized value for N. We present preliminary exploratory results and list future steps to improve upon and evaluate the efficacy of these personalized metrics., Comment: Accepted to evalRS 2023@KDD

We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of fields when the region of integration shrinks to a single point. We show that in most cases, convergence stably in distribution holds after a proper normalization. Furthermore, the limit random fields can be described in terms of stochastic integrals with respect to a L\'evy basis. We additionally discuss how our results can be used to measure the kinetic energy of a possibly turbulent flow., Comment: 23 pages, 0 figures

One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a new time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as $\hbar \rightarrow 0$., Comment: 12 pages, 8 figures, 1 table