arXiv subjects

Alexander Adam

Publications and source records attributed to Alexander Adam.

14 recordsLinked to original sources

arXiv2026

Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($\mu_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $\mu_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $\mu_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $\mu_B\approx500$~MeV.

hep-lat↗

arXiv2025

Finite density lattice QCD without extrapolations

Finite density lattice QCD usually relies on extrapolations in baryon chemical potential ($\mu_B$), be it Taylor expansion, T' expansion (\cite{Borsanyi:2021sxv}) or analytical continuation. However, their range of validity is difficult to control. In the canonical formulation, the baryon density is the parameter of the system, not $\mu_B$. Here we demonstrate that we can access finite density QCD in the canonical formulation with physical quark masses. We present first results with both the strangeness ($n_S$) and baryon ($n_B$) densities as parameters. Specifically, we compute the QCD pressure and chemical potentials as functions of $n_B$ and $n_S$. Our computations rely on high-statistics simulations with 2+1 4HEX-staggered fermions.

hep-lat↗

arXiv2025

High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on $16^3 \times 8$ lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero, and fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-Weiss periodicity, which are exact properties of the QCD free energy. We use this ansatz to estimate the position of Lee-Yang zeros in the complex chemical potential plane. The temperature dependence of the imaginary part of the Lee-Yang zeros is then fitted with ans\"atze motivated by the universal behavior of the free energy near a 3D Ising critical point. In principle, this allows one to estimate the temperature of the critical endpoint. We consider several sources of systematic errors. On this single lattice spacing we find that with $84\%$ probability, the chiral critical endpoint is either below $103$~MeV temperature or it does not exist. We also identify some caveats of the method, which do not disappear even with the extremely high statistics of this present study. We discuss to what extent these can be eliminated by future high statistics lattice analyses.

hep-lat↗

arXiv2025

SAR Object Detection with Self-Supervised Pretraining and Curriculum-Aware Sampling

Object detection in satellite-borne Synthetic Aperture Radar (SAR) imagery holds immense potential in tasks such as urban monitoring and disaster response. However, the inherent complexities of SAR data and the scarcity of annotations present significant challenges in the advancement of object detection in this domain. Notably, the detection of small objects in satellite-borne SAR images poses a particularly intricate problem, because of the technology's relatively low spatial resolution and inherent noise. Furthermore, the lack of large labelled SAR datasets hinders the development of supervised deep learning-based object detection models. In this paper, we introduce TRANSAR, a novel self-supervised end-to-end vision transformer-based SAR object detection model that incorporates masked image pre-training on an unlabeled SAR image dataset that spans more than $25,700$ km\textsuperscript{2} ground area. Unlike traditional object detection formulation, our approach capitalises on auxiliary binary semantic segmentation, designed to segregate objects of interest during the post-tuning, especially the smaller ones, from the background. In addition, to address the innate class imbalance due to the disproportion of the object to the image size, we introduce an adaptive sampling scheduler that dynamically adjusts the target class distribution during training based on curriculum learning and model feedback. This approach allows us to outperform conventional supervised architecture such as DeepLabv3 or UNet, and state-of-the-art self-supervised learning-based arhitectures such as DPT, SegFormer or UperNet, as shown by extensive evaluations on benchmark SAR datasets.

cs.CV↗

arXiv2025

Search for a Lee-Yang edge singularity in high-statistics Wuppertal-Budapest data

Near a critical endpoint the Lee-Yang edge singularity approaches the real axis in the complex chemical potential plane. In the vicinity of the critical point the functional form of this approach depends on the universality class. Assuming a three dimensional Ising critical point in the QCD phase diagram the location of the critical endpoint can be extrapolated provided that the position of the Lee-Yang edge singularity is known at multiple temperatures. A popular method to estimate the position of a singularity is to model the free energy as a rational function of the baryon chemical potential $\mu_\text{B}$. The parameters of this model can be constrained by the cumulants of the net baryon density taken at $\mu_\text{B}^2\leq0$ . Using high-statistics simulations on a lattice $16^3\times8$ by the Wuppertal-Budapest Collaboration we estimate the location of the closest singularity in the QCD phase diagram. We also compare various models for the functional form of the free energy and discuss the predictive power of this approach.

hep-lat↗

arXiv2023

Task-specific experimental design for treatment effect estimation

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

stat.ME↗

arXiv2021

Rotating black holes in Einstein-aether theory

We introduce new methods to numerically construct for the first time stationary axisymmetric black hole solutions in Einstein-aether theory and study their properties. The key technical challenge is to impose regularity at the spin-2, 1, and 0 wave mode horizons. Interestingly we find the metric horizon, and various wave mode horizons, are not Killing horizons, having null generators to which no linear combination of Killing vectors is tangent, and which spiral from pole to equator or vice versa. Existing phenomenological constraints result in two regions of coupling parameters where the theory is viable and some couplings are large; region I with a large twist coupling and region II with also a (somewhat) large expansion coupling. Currently these constraints do not include tests from strong field dynamics, such as observations of black holes and their mergers. Given the large aether coupling(s) one might expect such dynamics to deviate significantly from general relativity, and hence to further constrain the theory. Here we argue this is not the case, since for these parameter regions solutions exist where the aether is "painted" onto a metric background that is very close to that of general relativity. This painting for region I is approximately independent of the large twist coupling, and for region II is also approximately independent of the large expansion coupling and normal to a maximal foliation of the spacetime. We support this picture analytically for weak fields, and numerically for rotating black hole solutions, which closely approximate the Kerr metric.

gr-qc↗

arXiv2020

Generalized hypergeometric expansion related to the Hurwitz zeta function

We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series in hypergeometric functions on each side. These equalities capture basic analytic properties of the Hurwitz zeta function like meromorphic extension and the functional equation. We give rates of convergence for the involved series. As a special case we find that the exponential rate of convergence for the deformation of the log-sine to the fractional part in the imaginary component is carried over to these equalities.

math.NT↗

arXiv2018

Horocycle averages on closed manifolds and transfer operators

We adapt to $C^r$ Anosov flows on compact manifolds a construction for $C^r$ discrete-time hyperbolic dynamics ($r>1$), obtaining anisotropic Banach or Hilbert spaces on which the resolvent of the generator of weighted transfer operators for the flow is quasi-compact. We apply this to study the ergodic integrals of the horocycle flows $h_\rho$ of $C^r$ codimension one mixing Anosov flows. In dimension three, for any suitably bunched $C^3$ contact Anosov flow with orientable strong-stable distribution, we establish power-law convergence of the ergodic average. We thereby implement the program of Giulietti-Liverani in the "real-life setting" of geodesic flows in variable negative curvature, where nontrivial resonances exist.

math.DS↗

arXiv2018

Zero is a resonance of every Schottky surface

For certain spectral parameters we find explicit eigenfunctions of transfer operators for Schottky surfaces. Comparing the dimension of the eigenspace for the spectral parameter zero with the multiplicity of topological zeros of the Selberg zeta function, we deduce that zero is a resonance of every Schottky surface.

math.SP↗

arXiv2016

A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions

Over the last few years Pohl (partly jointly with coauthors) developed dual `slow/fast' transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces $\Gamma\backslash\mathbb{H}$ with cusps and all finite-dimensional unitary representations $\chi$ of $\Gamma$. The eigenfunctions with eigenvalue $1$ of the fast transfer operators determine the zeros of the Selberg zeta function for $(\Gamma,\chi)$. Further, if $\Gamma$ is cofinite and $\chi$ is the trivial one-dimensional representation then highly regular eigenfunctions with eigenvalue $1$ of the slow transfer operators characterize Maass cusp forms for $\Gamma$. Conjecturally, this characterization extends to more general automorphic functions as well as to residues at resonances. In this article we study, without relying on Selberg theory, the relation between the eigenspaces of these two types of transfer operators for any Hecke triangle surface $\Gamma\backslash\mathbb{H}$ of finite or infinite area and any finite-dimensional unitary representation $\chi$ of the Hecke triangle group $\Gamma$. In particular we provide explicit isomorphisms between relevant subspaces. This solves a conjecture by M\"oller and Pohl, characterizes some of the zeros of the Selberg zeta functions independently of the Selberg trace formula, and supports the previously mentioned conjectures.

math.SP↗

arXiv2016

Generic non-trivial resonances for Anosov diffeomorphisms

We study real analytic perturbations of hyperbolic linear automorphisms on the 2-torus. The Koopman and the transfer operator are nuclear of order 0 when acting on a suitable Hilbert space. We show the generic existence of non-trivial Ruelle resonances for both operators. We prove that some of the perturbations preserve the volume and some of them do not.

math.DS↗

arXiv2012

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schr\"odinger type via a z=2 QCP.

hep-th↗

arXiv2011

A numerical approach to finding general stationary vacuum black holes

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon this equation has previously been shown to be elliptic, and Ricci flow and Newton's method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes, considered previously by Harmark, general enough to include the asymptotically flat case in higher dimensions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson's boundary conditions. We demonstrate both Newton's method and Ricci flow to find these Lorentzian solutions.

gr-qc↗