267 research outputs found

    Excited states in Richardson pairing model: `probabilistic' approach

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    Richardson equations can be mapped on the classical electrostatic problem in two dimensions. We have recently suggested a new analytical approach to these equations in the thermodynamical limit, which is based on the `probability' of the system of charges to be in a given configuration at the effective temperature equal to the interaction constant. In the present paper, we apply this approach to excited states of the Richardson pairing model. We focus on the equally-spaced situation and address arbitrary fillings of the energy layer, where interaction acts. The `partition function' for the classical problem on the plane, which is given by Selberg-type integral, is evaluated exactly. Three regimes for the energy gap are identified, which can be treated as the dilute regime of pairs, BCS regime, and dilute regime of holes.Comment: 14 pages, 1 figur

    BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function

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    The Bogoliubov approach to superconductivity provides a strong mathematical support to the wave function ansatz proposed by Bardeen, Cooper and Schrieffer (BCS). Indeed, this ansatz --- with all pairs condensed into the same state --- corresponds to the ground state of the Bogoliubov Hamiltonian. Yet, this Hamiltonian only is part of the BCS Hamiltonian. As a result, the BCS ansatz definitely differs from the BCS Hamiltonian ground state. This can be directly shown either through a perturbative approach starting from the Bogoliubov Hamiltonian, or better by analytically solving the BCS Schr\"{o}dinger equation along Richardson-Gaudin exact procedure. Still, the BCS ansatz leads not only to the correct extensive part of the ground state energy for an arbitrary number of pairs in the energy layer where the potential acts --- as recently obtained by solving Richardson-Gaudin equations analytically --- but also to a few other physical quantities such as the electron distribution, as here shown. The present work also considers arbitrary filling of the potential layer and evidences the existence of a super dilute and a super dense regime of pairs, with a gap \emph{different} from the usual gap. These regimes constitute the lower and upper limits of density-induced BEC-BCS cross-over in Cooper pair systems.Comment: 15 pages, no figure

    From one to NN Cooper pairs, step by step

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    We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer where a small attraction acts. To do it, we solve Richardson's equations analytically in the dilute limit of pairs on the one-Cooper pair scale. We find, through only keeping the first order term in this expansion, that the NN correlated pair energy reads as the energy of NN isolated pairs within a N(N−1)N(N-1) correction induced by the Pauli exclusion principle which tends to decrease the average pair binding energy when the pair number increases. Quite remarkably, extension of this first-order result to the dense regime gives the BCS condensation energy exactly. This leads us to suggest a different understanding of the BCS condensation energy with a pair number equal to the number of pairs feeling the potential and an average pair binding energy reduced by Pauli blocking to half the single Cooper pair energy - instead of the more standard but far larger superconducting gap.Comment: 14 pages, 2 figure

    Effect of thermal fluctuations on spin degrees of freedom in spinor Bose-Einstein condensates

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    We consider the effect of thermal fluctuations on rotating spinor F=1 condensates in axially-symmetric vortex phases, when all the three hyperfine states are populated. We show that the relative phase among different components of the order parameter can fluctuate strongly due to the weakness of the interaction in the spin channel. These fluctuations can be significant even at low temperatures. Fluctuations of relative phase lead to significant fluctuations of the local transverse magnetization of the condensate. We demonstrate that these fluctuations are much more pronounced for the antiferromagnetic state than for the ferromagnetic one.Comment: 5 pages, 2 figures; final version, accepted for publication in Phys. Rev.

    Automatic Test Framework Anomaly Detection in Home Routers

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    In a modern world most people have a home network and multiple devices behind it. These devices include simple IoT, that require external protection not to join a botnet. This protection can be granted by a security router with a feature of determining the usual network traffic of a device and alerting its unusual behaviour. This work is dedicated to creating a testbed to verify such router's work. The test bed includes tools to capture IoT traffic, edit and replay it. Created tool supports UDP, TCP, partially ICMP and is extendable to other protocols. UDP and TCP protocols are replayed using OS sockets at transport network layer. The methods described have proved to work on a real setup
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