Quantum limit

Ainong the first TFIz mixers to be constructed were those based on room-temperature Schottky diodes [11]. Over the past decade, new mixers based on superconducting tunnel junctions have been developed that have effective noise levels only a few tunes the quantum limit of [12]. Flowever, certain conditions... 

The symmetry coefficient = —P d nk/dAE is usually close to j, in agreement with the Marcus formula. Turning to the quantum limit, one observes that the barrier transparency increases with increasing AE as a result of barrier lowering, as well as of a decrease of its width. Therefore, k grows faster than the Arrhenius rate constant. At 7 = 0... 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

With increasing values of P the molar volume is in progressively better agreement with the experimental values. Upon heating a phase transition takes place from the a phase to an orientationally disordered fee phase at the transition temperature where we find a jump in the molar volume (Fig. 6), the molecular energy, and in the order parameter. The transition temperature of our previous classical Monte Carlo study [290,291] is T = 42.5( 0.3) K, with increasing P, T is shifted to smaller values, and in the quantum limit we obtain = 38( 0.5) K, which represents a reduction of about 11% with respect to the classical value. 

Iik82] Likharev, K.K., Classical and quantum limitations on energy consumption in computation, Jnt. Jour. Thoo. Phys. 21 (1982) 311. 

Finally, although heterodyne receiver is basically an amplitude-phase detector, its detectivity as a power receiver is similar to a quantum limited detector ... 

The advantages of this type of detector are that even a noisy photodiode can easily be turned into a quantum limited detector and that the spectrum of the source can be analyzed precisely. 

The beating of a faint source with a high power coherent source is a well known process to detect its phase and amplitude. The same detection equipment allows the evaluation of the power of the source with theoretical limits similar to a noiseless photon counter. Such detection apparatus are limited by the bandwidth of the electronic component as this bandwidth is rapidly increasing, this may be a competitive solution for quantum limited detection in the far infra red. The phase of a thermal source is an useless information ... 

As is obvious from the table, Tc is almost doubled upon deuteration. These isotope effects are one of the largest observed in any solid state system. The question arises about isotope effects in non-hydrogen-bonded ferro- and antiferroelectrics. As already mentioned in the Introduction, within a mean-field scheme and in a purely ionic model it was predicted that these systems should not exhibit any isotope effect in the classical limit, which has been verified experimentally. Correspondingly, there was not much effort to look for these effects here. However, using a nonlinear shell-model representation it was predicted that in the quantum limit an isotope effect should... 

Interestingly, for the lower temperature case of 3 =8, the CMD method is in much better agreement with the exact result. In contrast, the classical result does not show any low temperature coherent behavior. The more accurate low temperature CMD result also suggests that CMD should not be labeled a quasiclassical method because the results actually improve in the more quantum limit for this system. The improvement of these results over the higher temperature case can be understood through an examination of the effective centroid potential. The degree of nonlinearity in the centroid potential is less at low temperature, so the correlation function dephases less. 

On the nonrelativistic quantum level, both the time-independent and time-dependent Schrodinger equations can be used to demonstrate the existence of RFR. As shown by Sakurai [68], the time-independent Schrodinger-Pauli equation can be used to demonstrate ordinary ESR and NMR in the nonrelativistic quantum limit. This method is adopted here to demonstrate RFR in nonrelativistic quantum mechanics with the time-independent Schrodinger-Pauli equation [68] ... 

To stress similarities and differences with thermal activation, we present the results in the form of Arrhenius-like plots. We plot log / in units of (G/Gq)4>o versus the dimensionless Ah/A- Thermal activation with the effective temperature given by (8) would give a straight line (dashed lines in the plot). By virtue of our approach, the rates should exceed the quantum limit logJA (G/G(.i)4>()- This means that the rates should saturate at this value provided If —> 0. For each choice of S(x) we plot two curves... 

The rate constant for hydrogen atom transfer (conversion II into III) spans six orders of magnitude in the range 290-80 K. The quantum limit of the rate constant and crossover temperature are 5xl0 3s 1 and 100 K, respectively. The ratio kH/ku increases from 10 to 5 x 103 as the temperature falls from 290 to 100 K. It is the H atom in position a that is transferred, since the substitution of deuterium atom at position b (R = H) does not change the rate constant. 

Note that the quantum limit on coherent receivers is 0.5hv/k or 0.024 K/GHz (Wright, 1999). This corresponds to 0.5 photons per mode. The 0.3 K/GHz for cryogenic HEMTs is about 7 photons/mode. At 72 GHz the CMB has only n = 0.4 photons per mode, where n = (exp[hv/kT] — l)-1 is the mean number of photons per mode. Thus a background-limited incoherent detector could be much more sensitive than a coherent radiometer using HEMTs. 

When first confronted with the oddities of quantum effects Bohr formulated a correspondence principle to elucidate the status of quantum mechanics relative to the conventional mechanics of macroscopic systems. To many minds this idea suggested the existence of some classical/quantum limit. Such a limit between classical and relativistic mechanics is generally defined as the point where the velocity of an object v —> c, approaches the velocity of light. By analogy, a popular definition of the quantum limit is formulated as h —> 0. However, this is nonsense. Planck s constant is not variable. 

Without this term the quantum equation becomes identical with the classical expression. The only factor which can cause Vq to vanish is the mass. Not surprisingly, massive macroscopic objects have Vq —> 0 and are predicted to behave classically whereas sub-atomic entities with appreciable quantum potential energy Vq > 0, are known to exhibit quantum behaviour. The clear implication that there is no sharply defined classical/quantum limit, but... 

In the case of angular momentum there is no conflict between the classical and quantum descriptions for an electron fluid and continuity across the classical/quantum limit presents no problem. 

Bohm s failure to give an adequate explanation to support the pilot-wave proposal does not diminish the importance of the quantum-potential concept. In all forms of quantum theory it is the appearance of Planck s constant that signals non-classical behaviour, hence the common, but physically meaningless, proposition that the classical/quantum limit appears as h —> 0. The actual limiting condition is Vq —> 0, which turns the quantum-mechanical... 

This problem relates to the question of where the so-called classical/quantum limit occurs. It has already been shown that Schrodinger s equation ... 

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