Quantum fluctuation

J. Troe Prof. Schinke, in your HCO results, when you compare the fluctuating quantum results with RRKM results, you observe that the RRKM curve is above the average quantum data. Can the reason be that you use an inadequate p( ) for the continuum energy range ... 

The index k(n) recalls that the nuclear fluctuation quantum states in eq.(l 1) are determined by the electronic quantum state via potential energy Een(7 )- Once the electronic problem is fully solved, via a complete set ofeq.(5), it is not difficult to see that pTif nk) multiplied by the box-normalized wave solutions (see p. 428, ref. [17] 2nd ed.) are eigenfunctions ofthehamiltonian H0and, for stationary global momentum solutions, the molecular hamiltonian is also diagonalized thereby solving eq. (2). 

Thus, the physical mechanism of intermolecular bonds that involves the van der Waals attraction is an interaction between electric dipoles of the molecules. Because of the fluctuating quantum mechanical behavior of the electrons in a molecule, all molecules have a fluctuating dipole moment, even though for many of them symmetry consideration requires that it fluctuates about an average value of zero. At a time when a molecule has a certain instantaneous dipole moment, its electric field will induce the dipole moment as a result of the charge redistribution in a nearby molecule. 

It can be observed from the Figure 1 that the sensitivity of I.I. system is quite low at lower thicknesses and improves as the thicknesses increase. Further the sensitivity is low in case of as observed images compared to processed images. This can be attributed to the quantum fluctuations in the number of photons received and also to the electronic and screen noise. Integration of the images reduces this noise by a factor of N where N is the number of frames. Another observation of interest from the experiment was that if the orientation of the wires was horizontal there was a decrease in the observed sensitivity. It can be observed from the contrast response curves that the response for defect detection is better in magnified modes compared to normal mode of the II tube. Further, it can be observed that the vertical resolution is better compared to horizontal which is in line with prediction by the sensitivity curves. 

It was found that that in the case of soft beta and X-ray radiation the IPs behave as an ideal gas counter with the 100% absorption efficiency if they are exposed in the middle of exposure range ( 10 to 10 photons/ pixel area) and that the relative uncertainty in measured intensity is determined primarily by the quantum fluctuations of the incident radiation (1). The thermal neutron absorption efficiency of the present available Gd doped IP-Neutron Detectors (IP-NDs) was found to be 53% and 69%, depending on the thicknes of the doped phosphor layer ( 85pm and 135 pm respectively). No substantial deviation in the IP response with the spatial variation over the surface of the IP was found, when irradiated by the homogeneous field of X-rays or neutrons and deviations were dominated by the incident radiation statistics (1). 

N is very large since the fluctuations around the average behave as 2. A quantum ideal gas with either Fenni or Bose statistics is treated in subsection A2.2.5.4. subsection A2.2.5.5. subsection A2.2.5.6 and subsection A2.2.5.7. 

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

VER occurs as a result of fluctuating forces exerted by the bath on the system at the system s oscillation frequency O [5]. Fluctuating dynamical forces are characterized by a force-force correlation function. The Fourier transfonn of this force correlation function at Q, denoted n(n), characterizes the quantum mechanical frequency-dependent friction exerted on the system by the bath [5, 8]. 

Consider an excited condensed-phase quantum oscillator Q, witli reduced mass p and nonnal coordinate q j. The batli exerts fluctuating forces on the oscillator. These fluctuating forces induce VER. The quantum mechanical Hamiltonian is [M, M]... 

The reason that non-adiabatic transitions must be included for protons is that fluctuations in the potential for the quantum degrees of freedom due to the environment (e.g. solvent) contain frequencies comparable to the transition frequencies between protonic quantum states. In such cases pure quantum states do not persist. 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

Other spectral densities correspond to memory effects in the generalized Langevin equation, which will be considered in section 5. It is the equivalence between the friction force and the influence of the oscillator bath that allows one to extend (2.21) to the quantum region there the friction coefficient rj and f t) are related by the fluctuation-dissipation theorem (FDT),... 

The analytic results for the spin-boson Hamiltonian with fluctuating tunneling matrix element (5.67) are investigated in detail by Suarez and Silbey [1991a]. Here we discuss only the situation when the qi vibration is quantum, i.e., (o P P 1. When the bath is classical, cojP, j 1, the rate... 

These quantum effects, though they do not generally affect significantly the magnitude of the resistivity, introduce new features in the low temperature transport effects [8]. So, in addition to the semiclassical ideal and residual resistivities discussed above, we must take into account the contributions due to quantum localisation and interaction effects. These localisation effects were found to confirm the 2D character of conduction in MWCNT. In the same way, experiments performed at the mesoscopic scale revealed quantum oscillations of the electrical conductance as a function of magnetic field, the so-called universal conductance fluctuations (Sec. 5.2). 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

Of the variety of quantum effects which are present at low temperatures we focus here mainly on delocalization effects due to the position-momentum uncertainty principle. Compared to purely classical systems, the quantum delocalization introduces fluctuations in addition to the thermal fluctuations. This may result in a decrease of phase transition temperatures as compared to a purely classical system under otherwise unchanged conditions. The ground state order may decrease as well. From the experimental point of view it is rather difficult to extract the amount of quantumness of the system. The delocahzation can become so pronounced that certain phases are stable in contrast to the case in classical systems. We analyze these effects in Sec. V, in particular the phase transitions in adsorbed N2, H2 and D2 layers. 

Now the problem being addressed is to quantify the effect of quantum fluctuation on the orientational ordering in this molecular system. 

The quantum generalization of the APR Hamiltonian results after supplementing this classical Hamiltonian with a non-commuting angular momentum part [Lj, p] = -ihSji which introduces quantum dispersion and thus qualitatively new effects due to additional fluctuations and tunnehng. 

The central quantity is the order parameter as a function of temperature (see Fig. 13). The phase transition temperature Tq of the classical system can be located around 38 K. At high temperatures, the quantum curve of the order parameter merges with the classical curve, whereas it starts to deviate below Tq. Qualitatively, quantum fluctuations lower the ordering and thus the quantum order parameter is always smaller than its classical counterpart. The inclusion of quantum effects results in a nearly 10% lowering of Tq (see Fig. 13). 

Furthermore, one can infer quantitatively from the data in Fig. 13 that the quantum system cannot reach the maximum herringbone ordering even at extremely low temperatures the quantum hbrations depress the saturation value by 10%. In Fig. 13, the order parameter and total energy as obtained from the full quantum simulation are compared with standard approximate theories valid for low and high temperatures. One can clearly see how the quasi classical Feynman-Hibbs curve matches the exact quantum data above 30 K. However, just below the phase transition, this second-order approximation in the quantum fluctuations fails and yields uncontrolled estimates just below the point of failure it gives classical values for the order parameter and the herringbone ordering even vanishes below... 

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