33,353 research outputs found
Quantum statistical correlations in thermal field theories: boundary effective theory
We show that the one-loop effective action at finite temperature for a scalar
field with quartic interaction has the same renormalized expression as at zero
temperature if written in terms of a certain classical field , and if
we trade free propagators at zero temperature for their finite-temperature
counterparts. The result follows if we write the partition function as an
integral over field eigenstates (boundary fields) of the density matrix element
in the functional Schr\"{o}dinger field-representation, and perform a
semiclassical expansion in two steps: first, we integrate around the
saddle-point for fixed boundary fields, which is the classical field ,
a functional of the boundary fields; then, we perform a saddle-point
integration over the boundary fields, whose correlations characterize the
thermal properties of the system. This procedure provides a
dimensionally-reduced effective theory for the thermal system. We calculate the
two-point correlation as an example.Comment: 13 pages, 1 figur
Dissipative quantum systems modeled by a two level reservoir coupling
The coupling between a quantum dynamical system and a two-level system
reservoir is analysed within the framework of the Feynman-Vernon theory. We
stress the differences between this new reservoir and the well-known bath of
oscillators and show that, in order to obtain the Langevin equation for the
system of interest in the high temperature regime, we have to choose a spectral
distribution function which is finite for .Comment: 6 pages, RevteX, preprint UNICAM
Correlations around an interface
We compute one-loop correlation functions for the fluctuations of an
interface using a field theory model. We obtain them from Feynman diagrams
drawn with a propagator which is the inverse of the Hamiltonian of a
Poschl-Teller problem. We derive an expression for the propagator in terms of
elementary functions, show that it corresponds to the usual spectral sum, and
use it to calculate quantities such as the surface tension and interface
profile in two and three spatial dimensions. The three-dimensional quantities
are rederived in a simple, unified manner, whereas those in two dimensions
extend the existing literature, and are applicable to thin films. In addition,
we compute the one-loop self-energy, which may be extracted from experiment, or
from Monte Carlo simulations. Our results may be applied in various scenarios,
which include fluctuations around topological defects in cosmology,
supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic
systems, interfaces separating Bose-Einstein condensates, and interfaces in
binary liquid mixtures.Comment: RevTeX, 13 pages, 6 figure
Challenging inequity in mathematics education by making pedagogy more visible to learners
This paper reports on initial findings from the Visible Maths Pedagogy research project, a collaboration between an academic researcher and two teacher researchers (the paper’s authors). The aim of the project was to explore the effects of making pedagogy more visible on students’ success in school mathematics. We adopted a Participatory Action Research methodology to plan and evaluate five strategies used alongside ‘progressive’ teaching approaches to make the teacher’s pedagogical rationale more visible to learners. Our findings show that students, particularly those from disadvantaged backgrounds, were initially prone to misinterpret the intentions of the teacher. However, the five strategies helped students gain a greater appreciation of the teacher’s pedagogical rationale and how to respond appropriately. We discuss the implications of these findings for enabling all students to access the benefits of progressive teaching approaches and for opening up to scrutiny what it means to be a successful learner of mathematics
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