Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

High-sensitivity charge detection using antisymmetric vibration in coupled micromechanical oscillators

Abstract: High-sensitivity charge detection using antisymmetric vibration in two coupled GaAs oscillators is demonstrated. The antisymmetric mode under in-phase simultaneous driving of the two oscillators disappears with perfect frequency tuning. The piezoelectric stress induced by a small gate-voltage modulation breaks the balance of the two oscillators, leading to the re-emergence of the antisymmetric mode. Measurement of the amplitude change enables detection of the applied voltage or, equivalently, added charges. In contrast to the frequency-shift detection using a single oscillator, our method allows a large readout up to the strongly driven nonlinear response regime, providing the high room-temperature sensitivity of 147 e/Hz0.5.

Spin recoupling and n-electron matrix elements

Abstract: For n-electron systems with well defined total spin antisymmetric states are constructed by successively coupling the spins associated with each orbital. A second quantized scheme is used and the matrix elements of these states are expressed both for spin-independent and spin-dependent interactions in terms of recoupling coefficients of SU(2). The latter are evaluated to give very simple expressions. As a particular case a simple formula for the matrix elements of generators of U(N) for two-column partitions is obtained.

Tearing mode instability in a multiple current sheet system

Abstract: The tearing mode and magnetic reconnection are studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations. Both the linear and nonlinear evolution of this process are anaylsed for laminar perturbations. The results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results (Otto and Birk, 1992). The nonlinear evolution shows a number of interesting new features and may explain some properties in corresponding studies of turbulent reconnection. For wavelengths larger than twice the current sheet separation the evolution of antisymmetric modes leads to an entire reconfiguration of the magnetic field and converts a major portion of the magnetic energy into kinetic energy. Antisymmetric modes with smaller wavelengths and symmetric modes are found to saturate. The influence of the value of the resistivity on the reconnection rate decreases in the nonlinear evolution, and the ratio of current sheet separation to wavelength seems to be of major importance. A comparion of the dynamics of periodic current sheets with the evolution of only two current sheets indicates that some of the results for the periodic system also apply to the evolution of only two interacting current sheets. The results are discussed with respect to observations of large-scale plasma and magnetic field reconfigurations in the magnetosheath and near the Earth's bow shock.

The Tensor Track V: Holographic Tensors

Abstract: We review the fast developing subject of tensor models for the NAdS$_2$/NCFT$_1$ holographic correspondence. We include a brief review of the Sachdev-Ye-Kitaev (SYK) model and then focus on the associated quantum mechanical tensor models (GW and CTKT). We examine their main features and how they compare with SYK. To end, we discuss different extensions: the large $D$ limit of matrix-tensor models, the large $N$ expansion of symmetric/antisymmetric tensors, the use of probes, the construction of a bilocal action for tensors, some attempts to extend the above models to higher dimensions and a proposal to break the tensor symmetry.