arXiv subjects

Alexander Hahn

Publications and source records attributed to Alexander Hahn.

At least 19 recordsLinked to original sources

arXiv2026

Typical entanglement in anyon chains: Page curves beyond Lie group symmetries

We study bipartite entanglement statistics in one-dimensional anyon chains, whose Hilbert spaces are constrained by fusion rules of unitary pre-modular categories. Our setup generalizes previous frameworks on symmetry-resolved entanglement entropy for non-abelian Lie group symmetries to the setting of quantum groups. We derive analytical expressions for the average anyonic entanglement entropy and its variance. Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(\sqrt{L})$ or $O(1)$ symmetry-type corrections except for a subleading topological correction term that produces a Page curve asymmetry. We further show that the variance decays exponentially with system size, establishing the typicality. Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions, supporting the use of eigenstate entanglement as a diagnostic of quantum chaos. Our results establish the anyonic Page curve as an appropriate chaotic benchmark in topological many-body systems and connect anyonic entanglement to Page-type universality in quantum many-body physics.

quant-ph↗

arXiv2026

Direct comparison of SiPMs and PMTs in operation with a bright background and prospects of using SPADs as truly digital sensors

The use of silicon photomultipliers (SiPMs) alongside conventional photomultiplier tubes (PMTs) is a remarkable technological development in modern ground-based very high energy gamma-ray astronomy. SiPMs exhibit comparable or even higher photon detection efficiencies (PDEs) than PMTs. The sensitivity of a PMT matches well the spectral shape of Cherenkov radiation from extended air showers. In contrast to a PMT, the sensitivity of a SiPM is shifted toward longer wavelengths, where the intensity of light of night sky (LoNS), considered as unwanted noise, increases significantly. It is obvious that a SiPM with a higher PDE will indeed measure more Cherenkov light than a PMT, but it will also detect significantly higher LoNS noise; the question is which factor will predominate in the signal-to-noise-ratio (SNR). To compare the performance of a PMT with that of a SiPM, we built SiPM-based modules and installed these and operated in parallel in the imaging camera of the 17 m diameter MAGIC telescope. Our long-term studies show that SiPM, despite their higher PDE, can deliver only a comparable to PMT performance. As already the name SiPM suggests, we use these semiconductor sensors analogously to classical PMTs: We amplify their small signals, digitize, and calibrate the converted amplitudes. Although SiPM is essentially a digital sensor, its common-anode design does not allow one to directly profit from it. Numerous arrays of single-photon avalanche diodes (SPADs) are being developed in various laboratories worldwide. Unlike SiPM, SPAD arrays digitize the incident photons from the outset and count their number. We will dwell on the potential further developments of SPADs.

astro-ph.IM↗

arXiv2025

A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions

Forgetting as a knowledge management operation deliberately ignores parts of the knowledge and beliefs of an agent, for various reasons. Forgetting has many facets, one may want to forget parts of the syntax, a proposition, or a conditional. In the literature, two main operators suitable for performing forgetting have been proposed and investigated in depth: First, variable elimination is a syntactical method that blends out certain atomic variables to focus on the rest of the language. It has been mainly used in the area of logic programming and answer set programming. Second, contraction in AGM belief revision theory effectively removes propositions from belief sets under logical deduction. Both operations rely mainly on classical logics. In this article, we take an epistemic perspective and study forgetting operations in epistemic states with richer semantic structures, but with clear links to propositional logic. This allows us to investigate what forgetting in the epistemic background means, thereby lifting well-known and novel forgetting operations to the epistemic level. We present five general types of epistemic forgetting and instantiate them with seven concrete forgetting operations for Spohn's ranking functions. We take inspiration from postulates of forgetting both from logic programming and AGM theory to propose a rich landscape of axioms for evaluating forgetting operations. Finally, we evaluate all concrete forgetting operations according to all postulates, leading to a novel comprehensive overview highlighting differences and commonalities among the forgetting operators.

cs.AI↗

arXiv2024

Lower Bounds for the Trotter Error

In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows tuning accuracy. The Trotter simulation precision will always be inexact for non-commuting operators, but it is currently unknown what the minimum possible error is. This is an important quantity because upper bounds for the Trotter error are known to often be vast overestimates. Here, we present explicit lower bounds on the error, in norm and on states, allowing to derive minimum resource requirements. Numerical comparison with the true error shows that our bounds offer accurate and tight estimates.

quant-ph↗

arXiv2024

Bath Dynamical Decoupling with a Quantum Channel

Bang-bang dynamical decoupling protects an open quantum system from decoherence due to its interaction with the surrounding bath/environment. In its standard form, this is achieved by strongly kicking the system with cycles of unitary operations, which average out the interaction Hamiltonian. In this paper, we generalize the notion of dynamical decoupling to repeated kicks with a quantum channel, which is applied to the bath. We derive necessary and sufficient conditions on the employed quantum channel and find that bath dynamical decoupling works if and only if the kick is ergodic. Furthermore, we study in which circumstances CPTP kicks on a mono-partite quantum system induce quantum Zeno dynamics with its Hamiltonian cancelled out. This does not require the ergodicity of the kicks, and the absence of decoherence-free subsystems is both necessary and sufficient. While the standard unitary dynamical decoupling is essentially the same as the quantum Zeno dynamics, our investigation implies that this is not true any more in the case of CPTP kicks. To derive our results, we prove some spectral properties of ergodic quantum channels, that might be of independent interest. Our approach establishes an enhanced and unified mathematical understanding of several recent experimental demonstrations and might form the basis of new dynamical decoupling schemes that harness environmental noise degrees of freedom.

quant-ph↗

arXiv2024

Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model

Dynamical decoupling is a technique aimed at suppressing the interaction between a quantum system and its environment by applying frequent unitary operations on the system alone. In the present paper, we analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment initially prepared in a thermal state. We find sufficient conditions under which dynamical decoupling works for such systems, and, most importantly, we find bounds for the convergence speed of the procedure. Our analysis is based on a new Trotter theorem for multiple Hamiltonians and involves a rigorous treatment of the evolution of mixed quantum states via unbounded Hamiltonians. A comparison with numerical experiments shows that our bounds reproduce the correct scaling in various relevant system parameters. Furthermore, our analytical treatment allows for quantifying the decoupling efficiency for boson baths with infinitely many modes, in which case a numerical treatment is unavailable.

quant-ph↗

arXiv2024

Detailed Analysis of Local Climate at the CTAO-North Site on La Palma from 20 Years of MAGIC Weather Station Data

The Observatorio del Roque de los Muchachos will host the northern site of the Cherenkov Telescope Array Observatory (CTAO), in an area about 200 m below the mountain rim, where the optical telescopes are located. The site currently hosts the MAGIC Telescopes, which have gathered a unique series of 20 years of weather data. We use advanced profile likelihood methods to determine seasonal cycles, the occurrence of weather extremes, weather downtime, and long-term trends correctly taking into account data gaps. The fractality of the weather data is investigated by means of multifractal detrended fluctuation analysis. The data are published according to the Findable, Accessible, Interoperable, and Reusable (FAIR) principles. We find that the behaviour of wind and relative humidity show significant differences compared to the mountain rim. We observe an increase in temperature of $0.55\pm0.07\mathrm{(stat.)}\pm0.07\mathrm{(syst.)}^\circ C$/decade, the diurnal temperature range of $0.13\pm0.04\mathrm{(stat.)}\pm0.02\mathrm{(syst.)}^\circ C$/decade (accompanied by an increase of seasonal oscillation amplitude of $\Delta C_m=0.29\pm0.10\mathrm{(stat.)}\pm0.04\mathrm{(syst.)}^\circ C$/decade) and relative humidity of $4.0\pm0.4\mathrm{(stat.)}\pm1.1\mathrm{(syst.)}$%/decade, and a decrease in trade wind speeds of $0.85\pm0.12\mathrm{(stat.)}\pm0.07\mathrm{(syst.)}$(km/h)/decade. The occurrence of extreme weather, such as tropical storms and long rains, remains constant over time. We find a significant correlation of temperature with the North Atlantic Oscillation Index and multifractal behaviour of the data. The site shows a weather-related downtime of 18.5%-20.5%, depending on the wind gust limits employed. No hints are found of a degradation of weather downtime under the assumption of a linear evolution of environmental parameters over time.

astro-ph.IM↗

arXiv2024

Characterisation of the Atmosphere in Very High Energy Gamma-Astronomy for Imaging Atmospheric Cherenkov Telescopes

Ground-based observations of Very High Energy (VHE) gamma rays from extreme astrophysical sources are significantly influenced by atmospheric conditions. This is due to the atmosphere being an integral part of the detector when utilizing Imaging Atmospheric Cherenkov Telescopes (IACTs). Clouds and dust particles diminish atmospheric transmission of Cherenkov light, thereby impacting the reconstruction of the air showers and consequently the reconstructed gamma-ray spectra. Precise measurements of atmospheric transmission above Cherenkov observatories play a pivotal role in the accuracy of the analysed data, among which the corrections of the reconstructed energies and fluxes of incoming gamma rays, and in establishing observation strategies for different types of gamma-ray emitting sources. The Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes and the Cherenkov Telescope Array Observatory (CTAO), both located on the Observatorio del Roque de los Muchachos (ORM), La Palma, Canary Islands, use different sets of auxiliary instruments for real-time characterisation of the atmosphere. In this paper, historical data taken by MAGIC LIDAR (LIght Detection And Ranging) and CTAO FRAM (F/Photometric Robotic Telescope) are presented. From the atmospheric aerosol transmission profiles measured by the MAGIC LIDAR and CTAO FRAM aerosol optical depth maps, we obtain the characterisation of the clouds above the ORM at La Palma needed for data correction and optimal observation scheduling.

astro-ph.IM↗

arXiv2024

The anisotropic square lattice Ising model with quenched surface disorder

Using exact enumeration, the surface free energy as well as the critical Casimir amplitude and Casimir force are calculated for the square lattice Ising model with anisotropic couplings and quenched surface disorder on one surface in cylinder geometry at criticality. The system shape is characterized by the aspect ratio $L/M$, where the cylinder length $L$ can take arbitrary values, including $L\to\infty$, while the circumference $M$ is varied from $M=4$ to $M=54$, resulting in up to $2^{54}$ numerically exact free energy calculations. A careful $M\to\infty$ extrapolation shows that quenched surface disorder is irrelevant in two dimensions, but gives rise to logarithmic corrections.

cond-mat.stat-mech↗

arXiv2024

On the Liouville-von Neumann equation for unbounded Hamiltonians

The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the Schr\"odinger equation: the Liouville-von Neumann equation. When the state space of the system is infinite-dimensional, the Liouville superoperator is unbounded whenever the corresponding Hamiltonian is. In this paper, we provide a rigorous, pedagogically-oriented, and self-contained introduction to the quantum Liouville formalism in the presence of unbounded operators. We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage; starting from that, we develop some simpler characterizations of the domain of the Liouvillian and its square. We also provide, with explicit proofs, some domains of essential self-adjointness (cores) of the Liouvillian.

quant-ph↗

arXiv2024

Categorical Quantum Volume Operator

We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with irreducible representations of $\mathrm{SU}(2)$. Here, we show two equivalent constructions that allow general objects in fusion categories as degrees of freedom. First, we compute the volume operator for ribbon fusion categories. This includes the important class of modular tensor categories (such as quantum doubles), which are the building blocks of anyon models. Second, we further generalize the volume operator to spherical fusion categories by relaxing the categorical analog of the closure constraint (known as tetrahedral symmetry). In both cases, we obtain a volume operator that is Hermitian, provided that the input category is unitary. As an illustrative example, we consider the case of $\mathrm{SU}(2)_k$ and show that the standard $\mathrm{SU}(2)$ volume operator is recovered in the limit $k\rightarrow\infty$.

gr-qc↗

arXiv2023

Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry

Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded operators remains unclear. Here, we present a general theory for error estimation, including higher-order product formulas, with explicit input state dependency. Our approach overcomes two limitations of the existing operator-norm estimates in the literature. First, previous bounds are too pessimistic as they quantify the worst-case scenario. Second, previous bounds become trivial for unbounded operators and cannot be applied to a wide class of Trotter scenarios, including atomic and molecular Hamiltonians. Our method enables analytical treatment of Trotter errors in chemistry simulations, illustrated through a case study on the hydrogen atom. Our findings reveal: (i) for states with fat-tailed energy distribution, such as low-angular-momentum states of the hydrogen atom, the Trotter error scales worse than expected (sublinearly) in the number of Trotter steps; (ii) certain states do not admit an advantage in the scaling from higher-order Trotterization, and thus, the higher-order Trotter hierarchy breaks down for these states, including the hydrogen atom's ground state; (iii) the scaling of higher-order Trotter bounds might depend on the order of the Hamiltonians in the Trotter product for states with fat-tailed energy distribution. Physically, the enlarged Trotter error is caused by the atom's ionization due to the Trotter dynamics. Mathematically, we find that certain domain conditions are not satisfied by some states so higher moments of the potential and kinetic energies diverge. Our analytical error analysis agrees with numerical simulations, indicating that we can estimate the state-dependent Trotter error scaling genuinely.

quant-ph↗

arXiv2023

Correcting Imaging Atmospheric Cherenkov Telescope data with atmospheric profiles obtained with an elastic light detecting and ranging system

Context. We are operating an elastic LIDAR for the monitoring of atmospheric conditions during regular observations of the MAGIC Telescopes. Aims. We present and evaluate methods to convert aerosol extinction profiles, obtained with the LIDAR, into corrections of the reconstructed gamma-ray event energy and Instrument Response Functions of Imaging Atmospheric Cherenkov Telescopes. Methods. We assess the performance of these correction schemes with almost seven years of Crab Nebula data taken by the MAGIC Telescopes under various zenith angles and different aerosol extinction scenarios of Cherenkov light. Results. The methods enable the reconstruction of data taken under non-optimal atmospheric conditions with aerosol transmissions down to around 0.65 with systematic uncertainties comparable to those for data taken under optimal conditions. For the first time, the correction of data affected by clouds has been included in the assessment. The data can also be corrected when the transmission is lower than 0.65, but the results are less accurate and suffer from larger systematics.

astro-ph.IM↗

arXiv2022

Error bounds for Lie Group representations in quantum mechanics

We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group.

quant-ph↗

arXiv2022

State-dependent Trotter Limits and their approximations

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.

quant-ph↗

arXiv2022

Transfer-matrix summation of path integrals for transport through nanostructures

On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme to a transfer-matrix approach, which is more accessible to physical interpretation, allows for a more transparent formulation of the theory, and substantially improves the efficiency. In particular, the stationary limit is directly implemented, without the need of extrapolation. The resulting new method, referred to as "transfer-matrix summation of path integrals" (TraSPI), is then applied to resonant electronic transport through a single-level quantum dot.

cond-mat.mes-hall↗

arXiv2022

Characterizing the aerosol atmosphere above the Observatorio del Roque de los Muchachos by analyzing seven years of data taken with an GaAsP HPD-readout, absolutely calibrated elastic LIDAR

We present a new elastic LIDAR concept, based on a bi-axially mounted Nd:YAG laser and a telescope with HPD readout, combined with fast FADC signal digitization and offline pulse analysis. The LIDAR return signals have been extensively quality checked and absolutely calibrated. We analyze seven years of quasi-continuous LIDAR data taken during those nights when the MAGIC telescopes were operating. Characterization of the nocturnal ground layer yields zenith and azimuth angle dependent aerosol extinction scale heights for clear nights. We derive aerosol transmission statistics for light emitted from various altitudes throughout the year and separated by seasons. We find further seasonal dependencies of cloud base and top altitudes, but none for the LIDAR ratios of clouds. Finally, the night sky background light is characterized using the LIDAR photon backgrounds. abstract.txt

astro-ph.IM↗

arXiv2021

Unification of Random Dynamical Decoupling and the Quantum Zeno Effect

Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

quant-ph↗