Search results for "Mathematical Physics"
showing 10 items of 2687 documents
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
2011
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identifi…
Multiple positive normalized solutions for nonlinear Schrödinger systems
2018
We consider the existence of multiple positive solutions to the nonlinear Schr\"odinger systems sets on $H^1(\mathbb{R}^N) \times H^1(\mathbb{R}^N)$, \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1 |u_1|^{r_1-2} u_1|u_2|^{r_2}, -\Delta u_2 &= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 + \beta r_2 |u_1|^{r_1} |u_2|^{r_2 -2} u_2, \end{aligned} \right. \] under the constraint \[ \int_{\mathbb{R}^N}|u_1|^2 \, dx = a_1,\quad \int_{\mathbb{R}^N}|u_2|^2 \, dx = a_2. \] Here $a_1, a_2 >0$ are prescribed, $\mu_1, \mu_2, \beta>0$, and the frequencies $\lambda_1, \lambda_2$ are unknown and will appear as Lagrange multipliers. Two cases are studied, the first …
Pants complex, TQFT and hyperbolic geometry
2021
We present a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, as developed by Blanchet, Habegger, Masbaum and Vogel, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this …
Balance equations-based properties of the Rabi Hamiltonian
2014
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.
Quantum and classical dynamics of heavy quarks in a quark-gluon plasma
2018
We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate…
Eos: conceptual design for a demonstrator of hybrid optical detector technology
2023
Abstract Eos is a technology demonstrator, designed to explore the capabilities of hybrid event detection technology, leveraging both Cherenkov and scintillation light simultaneously. With a fiducial mass of four tons, Eos is designed to operate in a high-precision regime, with sufficient size to utilize time-of-flight information for full event reconstruction, flexibility to demonstrate a range of cutting edge technologies, and simplicity of design to facilitate potential future deployment at alternative sites. Results from Eos can inform the design of future neutrino detectors for both fundamental physics and nonproliferation applications. This paper describes the conceptual design and po…
Twenty Years of Airborne Water Vapor and Total Water Measurements of a Diode Laser Based Photoacoustic Instruments
2020
We present relevant issues collected over twenty years of development and operation of an airborne water vapour / total water detector based on photoacoustic spectroscopy. The WaSulHygro instrument possesses high selectivity, short response time, and wide dynamic range, that are key requirements against trace gas measurement systems for applications in atmospheric sciences. Besides the major properties of WaSul-Hygro we discuss our efforts to develop a robust instruments that have proved its long-term reliability over the last fifteen years operating on-board a commercial aircraft within the framework of the CARIBIC project.2
Multi-parameter analysis of the obstacle scattering problem
2022
Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
Monitoring and data quality assessment of the ATLAS liquid argon calorimeter
2014
The liquid argon calorimeter is a key component of the ATLAS detector installed at the CERN Large Hadron Collider. The primary purpose of this calorimeter is the measurement of electron and photon kinematic properties. It also provides a crucial input for measuring jets and missing transverse momentum. An advanced data monitoring procedure was designed to quickly identify issues that would affect detector performance and ensure that only the best quality data are used for physics analysis. This article presents the validation procedure developed during the 2011 and 2012 LHC data-taking periods, in which more than 98% of the proton-proton luminosity recorded by ATLAS at a centre-of-mass ener…
Exponentiating derivations of quasi∗-algebras: possible approaches and applications
2005
The problem of exponentiating derivations of quasi∗-algebras is considered in view of applying it to the determination of the time evolution of a physical system. The particular case where observables constitute a properCQ∗-algebra is analyzed.