arXiv subjects

Klaus Richter

Publications and source records attributed to Klaus Richter.

At least 37 records · Page 2Linked to original sources

arXiv2025

Ensemble-averaged mean-field many-body level density: an indicator of integrable versus chaotic single-particle dynamics

According to the quantum chaos paradigm, the nature of a system's classical dynamics, whether integrable or chaotic, is universally reflected in the fluctuations of its quantum spectrum. However, since many-body spectra in the mean field limit are composed of independent single-particle energy levels, their spectral fluctuations always display Poissonian behavior and hence cannot be used to distinguish underlying chaotic from integrable single-particle dynamics. We demonstrate that this distinction can, instead, be revealed from the mean many-body level density (at fixed energy) and its variance after averaging over ensembles representing different types of single-particle dynamics. This is in strong contrast to the energy-averaged mean level density (of a given system) that is assumed not to carry such information and is routinely removed to focus on universal signatures. To support our claim we systematically analyze the role of single-particle level correlations, that enter through Poisson and random matrix statistics (of various symmetry classes) into the ensemble-averaged density of states and its variance, contrasting bosonic and fermionic many-body systems. Our analytical study, together with extensive numerical simulations for systems with $N \ge 5$ particles consistently reveal significant differences (up to an order of magnitude for fermions and even larger for bosons) in the mean many-body level densities, depending on the nature of the underlying dynamics. Notably, in the fermionic case Poisson-type single-particle level fluctuations precisely cancel contributions from indistinguishability, such that the average many-body spectral density equals the (Thomas-Fermi) volume term. We further highlight the difference between the mean level density and its variance as functions of the total energy $E$ and the excitation energy $Q$.

cond-mat.quant-gas↗

arXiv2024

Dirac Landau levels for surfaces with constant negative curvature

Studies of the formation of Landau levels based on the Schrödinger equation for electrons constrained to curved surfaces have a long history. These include as prime examples surfaces with constant positive and negative curvature, the sphere [Phys. Rev. Lett. 51, 605 (1983)] and the pseudosphere [Annals of Physics 173, 185 (1987)]. Now, topological insulators, hosting Dirac-type surface states, provide a unique platform to experimentally examine such quantum Hall physics in curved space. Hence, extending previous work we consider solutions of the Dirac equation for the pseudosphere for both, the case of an overall perpendicular magnetic field and a homogeneous coaxial, thereby locally varying, magnetic field. For both magnetic-field configurations, we provide analytical solutions for spectra and eigenstates. For the experimentally relevant case of a coaxial magnetic field we find that the Landau levels split and show a peculiar scaling $\propto B^{1/4}$, thereby characteristically differing from the usual linear $B$ and $B^{1/2}$ dependence of the planar Schrödinger and Dirac case, respectively. We compare our analytical findings to numerical results that we also extend to the case of the Minding surface.

cond-mat.mes-hall↗

arXiv2024

Radiation-induced dynamical formation of Floquet-Bloch bands in Dirac Hamiltonians

Recent experiments, combing ultrafast strong-field irradiation of surfaces with time- and angle-resolved photoemission spectroscopy, allow for monitoring the time-dependent charge carrier dynamics and the build-up of transient sidebands due to the radiation pulses. While these structures are reminiscent of Floquet-Bloch bands, standard Floquet theory is not applicable since it requires a strictly time-periodic driving field. To study the emergence and formation of such sidebands, i.e. to provide a link between common Floquet physics and dynamical mechanisms underlying short driving pulses, we consider a generalization of Floquet theory, the so-called $t-t^{\prime}$ formalism. This approach naturally extents Floquet theory to driving field amplitudes with a superimposed envelope shape. Motivated by experiments we study 2D Dirac Hamiltonians subject to linearly and circularly polarised light waves with a Gaussian field envelope of a few cycles. For these Floquet-Bloch Hamiltonians we study the evolution of their Floquet-Bloch spectra, accompanied by a systematic analysis of the time-dependent (sideband) transitions. We show that sideband occupation requires circularly polarized light for linear Dirac systems such as graphene, while for Dirac models with trigonal warping, describing surface states of topological insulators such as Bi$_2$ Se$_3$, both linearly and circularly polarised pulses induce sideband excitations.

cond-mat.mes-hall↗

arXiv2024

Controlling Many-Body Quantum Chaos: Bose-Hubbard systems

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).

cond-mat.quant-gas↗

arXiv2024

Tracing Dirac points of topological surface states by ferromagnetic resonance

Ferromagnetic resonance is used to reveal features of the buried electronic band structure at interfaces between ferromagnetic metals and topological insulators. By monitoring the evolution of magnetic damping, the application of this method to a hybrid structure consisting of a ferromagnetic layer and a 3D topological insulator reveals a clear fingerprint of the Dirac point and exhibits additional features of the interfacial band structure not otherwise observable. The underlying spin-pumping mechanism is discussed in the framework of dissipation of angular momentum by topological surface states (TSSs). Tuning of the Fermi level within the TSS was verified both by varying the stoichiometry of the topological insulator layer and by electrostatic backgating and the damping values obtained in both cases show a remarkable agreement. The high energy resolution of this method additionally allows us to resolve the energetic shift of the local Dirac points generated by local variations of the electrostatic potential. Calculations based on the chiral tunneling process naturally occurring in TSS agree well with the experimental results.

cond-mat.mes-hall↗

arXiv2024

Periodic orbit theory of Bethe-integrable quantum systems: an $N$-particle Berry-Tabor trace formula

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.

quant-ph↗

arXiv2024

Electron quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in many aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, \eg, snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

cond-mat.mes-hall↗

arXiv2023

Controlling quantum chaos: time-dependent kicked rotor

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 $\hbar \rightarrow 0$.

quant-ph↗

arXiv2023

Dynamical transition from localized to uniform scrambling in locally hyperbolic systems

Fast scrambling of quantum correlations, reflected by the exponential growth of Out-of-Time-Order Correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum systems with a classical limit. In two recent works [Phys. Rev. Lett. 123, 160401 (2019)] and [Phys. Rev. Lett. 124, 140602 (2020)], a significant difference in the scrambling rate of integrable (many-body) systems was observed, depending on the initial state being semiclassically localized around unstable fixed points or fully delocalized (infinite temperature). Specifically, the quantum Lyapunov exponent $λ_{\rm q}$ quantifying the OTOC growth is given, respectively, by $λ_{\rm q}=2λ_{\rm s}$ or $λ_{\rm q}=λ_{\rm s}$ in terms of the stability exponent $λ_{\rm s}$ of the hyperbolic fixed point. Here we show that a wave packet, initially localized around this fixed point, features a distinct dynamical transition between these two regions. We present an analytical semiclassical approach providing a physical picture of this phenomenon and support our findings by extensive numerical simulations in the whole parameter range of locally unstable dynamics of a Bose-Hubbard dimer. Our results suggest that the existence of this crossover is a hallmark of unstable separatrix dynamics in integrable systems, thus opening the possibility to distinguish the latter, on the basis of this particular observable, from genuine chaotic dynamics generally featuring uniform exponential growth of the OTOC.

quant-ph↗

arXiv2023

Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity

Based on the discovery of the duality between Jackiw-Teitelboim quantum gravity and a double-scaled matrix ensemble by Saad, Shenker and Stanford in 2019, we show how consistency between the two theories in the universal Random Matrix Theory (RMT) limit imposes a set of constraints on the volumes of moduli spaces of Riemannian manifolds. These volumes are given in terms of polynomial functions, the Weil-Petersson volumes, solving a celebrated nonlinear recursion formula that is notoriously difficult to analyze. Since our results imply linear relations between the coefficients of the Weil-Petersson volumes, they therefore provide both a stringent test for their symbolic calculation and a possible way of simplifying their construction. In this way, we propose a long-term program to improve the understanding of mathematically hard aspects concerning moduli spaces of hyperbolic manifolds by using universal RMT results as input.

hep-th↗

arXiv2023

Quantum capacitive coupling between large-angle twisted graphene layers

Large-angle twisted bilayer graphene (tBLG) is known to be electronically decoupled due to the spatial separation of the Dirac cones corresponding to individual graphene layers in the reciprocal space. The close spacing between the layers causes strong capacitive coupling, opening possibilities for applications in atomically thin devices. Here, we present a self-consistent quantum capacitance model for the electrostatics of decoupled graphene layers, and further generalize it to deal with decoupled tBLG at finite magnetic field and large-angle twisted double bilayer graphene at zero magnetic field. We probe the capacitive coupling through the conductance, showing good agreement between simulations and experiments for all the systems considered. We also propose a new experiment utilizing the decoupling effect to induce a huge and tunable bandgap in bilayer graphene by applying a moderately low bias. Our model can be extended to systems composed of decoupled graphene multilayers as well as non-graphene systems, opening a new realm of quantum-capacitively coupled materials.

cond-mat.mes-hall↗

arXiv2022

Genuine many-body quantum scars along unstable modes in Bose-Hubbard systems

The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.

cond-mat.quant-gas↗

arXiv2022

Semiclassical roots of universality in many-body quantum chaos

Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classically chaotic dynamics and corresponding universal features at the quantum level. Recently, single-particle techniques dealing with ergodic wave interference in the usual semiclassical limit $\hbar \rightarrow 0$ have begun to be transformed into the field theoretical domain of N-particle systems in the analogous semiclassical limit $\hbar_{eff} = 1/N \rightarrow 0$, thereby accounting for genuine many-body quantum interference. This semiclassical many-body theory provides a unified framework for understanding random-matrix correlations of both single-particle and many-body quantum chaotic systems. Certain braided bundles of classical orbits, and of mean field modes, govern interference, respectively, and provide the key to the foundation of universality. Case studies presented include a many-body version of Gutzwiller's trace formula for the spectral density and out-of-time-order correlators along with brief remarks on where further progress may be forthcoming.

quant-ph↗

arXiv2022

Controlling Quantum Chaos: Optimal Coherent Targeting

One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as $\hbar \rightarrow 0$

nlin.CD↗

arXiv2022

Supercurrent interference in HgTe Josephson junctions

Wires made of topological insulators (TI) are a promising platform for searching for Majorana bound states. These states can be probed by analyzing the fractional ac Josephson effect in Josephson junctions with the TI wire as a weak link. An axial magnetic field can be used to tune the system from trivial to topologically nontrivial. Here we investigate the oscillations of the supercurrent in such wire Josephson junctions as a function of the axial magnetic field strength and different contact transparencies. Although the current flows on average parallel to the magnetic field we observe $h/2e$, $h/4e$- and even $h/8e$-periodic oscillations of the supercurrent in samples with lower contact transparencies. Corresponding tight-binding transport simulations using a Bogoliubov-de Gennes model Hamiltonian yield the supercurrent through the Josephson junctions, showing in particular the peculiar $h/4e$-periodic oscillations observed in experiments. A further semiclassical analysis based on Andreev-reflected trajectories connecting the two superconductors allows us to identify the physical origin of these oscillations. They can be related to flux-enclosing paths winding around the TI-nanowire, thereby highlighting the three-dimensional character of the junction geometry compared to common planar junctions.

cond-mat.mes-hall↗

arXiv2021

Dirac fermion optics and directed emission from single- and bilayer graphene cavities

High-mobility graphene hosting massless charge carriers with linear dispersion provides a promising platform for electron optics phenomena. Inspired by the physics of dielectric optical micro-cavities where the photon emission characteristics can be efficiently tuned via the cavity shape, we study corresponding mechanisms for trapped Dirac fermionic resonant states in deformed micro-disk graphene billiards and directed emission from those. In such graphene devices a back-gate voltage provides an additional tunable parameter to mimic different effective refractive indices and thereby the corresponding Fresnel laws at the boundaries. Moreover, cavities based on single-layer and double-layer graphene exhibit Klein- and anti-Klein tunneling, respectively, leading to distinct differences with respect to dwell times and resulting emission profiles of the cavity states. Moreover, we find a variety of different emission characteristics depending on the position of the source where charge carriers are fed into the cavites. Combining quantum mechanical simulations with optical ray tracing and a corresponding phase-space analysis, we demonstrate strong confinement of the emitted charge carriers in the mid field of single-layer graphene systems and can relate this to a lensing effect. For bilayer graphene, trapping of the resonant states is more efficient and the emission characteristics do less depend on the source position.

cond-mat.mes-hall↗

arXiv2021

Ergodic and non-ergodic many-body dynamics in strongly nonlinear lattices

The study of non-linear oscillator chains in classical many-body dynamics has a storied history going back to the seminal work of Fermi, Pasta, Ulam and Tsingou (FPUT). We introduce a new family of such systems which consist of chains of $N$ harmonically coupled particles with the non-linearity introduced by confining the motion of each individual particle to a box/stadium with hard walls. The stadia are arranged on a one dimensional lattice but they individually do not have to be one dimensional thus permitting the introduction of chaos already at the lattice scale. For the most part we study the case where the motion is entirely one dimensional. We find that the system exhibits a mixed phase space for any finite value of $N$. Computations of Lyapunov spectra at randomly picked phase space locations and a direct comparison between Hamiltonian evolution and phase space averages indicate that the regular regions of phase space are not significant at large system sizes. While the continuum limit of our model is itself a singular limit of the integrable sinh-Gordon theory, we do not see any evidence for the kind of non-ergodicity famously seen in the FPUT work. Finally, we examine the chain with particles confined to two dimensional stadia where the individual stadium is already chaotic, and find a much more chaotic phase space at small system sizes.

nlin.CD↗

arXiv2021

Emergence of a Renormalized $1/N$ Expansion in Quenched Critical Many-Body Systems

We consider the fate of $1/N$ expansions in unstable many-body quantum systems, as realized by a quench across criticality, and show the emergence of ${\rm e}^{2λt}/N$ as a renormalized parameter ruling the quantum-classical transition and accounting nonperturbatively for the local divergence rate $λ$ of mean-field solutions. In terms of ${\rm e}^{2λt}/N$, quasiclassical expansions of paradigmatic examples of criticality, like the self-trapping transition in an integrable Bose-Hubbard dimer and the generic instability of attractive bosonic systems toward soliton formation, are pushed to arbitrarily high orders. The agreement with numerical simulations supports the general nature of our results in the appropriately combined long-time $λt\to \infty$ quasiclassical $N\to \infty$ regime, out of reach of expansions in the bare parameter $1/N$. For scrambling in many-body hyperbolic systems, our results provide formal grounds to a conjectured multiexponential form of out-of-time-ordered correlators.

quant-ph↗