Zeta-regularized vacuum expectation values

It has recently been shown that vacuum expectation values and Feynman path integrals can be regularized using Fourier integral operator $\zeta$-function, yet the physical meaning of these $\zeta$-regularized objects was unknown. Here we show that $\zeta$-regularized vacuum expectations appear as continuum limits using a certain discretization scheme. Furthermore, we study the rate of convergence for the discretization scheme using the example of a one-dimensional hydrogen atom in $(-\pi,\pi)$ which we evaluate classically, using the Rigetti Quantum Virtual Machine, and on the Rigetti 8Q quantum chip "Agave" device. We also provide the free radiation field as an example for the computation of $\zeta$-regularized vacuum expectation values in a gauge theory.Comment: 36 pages, 2 figures; accepted version (Journal of Mathematical Physics

Imperial Systems of Power, Colonial Forces, and the Making of Modern Southeast Asia

Why do colonial subjects choose to enlist and to court death under the command of officers who come from thousands of miles away? Under what conditions do they stay loyal? When, why and with what results do they revolt? Questions such as these can be answered only with the greatest diffculuty. In part this is because comparative work on colonial forces is rare, restricted to a few short introductions to edited volumes, whose collections of articles at first seem to invite contrast, rather than comparison. This is compounded by a second problem: the careless use of concepts. the terms colonial armies, colonialism and imperialism have been employed so loosely as to spread confusion. For this reason, we must begin by examining the terminology surrounding "colonial armies" and what we call "imperial systems of power"

Control Strategies for the Fokker-Planck Equation

Using a projection-based decoupling of the Fokker-Planck equation, control strategies that allow to speed up the convergence to the stationary distribution are investigated. By means of an operator theoretic framework for a bilinear control system, two different feedback control laws are proposed. Projected Riccati and Lyapunov equations are derived and properties of the associated solutions are given. The well-posedness of the closed loop systems is shown and local and global stabilization results, respectively, are obtained. An essential tool in the construction of the controls is the choice of appropriate control shape functions. Results for a two dimensional double well potential illustrate the theoretical findings in a numerical setup

Fitting a function to time-dependent ensemble averaged data

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.Comment: 47 pages (main text: 15 pages, supplementary: 32 pages

Weathering the storm: Children’s resilience against bullying and harassment

Resilience is a concept of growing interest in the research field, as well as bullying and quality of life. Resilience has gained rising interest over the past decade because it has capacity for systematically informed prevention and intervention (Elbau et al. 2019). This study looks at data from a former study “Trivsel I Tromsø” with children and adolescence victims to bullying and harassment (N=237) and a control group (N=735). In total (N=952). The pupils that matched the criteria, were from 9 to 16 years, who bullied and/or harassed at the cut off-point 3 or more times a month. The aim of the study was to look for any evidence of resilience within the bullied and harassed group. To assess this The Strenghts and Difficulties Questionnaire (SDQ) were used, and resilience was defined within the children or adolescence who scored in the normal range of total difficulty. Furthermore, KINDLR and the SDQ Pro-social score was used in effort to map out trends of resilience within the dataset. This is followed by regression analyses to sort out which variables had the most resistance towards the negative impacts. Main result of this study shows that 176 (74%) of the pupils were resilient towards the bullying and harassment. A moderate resiliency was considered within the borderline N=35 (14,7%), the last group N=26 (10,9%) were associated with low resilience. Compared to the control group, the most important protective factors were friends, the school environment, and emotional well-being in reducing the negative impacts displayed by the SDQ (with some reservations during overlap issues). The also study notes that physical well-being and self-esteem, and pro-social factors has effects against bullying and suggests that family has an effect in lowering the negative impacts of the bulling and harassment

Tracer particle diffusion in a system with hardcore interacting particles

In this study, inspired by the work of K. Nakazato and K. Kitahara [Prog. Theor. Phys. 64, 2261 (1980)], we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on regular Bravais lattices we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.Comment: 28 pages with appendix, 5 figure. To appear in JSTA