We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.

The Mixed Quantum-Classical Initial Value Representation (MQC-IVR) is a recently introduced approximate semiclassical (SC) method for the calculation of real-time quantum correlation functions. MQC-IVR employs a modified Filinov filtration (MFF) scheme to control the overall phase of the SC integrand, extending the applicability of SC methods to complex systems while retaining their ability to accurately describe quantum coherence effects. Here, we address questions regarding the effectiveness of the MFF scheme in combination with SC dynamics. Previous work showed that this filtering scheme is of limited utility in the context of semiclassical wavepacket propagation, but we find the MFF is extraordinarily powerful in the context of correlation functions. By examining trajectory phase and amplitude contributions to the real-time SC correlation function in a model system, we clearly demonstrate that the MFF serves to reduce noise by damping amplitude only in regions of highly oscillatory phase leading to a reduction in computational effort while retaining accuracy. Further, we introduce a novel and efficient MQC-IVR formulation that allows for linear scaling in computational cost with the total simulation length, a significant improvement over the more-than quadratic scaling exhibited by the original method.

We measure the direct detection effect in a small volume ͑0.15 m ϫ 1 m ϫ 3.5 nm͒ quasioptical NbN phonon cooled hot electron bolometer mixer at 1.6 THz. We find that the small signal sensitivity of the receiver is underestimated by 35% due to the direct detection effect and that the optimal operating point is shifted to higher bias voltages when using calibration loads of 300 K and 77 K. Using a 200 GHz bandpass filter at 4.2 K the direct detection effect virtually disappears. This has important implications for the calibration procedure of these receivers in real telescope systems. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1887812͔ NbN phonon cooled hot electron bolometer ͑HEB͒ mixers are currently the most sensitive heterodyne detectors at frequencies above 1.2 THz.1,2 They combine a good sensitivity ͑8-15 times the quantum limit͒, an IF bandwidth of the order of 4 -6 GHz, 3-6 and a wide RF bandwidth from 0.7 to 5.2 THz. However, for use in a space based observatory, such as Herschel, it is of vital importance that the local oscillator ͑LO͒ power requirement of the mixer is compatible with the low output power of present day THz LO sources. 7 This can be achieved by reducing the mixer volume and critical current density.5 However, the large RF bandwidth and low LO power requirement of such a mixer result in a direct detection effect, characterized by a change in the bias current of the HEB when changing the RF signal from a black body load at 300 K to one at 77 K. [8][9][10][11] As a result the measured sensitivity using a 300 K and 77 K calibration load differs significantly from the small signal sensitivity relevant for astronomical observations. In this article we describe a set of dedicated experiments to characterize the direct detection effect for a small volume quasioptical NbN phonon cooled HEB mixer.The devices are fabricated on a high purity Si wafer that is covered at MSPU, Moscow with a NbN film with T c = 9.3 K and an expected thickness of 3.5 nm. The fabrication is mostly identical to the process described in Refs. 3 and 12, however, in stead of a spiral antenna we use a twin slot antenna with a center frequency of 1.6 THz and a bandwidth of 0.9 THz. The bolometer length is 0.15 m, the width 1 m, the critical current I c =68 A at 4.2 K and the normal state resistance is 170 ⍀ at 11 K. In the experiment we use a quasi-optical coupling scheme in which the HEB mixer chip is glued to the center of an uncoated elliptical Si lens. The lens is placed in a mixerblock thermally anchored to the 4.2 K plate of a liquid Helium cryostat. We use one Zytex G104® at 77 K as infrared filter and 0.9 mm HDPE as vacuum window. The LO power required to reach the optimal pumping level of the mixer, as determined by the isothermal technique, P LO,iso = 30 nW. The real LO power need P LO , determined from the output power of a calibrated LO source and the known optics losses, has been estimated to be 2.4 times larger for similar mixers, 13 hence P LO = 70 nW. In the first experiment we measure the uncor...

Radiative association of CN is simulated using a quantum dynamical as well as a semiclassical approach. A comparison of the resulting energy-resolved cross sections reveals striking quantum effects that are due to shape resonances. These, in turn, arise because of states that are quasibound by the centrifugal barrier. The quantal rate coefficient for temperatures from 40 to 1900 K has been computed using the Breit-Wigner theory to account for the resonances. Comparison with the results obtained by Singh and Andreazza [Astrophys. J. 537, 261 (2000)] shows that the semiclassical method, which completely omits the shape resonances, is accurate to within 25% above room temperature. At lower temperatures the contribution from the shape resonances to the radiative association rate is more significant.

Radiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory at high energies. The high energy cross section is overestimated if conventional semiclassical theory is used. The modified semiclassical theory should be valid in general for radiative association transitions from an upper to a lower electronic state. We also implement a quantum dynamical optical potential method with the same type of modification. The rate coefficient is calculated using Breit-Wigner theory and the modified semiclassical formula for the resonance and direct contributions, respectively, for temperatures from 10 K to 20,000 K. A rapid decrease in the rate constant for formation of ground state SiN is observed above 2000 K which was not seen previously.