The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for description of unstable systems. One of our results concerned the initial decay rate. Generalizing the earlier results of Horwitz and Marchand (see [2] and other references contained in [1]) we proved there, that the initial decay rate of any pure state of the unstable system equals to zero, if this state is so called finite energy state. Here we shall be interested in the same problem, assuming now the state of the decaying system to be in general mixed. Such assumption seems to be reasonable: firstly, from the point of view of an experiment it is too restrictive to treat only pure states of unstable systems. In particular, mixed states are generally considered in the recent studies about the influence of measuring devices on the time evolution of the unstable system [3

We study the relationship between TsT transformations, marginal deformations of string theory on AdS3 backgrounds, and irrelevant deformations of 2d CFTs. We show that TsT transformations of NS-NS backgrounds correspond to instantaneous deformations of the worldsheet action by the antisymmetric product of two Noether currents, holographically mirroring the definition of the TT¯, JT¯, TJ¯, and JJ¯ deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ ×S^3×M^4 we obtain a general class of rotating black string solutions, including the Horne-Horowitz and the Giveon-Itzhaki-Kutasov ones as special cases, which we show are holographically dual to thermal states in single-trace TT¯-deformed CFTs. We also find a smooth solution interpolating between global AdS3 in the IR and a linear dilaton background in the UV that is interpreted as the NS-NS ground state in the dual TT¯-deformed CFT. This background suggests the existence of an upper bound on the deformation parameter above which the solution becomes complex. We find that the worldsheet spectrum, the thermodynamics of the black strings (in particular their Bekenstein-Hawking entropy), and the critical value of the deformation parameter match the corresponding quantities obtained from single-trace TT¯ deformations.

abstract

In this paper, gold ball wire bonding at low temperature using a high frequency transducer was evaluated. The substrates used were FR-4 laminates with two different gold-plated surface finishes: electrolytic and immersion gold-plated. Bonding temperatures of 120/spl deg/C, 80/spl deg/C and 40/spl deg/C were investigated with 1 mil fine pitch gold wire. Prior to wire bonding, the laminates and dice were plasma treated. The surfaces were analyzed prior to and after plasma treatment before wire bonding using XPS and AFM. Bonded areas were also analyzed using SEM. Design of experiment (DOE) techniques have been employed to optimize the bonding parameters at each temperature. The response of the DOE was evaluated by using bond shear and bond pull. The results show that bonding at low temperature is viable with the use of a high frequency transducer wire bonder.

We propose a model for scattering in a flat resonator with a thin antenna. The results are applied to rectangular microwave cavities. We compute the resonance spacing distribution and show that it agrees well with experimental data provided the antenna radius is much smaller than wavelengths of the resonance wavefunctions.