Search results for "Mathematical physics"

Integrable systems and moduli spaces of curves

2016

This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and mirror symmetry. The text contains a short introduction to the main ideas and prerequisites of the subject from geometry and mathematical physics, followed by a synthetic review of some of my papers (listed below) starting from my PhD thesis (October 2008), and with some open questions and future developements. My results include: • the triple mirror symmetry among P 1-orbifolds with positive Euler characteristic , the Landau-Ginzburg model with superpotential −xyz + x p + y q + z r with 1 p + …

The upgraded HADES trigger and data acquisition system

2011

The HADES experiment is a High Acceptance Di-Electron Spectrometer located at GSI in Darmstadt, Germany. Recently, its trigger and data acquisition system was upgraded. The main goal was to substantially increase the event rate capability by a factor of up to 20 to reach 100 kHz in light and 20 kHz in heavy ion reaction systems. The total data rate written to storage is about 400 MByte/s in peak.In this context, the complete read-out system was exchanged to FPGA-based platforms using optical communication. For data transport a general-purpose real-time network protocol was developed to meet the strong requirements of the system. In particular, trigger information has to reach all front-end …

An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator

2001

Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.

Evanescent wave approximation for non-Hermitian Hamiltonians

2020

The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decay. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics, which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.

Hardware and firmware developments for the upgrade of the ATLAS Level-1 Central Trigger Processor

2014

The Central Trigger Processor (CTP) is the final stage of the ATLAS first level trigger system which reduces the collision rate of 40 MHz to a Level-1 event rate of 100 kHz. An upgrade of the CTP is currently underway to significantly increase the number of trigger inputs and trigger combinations, allowing additional flexibility for the trigger menu. We present the hardware and FPGA firmware of the newly designed core module (CTPCORE+) module of the CTP, as well as results from a system used for early firmware and software prototyping based on commercial FPGA evaluation boards. First test result from the CTPCORE+ module will also be shown.

INTERFACE TENSION AND CORRELATION LENGTH OF 2D POTTS MODELS: NUMERICAL VERSUS EXACT RESULTS

1994

I briefly review new analytical formulas for the correlation length and interface tension of two-dimensional q-state Potts models and compare them with numerical results from recent Monte Carlo simulation studies.

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

2013

Combinatorial proofs of two theorems of Lutz and Stull

2021

Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…

Efficient Quantum Algorithms for (Gapped) Group Testing and Junta Testing

2015

In the k-junta testing problem, a tester has to efficiently decide whether a given function f: {0, 1}n → {0, 1} is a k-junta (i.e., depends on at most fc of its input bits) or is ε-far from any k-junta. Our main result is a quantum algorithm for this problem with query complexity Õ([EQUATION]) and time complexity Õ(n[EQUATION]). This quadratically improves over the query complexity of the previous best quantum junta tester, due to Atıcı and Servedio. Our tester is based on a new quantum algorithm for a gapped version of the combinatorial group testing problem, with an up to quartic improvement over the query complexity of the best classical algorithm. For our upper bound on the time complex…

A Convolutional Neural Network based Cascade Reconstruction for the IceCube Neutrino Observatory

2021

Continued improvements on existing reconstruction methods are vital to the success of high-energy physics experiments, such as the IceCube Neutrino Observatory. In IceCube, further challenges arise as the detector is situated at the geographic South Pole where computational resources are limited. However, to perform real-time analyses and to issue alerts to telescopes around the world, powerful and fast reconstruction methods are desired. Deep neural networks can be extremely powerful, and their usage is computationally inexpensive once the networks are trained. These characteristics make a deep learning-based approach an excellent candidate for the application in IceCube. A reconstruction …