372 research outputs found

    PHIL 463.01: Aristotle

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    PHIL 211.01: Introduction to Logic - Applied Logic

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    Superconductors with Magnetic Impurities: Instantons and Sub-gap States

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    When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

    Twisted boundary states in c=1 coset conformal field theories

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    We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the diagonal modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine Lie algebra. As a check of our argument, we study the diagonal coset theory so(2n)_1 \oplus so(2n)_1/so(2n)_2, which is equivalent with the orbifold S^1/\Z_2. We construct the boundary states twisted by the automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual consistency by identifying their counterpart in the orbifold. For the triality of so(8), the twisted states of the coset theory correspond to neither the Neumann nor the Dirichlet boundary states of the orbifold and yield the conformal boundary states that preserve only the Virasoro algebra.Comment: 44 pages, 1 figure; (v2) minor change in section 2.3, references adde

    On Online Collaboration and Construction of Shared Knowledge: Assessing Mediation Capability in Computer Supported Argument Visualization Tools

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    Collaborative Computer-Supported Argument Visualization (CCSAV) has often been proposed as an alternative over more conventional, mainstream platforms for online discussion (e.g., online forums and wikis). CCSAV tools require users to contribute to the creation of a joint artifact (argument map) instead of contributing to a conversation. In this paper we assess empirically the effects of this fundamental design choice and show that the absence of conversational affordances and socially salient information in representation-centric tools is detrimental to the users' collaboration experience. We report empirical findings from a study in which subjects using different collaborative platforms (a forum, an argumentation platform, and a socially augmented argumentation tool) were asked to discuss and predict the price of a commodity. By comparing users' experience across several metrics we found evidence that the collaborative performance decreases gradually when we remove conversational interaction and other types of socially salient information. We interpret these findings through theories developed in conversational analysis (common ground theory) and communities of practice and discuss design implications. In particular, we propose balancing the trade-off between knowledge reification and participation in representation-centric tools with the provision of social feedback and functionalities supporting meaning negotiation
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