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The search results for "math.ST" include diverse topics such as advancements in magnetometry and particle tracking. Notably, one study demonstrates improved sensitivity in atomic magnetometers using squeezed light for magnetic field measurements, while another re-evaluates particle tracking resolution, suggesting it can vary linearly with detection layers, surpassing traditional limits. Additionally, explorations into unitary representation theory and philosophical approaches to quantum mechanics signal ongoing interdisciplinary dialogues in statistical mathematics.
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arxiv.org
Improving Sensitivity of an Amplitude-Modulated Magneto-Optical Atomic Magnetometer using Squeezed Light

We experimentally demonstrate that a squeezed probe optical field can improve the sensitivity of the magnetic field measurements based on nonlinear magneto-optical rotation (NMOR) with an amplitude-modulated pump when compared to a coherent probe field under identical conditions. To realize an all-a…

quant-ph physics.atom-ph physics.optics
arxiv.org
Granularity Noise Limit in Atomic-Ensemble-Based Metrology

Conventional noise analysis in atomic-ensemble sensing assumes a continuous-medium approximation, thereby treating the atomic system as a deterministic dielectric. Here, we demonstrate that this assumption breaks down due to the discrete, particulate nature of the ensemble, giving rise to an intrins…

quant-ph physics.atom-ph
arxiv.org
Heteroscedasticity and angle resolution in high-energy particle tracking: revisiting "Beyond the $\sqrt{\mathrm{N}}$ limit of the least squares resolution and the lucky model", by G. Landi and G. E. Landi

I re-examine a recent work by G. Landi and G. E. Landi. [arXiv:1808.06708 [physics.ins-det]], in which the authors claim that the resolution of a tracker ca vary linearly with the number of detection layers, $N$, that is, faster than the commonly known $\sqrt{N}$ variation, for a tracker of fixed le…

physics.data-an physics.ins-det
arxiv.org
On the unitary representation theory of locally compact contraction groups

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this article provides a stepping stone towards a solution to this probl…

math.GR math.OA math.RT
arxiv.org
A structural theory of everything

In this paper it is argued that Barad's Agential Realism, an approach to quantum mechanics originating in the philosophy of Niels Bohr, can be the basis of a 'theory of everything' consistent with a proposal of Wheeler that observer-participancy is the foundation of everything. On the one hand, agen…

physics.gen-ph physics.hist-ph quant-ph
arxiv.org
There is no "Theory of Everything" inside E8

We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical rea…

math.RT hep-th
arxiv.org
No single unification theory of everything

In light of Gödel's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification theory of everything. The Universe is dynamic and so are the un…

physics.gen-ph
arxiv.org
Protein Folding: A Perspective From Statistical Physics

In this paper, we introduce an approach to the protein folding problem from the point of view of statistical physics. Protein folding is a stochastic process by which a polypeptide folds into its characteristic and functional 3D structure from random coil. The process involves an intricate interplay…

cond-mat.stat-mech cond-mat.soft physics.bio-ph q-bio.BM
arxiv.org
The impact of startup costs and the grid operator on the power price equilibrium

In this paper we propose a quadratic programming model that can be used for calculating the term structure of electricity prices while explicitly modeling startup costs of power plants. In contrast to other approaches presented in the literature, we incorporate the startup costs in a mathematically …

q-fin.PR math.OC
arxiv.org
Optimal Down Regulation of mRNA Translation

Down regulation of mRNA translation is an important problem in various bio-medical domains ranging from developing effective medicines for tumors and for viral diseases to developing attenuated virus strains that can be used for vaccination. Here, we study the problem of down regulation of mRNA tran…

q-bio.GN