Searcharxiv⌕ Search

arXiv subjects

Robin Kaiser

Publications and source records attributed to Robin Kaiser.

At least 19 recordsLinked to original sources
arXiv2026

Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices

We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configuration. We then investigate the shape of avalanches induced by adding a particle at the origin in finite boxes of size $(2n+1)\times(2n+1)$ around the origin. In the stationary distribution on these finite boxes, we show that avalanches reach the boundary along the vertical teeth with probability tending to $1$, while the horizontal spread is of order $\sqrt{n}$. Finally, we establish that the single-source limit shape for abelian sandpiles on the comb lattice agrees with the corresponding limit shapes for the divisible sandpile, internal diffusion-limited aggregation (IDLA), and rotor-router aggregation models. This establishes limit shape universality on the comb lattice.

math.PR↗
arXiv2026

Phase transition for the asymptotic entropy of branching random walks on groups

We consider supercritical branching random walks (BRW) on countable groups $G$ and we prove that the asymptotic entropy of the empirical distributions of the BRW has a phase transition at $ρ_* = e^{h(μ)}$, where $h(μ)$ is the asymptotic entropy of the underlying random walk on $G$ with step distribution $μ$. Below this value $ρ_*$, the asymptotic empirical entropy of BRW equals the logarithm of the exponential growth rate of the population. Above this value, it is constantly equal to the asymptotic entropy of the underlying random walk. In particular, this answers questions from Kaimanovich-Woess [MR4663513, Section 6.3] about the existence and the behavior of the asymptotic entropy.

math.PR↗
arXiv2026

Maximal and minimal displacement of supercritical branching random walks on free products of groups

We prove that the maximal and minimal displacement of branching random walks with mean offspring number $ρ>1$ on free products of finite groups grows linearly almost surely. More precisely, we establish that the linear speed for the maximal (respectively minimal) displacement is given by the largest (respectively smallest) intersection point of the large deviation rate function of the underlying random walk with the horizontal line at height $\logρ$. The proof is based on constructing an associated multitype branching process which consists of particles that travel fast enough, and distinguishing the types via the suffix of the particles locations.

math.PR↗
arXiv2026

In Situ Coherence Measurements of Scattered Light in Magnetically Trapped Cold Atomic Clouds: Probe-Driven Atomic Dynamics

The use of temporal correlations in scattered photons to probe the microscopic dynamics of ultracold quantum gases has emerged as a powerful, minimally destructive approach for in situ analysis. Here, we demonstrate that temporal coherence spectroscopy can quantitatively characterize atomic motion in a magnetic trap, despite the perturbative effects of the probing light. By measuring the first-order correlation function g (1) ($τ$ ) of light scattered by a 87 Rb cloud confined in a quadrupole trap, we identify radiation-pressure-induced acceleration and heating as the origin of the apparent discrepancy between coherence spectra and temperatures inferred from time-of-flight measurements. A simple dynamical model incorporating these effects restores agreement between theory and experiment, establishing coherence spectroscopy as a reliable in situ probe of velocity distributions in trapped atomic ensembles. Our results pave the way for time-resolved studies of nonequilibrium dynamics and thermalization processes in confined cold gases, complementing conventional destructive imaging techniques.

physics.atom-ph↗
arXiv2026

All-Optical Control of Birefringence in a Cold Atomic Ensemble

We demonstrate all-optical control of birefringence in a cold atomic cloud of ytterbium. By optically dressing the excited $^{3}\mathrm{P}_1$ state via an off-resonant coupling to the $^{3}\mathrm{D}_1$ level, we induce polarization-dependent light shifts of the Zeeman sublevels, resulting in a tunable polarization-dependent refractive index. For a circularly polarized dressing beam, we observe a rotation of the probe linear polarization, characteristic of the Faraday effect, in the absence of any magnetic field. In addition, for a linearly polarized dressing beam, the probe acquires ellipticity without rotation, corresponding to linear birefringence. More generally, the polarization of the dressing beam controls the axis of rotation of the probe polarization on the Poincaré sphere. Our results establish cold atoms as a versatile platform for engineering and controlling light-induced birefringence and open new perspectives for the fast and reconfigurable control of optical response of resonant media.

physics.atom-ph↗
arXiv2026

Law of the Iterated Logarithm for $p$-Walks on $\mathbb{Z}$

The $p$-rotor walk on $\mathbb{Z}$ is a self-interacting walk that interpolates between the simple random walk and the deterministic rotor walk. While the weak convergence of this model to a perturbed Brownian motion is known, its almost sure asymptotic boundaries have not been characterized. In this paper, we establish the exact Law of the Iterated Logarithm (LIL) for the $p$-rotor walk. Utilizing the decomposition of the walk into a martingale perturbed by its running extrema, we obtain first a functional Law of the Iterated Logarithm for the linearly interpolated paths of the $p$-walk. We then obtain the classical LIL constants by solving a calculus of variations problem over the perturbed Strassen set.

math.PR↗
arXiv2026

On the structure of the sandpile identity element on Sierpinski gasket graphs

We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpinski gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs.

math.CO↗
arXiv2026

Limit shape of single-source stochastic sandpiles with $p$-topplings on $\mathbb{Z}$

We investigate the limit shape of the single-source model for stochastic sandpiles on the integer line subject to $p$--topplings. In this model, an initial configuration of $n\in\mathbb{N}$ particles is placed at the origin and stabilized according to a random toppling rule depending on $p\in (0,1)$: an unstable vertex sends exactly one particle to its left neighbor with probability $p$, and independently sends exactly one particle to its right neighbor with probability $p$. We prove that as $n \to \infty$, the macroscopic limit shape of the final stable configuration is a symmetric interval around the origin. Furthermore, by analyzing the center of mass martingale, we establish a central limit theorem for the boundary fluctuations, showing that after proper rescaling, they converge to a Gaussian distribution.

math.PR↗
arXiv2026

Validating the Angular Sizes of Red Clump Stars with Intensity Interferometry

The surface-brightness-color (SBC) relationship for Red Clump stars provides a critical foundation for precision distance ladder measurements, including the 1\% distance determination to the Large Magellanic Cloud. Current SBC calibrations rely on angular diameter measurements of nearby Red Clump stars obtained through long-baseline optical interferometry using the Very Large Telescope Interferometer. We explore the application of intensity interferometry to measure limb-darkened angular diameters of Red Clump stars, offering a complementary approach to traditional amplitude interferometry. We describe the framework for extracting angular diameters from squared visibility measurements in intensity interferometry, accounting for limb darkening through the stellar atmosphere models. For the Red Clump star HD~17652, we show that intensity interferometry in the $H$ band at baselines matching PIONIER ($\sim$100~m) could achieve $<1$\% angular size uncertainties in 2-hour exposures by measuring the primary peak of the visibility function, enabling direct comparison with existing measurements. Critically, observations at shorter wavelengths probe the secondary visibility maximum, providing independent checks of both measurement and systematic errors that are largely insensitive to limb-darkening assumptions. Exploiting the multiplex advantage of simultaneous multi-bandpass observations and the large number of baselines available with telescope arrays such as the Cherenkov Telescope Array Observatory can reduce observing times to practical levels, making intensity interferometry a viable tool for validating the angular sizes for a subset of the Red Clump star calibration sample.

astro-ph.SR↗
arXiv2026

Stabilization of stochastic networks in Markovian environment

We establish criteria under which stochastic networks in a Markovian environment stabilize, thus confirming Conjecture 7.2 from Levine-Greco [GL23]. The networks evolve on finite connected graphs $G=(V,E)$, and their dynamics are encoded by $V \times V$ toppling matrices $M$, whose columns record the expected number of topplings when the environment is in stationarity. Stabilization and non-stabilization are characterized by a parameter $ρ$ which depends on the largest eigenvalue of the matrix $M+αI$, with $α=1+\max\{-M(v,v):v\in V\}$. The proofs rely on the toppling random walk, in which toppled vertices are sampled according to the eigenvector associated with the largest eigenvalue of $M$.

math.PR↗
arXiv2026

Stochastic Sandpiles with Uniform Toppling Rule on the Line

We consider the stochastic sandpile model with uniform toppling rule on the integer line. During a uniform toppling, with probability $1/3$ one particle is sent to the right of the toppled vertex, with probability $1/3$ one particle is sent to the left, and with probability $1/3$ two particles are sent out, one to the right and one to the left. We calculate exactly the stationary distribution of the stochastic sandpile Markov chain with this toppling rule on finite, connected subsets of the integers, and show that the infinite volume limit exists and is equal to the Dirac measure of the full configuration. For this end, we analyze where the excess mass leaves the system, when stabilizing the full configuration plus one additional particle on finite, connected subsets of the integers.

math.PR↗
arXiv2026

Interference of photons from independent hot atoms

The coherence of light from independent ensembles of elementary atomic emitters plays a paramount role in diverse areas of modern optics. We demonstrate the interference of photons scattered from independent ensembles of warm atoms in atomic vapor. It relies on the feasibility of the preservation of coherence of light scattered elastically in the forward and backward directions from Doppler-broadened atomic ensembles, such that photons with chaotic photon statistics from two opposite atomic velocity groups contribute to the same detection mode. While the random phase fluctuations of the scattered light caused by a large thermal motion prevent direct observability of the interference in the detected photon rate, the stable frequency difference between photons collected from scattering off counter-propagating laser beams provides strong periodic modulation of the photon coincidence rate with the period given by the detuning of the excitation laser from the atomic resonance. The presented interferometry represents a sensitive and robust methodology for Doppler-free optical atomic and molecular spectroscopy based on photon correlation measurements on scattered light.

quant-ph↗
arXiv2026

ESO White Paper on Intensity Interferometry: Cosmology, Fundamental Physics, Quantum Optics

In this whitepaper, we outline how recent technological advances and ongoing developments open qualitatively new science opportunities in cosmology, fundamental physics, and quantum astrophysics. First, intensity interferometry can contribute to one of the most foundational observables in cosmology: the expansion rate of the Universe. Its angular resolution allows it to resolve the angular extent of extragalactic objects such as supernovae or quasars; combined with a physical scale local to the source, this yields an angular diameter distance and hence a 'Hubble diagram'. Second, the nature of dark matter can be probed via the astrometric lensing signatures of tiny dark matter halos. Third, intensity interferometry gives direct access to second-order coherence properties of astrophysical emission, opening a window onto genuinely quantum aspects of astrophysical light.

astro-ph.IM↗
arXiv2026

Collective resonance displacement in strongly driven cold atoms

Cold atoms are promising platforms for metrology and quantum computation, yet their many-body dynamics remains largely unexplored. We here investigate Rabi oscillations from optically-thick cold clouds, driven by high-intensity coherent light. A dynamical displacement from the atomic resonance is predicted, which can be detected through the collective Rabi oscillations of the atomic ensemble. Different from linear-optics shifts, this dynamical displacement grows quadratically with the optical depth, yet it reduces with increasing pump power as dipole-dipole interactions are less effective.

physics.atom-ph↗
arXiv2025

Towards measuring astrophysical third order correlation functions with the H.E.S.S. optical intensity interferometer

The closure phase, the sum of the three Fourier phases in a telescope triangle, is an important tool in astronomical interferometry, helping to reconstruct the geometries of the observed objects. While already established in amplitude interferometry, for the recently expanding field of intensity interferometers the closure phase enables recovering information of the interferometric phases that are otherwise inaccessible with this technique. To extract the (cosine of) the closure phase ($\cos ϕ$) in intensity interferometry, third-order correlations between three simultaneously measuring telescopes have to be computed. As the signal-to-noise of such three-photon correlations is too small for current generation intensity interferometers, no third-order correlations of astrophysical targets have been recorded so far. In this paper we present the first measurements of third order correlation functions of two stellar systems, Nunki ($σ$ Sgr) and Dschubba ($δ$ Sco), observed with the H.E.S.S. intensity interferometer in 2023. We show how to isolate the three-photon contribution term from the two-photon contributions, in order to access $\cos ϕ$. For the observed stellar targets the sensitivity is not high enough to extract closure phase information. To demonstrate that the analysis works well we further extract $\cos ϕ$ in a laboratory experiment, using the H.E.S.S. intensity interferometer and a pseudo-thermal light source.

astro-ph.IM↗
arXiv2025

Locally Markov walks on finite graphs

Locally Markov walks are natural generalizations of classical Markov chains, where instead of a particle moving independently of the past, it decides where to move next depending on the last action performed at the current location. We introduce the concept of locally Markov walks and we describe their stationary distribution and recurrent states, and we prove several properties such as irreducibility and ergodicity. For a particular locally Markov walk - the uniform unicycle walk on the complete graph - we investigate the mixing time and we prove that it exhibits cutoff.

math.PR↗
arXiv2025

Collective early-time spontaneous decay of a strongly driven cold atomic ensemble

In this work we present a numerical and experimental investigation of the collective early-time decay rates of a strongly driven and optically dense cold atomic cloud. We prepare the atomic ensemble by driving the system to its steady state with varying Rabi frequencies $Ω$ that go from the weak $Ω\ll Γ$ to the strong driving regime $Ω\gg Γ$, where $Γ$ is the single-atom decay rate. We investigate the early-time dynamics in the transition between the strong and weak driving regimes using: i) angular-dependent observables such as the light emitted by the cloud, and ii) global observables, i.e., the excited state population. When driving the cloud on-resonance, we find that as a function of the driving frequency, the behavior of the collected light at certain angles transitions from the single-photon subradiant regime to a superradiant regime while the behavior of the excited state population does not show superradiance. The experiment shows good agreement with numerical predictions in the regime of parameters under study.

quant-ph↗