The conductance of a quantum point contact (QPC) shows several features that result from many-body electron interactions. The spin degeneracy in zero magnetic field appears to be spontaneously lifted due to the so-called 0.7 anomaly. Further, the g-factor for electrons in the QPC is enhanced, and a zero-bias peak in the conductance points to similarities with transport through a Kondo impurity. We report here how these many-body effects depend on QPC geometry. We find a clear relation between the enhanced g-factor and the subband spacing in our QPCs, and can relate this to the device geometry with electrostatic modeling of the QPC potential. We also measured the zero-field energy splitting related to the 0.7 anomaly, and studied how it evolves into a splitting that is the sum of the Zeeman effect, and a field-independent exchange contribution when applying a magnetic field. While this exchange contribution shows sample-to-sample fluctuations and no clear dependence on QPC geometry, it is for all QPCs correlated with the zero-field splitting of the 0.7 anomaly. This provides evidence that the splitting of the 0.7 anomaly is dominated by this field-independent exchange splitting. Signatures of the Kondo effect also show no regular dependence on QPC geometry, but are possibly correlated with splitting of the 0.7 anomaly.

In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh-Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic.

A general explicit coupling for mutual synchronization of two arbitrary identical continuous systems is proposed. The synchronization is proved analytically. The coupling is given for all 19 systems from Sprott's collection. For one of the systems the numerical results are shown in detail. The method could be adopted for the teaching of the topic. * Electronic address: a.i.lerescu@rug.nl † Electronic address: igrosu@umfiasi.ro

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The spin degeneracy of the lowest subband that carries one-dimensional electron transport in quantum point contacts appears to be spontaneously lifted in zero magnetic field due to a phenomenon that is known as the 0.7 anomaly. We measured this energy splitting, and studied how it evolves into a splitting that is the sum of the Zeeman effect and a field-independent exchange contribution when applying a magnetic field. While this exchange contribution shows sample-tosample fluctuations, it is for all QPCs correlated with the zero-field splitting of the 0.7 anomaly. This provides evidence that the splitting of the 0.7 anomaly is dominated by this field-independent exchange splitting.