Quantum drops

THEORY OF THE PRODUCTION AND PROPERTIES OF POLYMER NANOPARTICLES QUANTUM DROPS... 

We have previously presented results of calculations showing that polymer nanoparticles with excess electrons exhibit discrete electronic structure and chemical potential in close analog with semi-conductor quantum dots. The dynamics of the formation of polymer nanoparticles can be simulated by the use of molecular dynamics and the morphology of these particles may be predicted. The production method that is used for the creation of these polymer particles can also be used to mix polymer components into a nanoparticle when otherwise they are immiscible in the bulk Quantum drops, unlike the semiconductor quantum dots, can be generated on demand and obtained in the gas phase. In the gas phase, these new polymer nanoparticles have the capacity to be used for catalytic purposes which may involve the deUveiy of electrons with chosen chemical potential. Finally, quantum drops have unusual properties in magnetic and electric fields, which make them suitable for use in applications ranging from catalysis to quantum computation. 

Table 1. The four lowest energy levels for a quantum drop with three electrons.

Figure 2 Electron trajectories on a -lOnm quantum drop with four electrons in the case of no external field...

Figures Top view (North Pole) ofelectron trajectories on a-lOnrn quantum drop with four electrons in a235 Tesla magnetic field...

Table 3. The three lowest energy levels for a quantum drop with four electrons in a 5000 KV/m electric field compared to the field-free levels... 

Physical properties for excess electrons on polymer nanoparticles Quantum drops... 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

As the temperature drops, (5.80) starts to incorporate quantum corrections. When friction increases, T u decreases and the prefactor in (5.80) increases. This means that the reaction becomes more adiabatic. However, the rise of the prefactor is suppressed by the strong decrease in the leading exponent itself The result (5.80) may be recast in a TST-like form. If the transition were classical, the rate constant could be calculated as the average flux towards the product valley... 

These days students are presented with the four quantum number description of electrons in many-electron atoms as though these quantum numbers somehow drop out of quantum mechanics in a seamless manner. In fact, they do not and furthermore they emerged, one at a time, beginning with Bohr s use of just one quantum number and culminating with Pauli s introduction of the fourth quantum number and his associated Exclusion Principle. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

The Bohr quantization condition, with quantum number v, corresponds to choosing the lowest Riemann sheet, which requires an additional phase correction of —2ti on crossing the branch cut, which is taken along the positive -axis. Thus the phase term cj) rises to ti at = 0+ and > 0, drops abruptly to —71 on crossing the positive fe = 0 axis, and returns to zero on the negative... 

When atoms absorb a photon, an electron leaves the ground state for a more energetic orbital. When the electron drops to a lower-energy orbital, it gives out energy, often in the form of a photon. Spectroscopy is the branch of science that investigates that quantum of emitted or absorbed radiation. 

The result depends only on the principal quantum number n, so we may drop the subscript 1. A comparison with equation (6.57) shows that the total energy is equal to one-half of the average potential energy... 

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