arXiv subjects

Arnd Bäcker

Publications and source records attributed to Arnd Bäcker.

At least 19 recordsLinked to original sources

arXiv2026

Semiclassical foundation of universality in chaotic quantum circuits

The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess characteristics different from the single-particle theory. We present a periodic orbit theory for many-body systems with well defined semiclassical limit. For this we identify periodic orbit families arising exclusively in the many-body setting and implement a central limit theorem characterizing their correlations. Based on this we demonstrate that spectral correlations in chaotic quantum circuits are characterized by the breaking of individual time translation invariance of periodic orbits in the subsystems into residual synchronous time translations only. This provides a systematic approach to confirming random matrix universality in deterministic many-body systems.

quant-ph↗

arXiv2026

Timescales for Deep and Full Thermalization

Isolated quantum systems typically approach thermal equilibrium as described by the Eigenstate Thermalization Hypothesis (ETH). Going beyond this involves either higher order correlators (full thermalization) or the formation of state designs, i.e., the approach of moments of state ensembles after a projective measurement towards thermal equilibrium (deep thermalization). We compare these two extensions of ETH using extensive numerical studies within a paradigmatic model for chaotic many-body quantum dynamics. For this we find exponential relaxation for both extensions: For deep thermalization all moments relax with the same rate, which approximately equals the relaxation rate of the autocorrelation function captured by ETH. In contrast, higher order correlation functions in full thermalization approach equilibrium faster. This means that at higher orders full thermalization is faster than deep thermalization.

quant-ph↗

arXiv2025

Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor

While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. Here, we study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit. We compute the latter for a finite subsystem in a brickwork circuit coupled to an infinite complement. For initial times, shorter than the subsystem's size, spatial locality and (dual) unitarity implies a constant partial spectral form factor, clearly deviating from the linear ramp of the random matrix prediction. In contrast, for larger times we prove, that the partial spectral form factor follows the random matrix result up to exponentially suppressed corrections. We supplement our exact analytical results by semi-analytic computations performed in the thermodynamic limit as well as with numerics for finite-size systems.

quant-ph↗

arXiv2025

Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains

It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average eigenstate entanglement indeed approaches the random matrix result. However, the distribution of the eigenstate entanglement differs significantly. While for autonomous systems such deviations are expected, they are surprising for the more scrambling kicked systems. Similar deviations occur in a tensor-product random matrix model with all-to-all interactions. Therefore, we attribute the origin of the deviations for the kicked spin-chain models to the tensor-product structure of the Hilbert spaces. As a consequence, this would mean that such many body systems cannot be described by the standard random matrix ensembles.

quant-ph↗

arXiv2023

Classical Drift in the Arnold Web Induces Quantum Delocalization Transition

We demonstrate that quantum dynamical localization in the Arnold web of higher-dimensional Hamiltonian systems is destroyed by an intrinsic classical drift. Thus quantum wave packets and eigenstates may explore more of the intricate Arnold web than previously expected. Such a drift typically occurs, as resonance channels widen toward a large chaotic region or toward a junction with other resonance channels. If this drift is strong enough, we find that dynamical localization is destroyed. We establish that this drift-induced delocalization transition is universal and is described by a single transition parameter. Numerical verification is given using a time-periodically kicked Hamiltonian with a four-dimensional phase space.

nlin.CD↗

arXiv2023

Fast Bit-Flipping based on a Stability Transition of Coupled Spins

A bipartite spin system is proposed for which a fast transfer from one defined state into another exists. For sufficient coupling between the spins, this implements a bit-flipping mechanism which is much faster than that induced by tunneling. The states correspond in the semiclassical limit to equilibrium points with a stability transition from elliptic-elliptic stability to complex instability for increased coupling. The fast transfer is due to the spiraling characteristics of the complex unstable dynamics. Based on the classical system we find a universal scaling for the transfer time, which even applies in the deep quantum regime. By investigating a simple model system, we show that the classical stability transition is reflected in a fundamental change of the structure of the eigenfunctions.

quant-ph↗

arXiv2023

Characterizing quantum chaoticity of kicked spin chains

Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory. Using the example of the kicked Ising chain we demonstrate that even if both level spacing distribution and eigenvector statistics agree well with random matrix predictions, the entanglement entropy deviates from the expected Page curve. To explain this observation we propose a new measure of the effective spin interactions and obtain the corresponding random matrix result. By this the deviations of the entanglement entropy can be attributed to significantly different behavior of the $k$-spin interactions compared with RMT.

quant-ph↗

arXiv2023

Quantum transport through partial barriers in higher-dimensional systems

Partial transport barriers in the chaotic sea of Hamiltonian systems influence classical transport, as they allow for a small flux between chaotic phase-space regions only. We establish for higher-dimensional systems that quantum transport through such a partial barrier follows a universal transition from quantum suppression to mimicking classical transport. The scaling parameter involves the flux, the size of a Planck cell, and the localization length due to dynamical localization along a resonance channel. This is numerically demonstrated for coupled kicked rotors with a partial barrier that generalizes a cantorus to higher dimensions.

nlin.CD↗

arXiv2022

Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations

We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on multifractality and universal fluctuations, which is conceptually different from periodic-orbit scarring.

physics.optics↗

arXiv2022

Partial barriers to chaotic transport in 4D symplectic maps

Chaotic transport in Hamiltonian systems is often restricted due to the presence of partial barriers, leading to a limited flux between different regions in phase phase. Typically, the most restrictive partial barrier in a 2D symplectic map is based on a cantorus, the Cantor set remnants of a broken 1D torus. For a 4D symplectic map we establish a partial barrier based on what we call a cantorus-NHIM, a normally hyperbolic invariant manifold (NHIM) with the structure of a cantorus. Using a flux formula, we determine the global 4D flux across a partial barrier based on a cantorus-NHIM by approximating it with high-order periodic NHIMs. In addition, we introduce a local 3D flux depending on the position along a resonance channel, which is relevant in the presence of slow Arnold diffusion. Moreover, for a partial barrier composed of stable and unstable manifolds of a NHIM we utilize periodic NHIMs to quantify the corresponding flux.

nlin.CD↗

arXiv2022

Creating triple-NOON states with ultracold atoms via chaos-assisted tunneling

Triple-NOON states are superpositions of the form $e^{i φ_1} |{N,0,0}\rangle + e^{i φ_2} |{0,N,0}\rangle + e^{i φ_3} |{0,0,N}\rangle$ involving $N$ bosonic quanta distributed over three modes. We theoretically show how such highly entangled states can be generated with interacting ultracold bosonic atoms in a symmetric three-site lattice. The basic protocol consists in preparing all atoms on one site of the lattice and then letting the system evolve during a specific time such that collective tunneling of the atoms to the other two sites takes place. The key point put forward here is that this evolution time can be reduced by several orders of magnitude via the application of a periodic driving of the lattice, thereby rendering this protocol feasible in practice. This driving is suitably tuned such that classical chaos is generated in the entire accessible phase space except for the Planck cells that host the states participating at the above triple-NOON superposition. Chaos-assisted tunneling can then give rise to a dramatic speed-up of this collective tunneling process, without significantly affecting the purity of this superposition. A triple-NOON state containing $N = 5$ particles can thereby be realized with $^{87}$Rb atoms on time scales of the order of a few seconds.

cond-mat.quant-gas↗

arXiv2022

Quantum coherence controls the nature of equilibration in coupled chaotic systems

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax towards an equilibrium. It is found that quantum coherence of the initial product states in the uncoupled eigenbasis can be viewed as a resource for equilibration and approach to thermalization as manifested by the entanglement. Results are given for four distinct perturbation strength regimes, the ultra-weak, weak, intermediate, and strong regimes. For each, three types of initially unentangled states are considered, coherent random-phase superpositions, random superpositions, and eigenstate products. A universal time scale is identified involving the interaction strength parameter. Maximally coherent initial states thermalize for any perturbation strength in spite of the fact that in the ultra-weak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. In contrast to the widespread linear behavior, in this regime the entanglement initially grows quadratically in time.

quant-ph↗

arXiv2021

Universal intensity statistics of multifractal resonance states

We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system and the decay rate of the resonance state. We numerically support the conjecture by studying the phase-space Husimi function and the position representation of resonance states of the chaotic standard map, the baker map, and a random matrix model, each with partial escape.

nlin.CD↗

arXiv2020

Structure of resonance eigenfunctions for chaotic systems with partial escape

Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally-invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multi-fractal phase space distribution, their product structure along stable/unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases.

nlin.CD↗

arXiv2020

Geometry of complex instability and escape in four-dimensional symplectic maps

In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter variation. The change in the geometry of regular structures is visualized using 3D phase-space slices and in frequency space using the example of two coupled standard maps. The chaotic dynamics is studied using escape time plots and by computations of the 2D invariant manifolds associated with the complex unstable fixed point. Based on a normal-form description, we investigate the underlying transport mechanism by visualizing the escape paths and the long-time confinement in the surrounding of the complex unstable fixed point. We find that the escape is governed by the transport along the unstable manifold across invariant planes of the normal-form.

nlin.CD↗

arXiv2020

Linear and logarithmic entanglement production in an interacting chaotic system

We investigate entanglement growth for a pair of coupled kicked rotors. For weak coupling, the growth of the entanglement entropy is found to be initially linear followed by a logarithmic growth. We calculate analytically the time after which the entanglement entropy changes its profile, and a good agreement with the numerical result is found. We further show that the different regimes of entanglement growth are associated with different rates of energy growth displayed by a rotor. At a large time, energy grows diffusively, which is preceded by an intermediate dynamical localization. The time-span of intermediate dynamical localization decreases with increasing coupling strength. We argue that the observed diffusive energy growth is the result of one rotor acting as an environment to the other which destroys the coherence. We show that the decay of the coherence is initially exponential followed by a power-law.

quant-ph↗

arXiv2019

Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map

Understanding stickiness and power-law behavior of Poincaré recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees-of-freedom. We study such intermittent behavior of chaotic orbits in three-dimensional volume-preserving systems using the example of the Arnold-Beltrami-Childress map. The map has a mixed phase space with a cylindrical regular region surrounded by a chaotic sea for the considered parameters. We observe a characteristic overall power-law decay of the cumulative Poincaré recurrence statistics with significant oscillations superimposed. This slow decay is caused by orbits which spend long times close to the surface of the regular region. Representing such long-trapped orbits in frequency space shows clear signatures of partial barriers and reveals that coupled resonances play an essential role. Using a small number of the most relevant resonances allows for classifying long-trapped orbits. From this the Poincaré recurrence statistics can be divided into different exponentially decaying contributions which very accurately explains the overall power-law behavior including the oscillations.

nlin.CD↗

arXiv2019

Resonance--Assisted Tunneling in Deformed Optical Microdisks with a Mixed Phase Space

The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance--assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

physics.optics↗