Quantum phenomena

This section attempts a brief review of several areas of research on the significance of phases, mainly for quantum phenomena in molecular systems. Evidently, due to limitation of space, one cannot do justice to the breadth of the subject and numerous important works will go unmentioned. It is hoped that the several cited papers (some of which have been chosen from quite recent publications) will lead the reader to other, related and earlier, publications. It is essential to state at the outset that the overall phase of the wave function is arbitrary and only the relative phases of its components are observable in any meaningful sense. Throughout, we concentrate on the relative phases of the components. (In a coordinate representation of the state function, the phases of the components are none other than the coordinate-dependent parts of the phase, so it is also true that this part is susceptible to measurement. Similar statements can be made in momentum, energy, etc., representations.)... 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

Other early designs of classical reversible computers included Landauer s Bag and Pipes Model [land82a] (in which pipes are used as classical mechanical conduits of information carried by balls). Brownian motion reversible computers ([benn88], [keyesTO]) and Likharev s model based on the Josephson junction [lik82]. One crucial drawback to these models (aside from their impracticality), however, is that they are all decidedly macroscopic. If we are to probe the microscopic limits of computation, we must inevitably deal with quantum phenomena and look for a quantum mechanical reversible computer. 

I, Introduction to quantum phenomena. This section takes the students into the realm of atoms and molecules and uses mathematical modeling and computer simulation, animations and visualization to give them experience in the phenomena that must be described by QM and cannot be described by NM. The simulations could cover the following processes among others ... 

IX. SINGLE-ELECTRON AND QUANTUM PHENOMENA IN ULTRASMALL PARTICLES... 

Quantum theory was developed during the first half of the twentieth century through the efforts of many scientists. In 1926, E. Schrbdinger inteijected wave mechanics into the array of ideas, equations, explanations, and theories that were prevalent at the time to explain the growing accumulation of observations of quantum phenomena. His theory introduced the wave function and the differential wave equation that it obeys. Schrodinger s wave mechanics is now the backbone of our current conceptional understanding and our mathematical procedures for the study of quantum phenomena. 

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, Chemistry — whither the future of controlling quantum phenomena Science 288, 824 (2000). 

V. P. Parkhutik, in Proceedings of the International Conference Telavi- 4 Electrodynamics and Quantum Phenomena at Interfaces, Tbilisi, Mecniereba, 1984, p. 385. 

The second goal of this section is to point out that quantum phenomena in diffusion can have other experimentally observable consequences even more interesting than large isotope effects. One such, that has frequently been noted, is apparent in the curves of Fig. 7 the Arrhenius slope decreases at low temperatures, because the hoppping can be dominated at... 

Macroscopic descriptions of matter and radiation are adequate without taking the discontinuous nature of matter and/or radiation into account. However, when dealing with particles approaching the size of elementary quanta, the quantum effects become increasingly important and must be taken into account explicitly in the mechanical description of these particles. Unlike relativistic mechanics, quantum mechanics cannot be used to describe macroscopic events. There is a fundamental difference between classical and non-classical, or quantum, phenomena and the two systems are complimentary rather than alternatives. 

Experimental chemists are rarely concerned with quantum effects and it s not unusual to find them ignoring this fundamental theory altogether. Even when an effort is made to explore the topic more deeply traditional quantum phenomena like black-body radiation, Compton scattering and even the photoelectric effect may appear to be of somewhat limited importance. Experimentalists who rely on spectroscopic measurements get by with interpretations based on a few simple semi-classical rules, and without ever appreciating the deep significance of quantum theory. Maybe there is a problem with the rigorous mathematical formulation of quantum theory and too little emphasis on quantum effects routinely encountered in chemistry. 

The natural enabling theories behind chemistry have been left dormant for so long that they are no longer recognized as part of the discipline. It is rarely appreciated that the theories of relativity, quantum phenomena and... 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

At the Faraday meeting, Langmuir had emphasized the necessity for chemists to explain phenomena in terms of quantum relationships, insisting "A molecule cannot dissociate by a continuous process.. . . We ought to consider these phenomena frankly as quantum phenomena." For Langmuir, it made no sense to talk of a series of frequencies "It is very difficult to get a physical conception of a mechanism which involves the product of several intensities."93 To this, Perrin replied that he meant that the reaction takes place in "steps" in response to different radiation frequencies. 94 Langmuir remained unconvinced in 1929, when he wrote in an article, "Modern Concepts in Physics and Their Relation to Chemistry,"... 

From that time on, many causal theories were developed. In this work, we shall only refer to the causal theory proposed by de Broglie [2] and known as the double-solution theory. This theory, as well as Bohm s theory, are the most developed of all causal theories they are both able to explain and predict, practically all quantum phenomena. 

Fig 2. The components forming a closed loop apparatus for control quantum phenomena. Using a new sample upon each cycle of the loop sidesteps the issue of the observation process disturbing the system in an unknown way. The key to success of such control experiments lies in the ability to traverse the loop under very high duty cycle to rapidly home in on the target physical objective. 

This chapter has emphasized the special and central role that feedback plays in virtually all aspects of control over molecular quantum phenomena. In terms of applications, the manipulation of chemical reactions still stands as a prime historical objective. However, other rich applications abound. For example, the growing interest in the field of quantum computing is a potentially exciting area [14], and any practical realization of quantum computers will surely entail control over quantum phenomena. Other unforeseen applications may also lie ahead. 

Let us follow Ya.B. s role in solving the two questions above. Evaporation of black holes is meaningful only for very small black holes whose masses are very small compared to stellar masses. The immediate significance of the possibility of black minihole formation for cosmology has already been noted. Here we note only that without the concept of a small black hole, there can be no question of quantum phenomena in its vicinity or, in particular, of its evaporation. 

As is well known, de Broglie abandoned his attempts at a realistic account of quantum phenomena for many years until David Bohm s discovery of a solution of Schrodinger s equation that lends itself to an interpretation involving a physical particle traveling under the influence of a so-called quantum potential. 

Consider the one dimensional TISE in Eq. (24), where we allow x to vary between -L and L, i.e., in the interaction region only. In order to solve this equation, we must supplement it with some boundary conditions. Although motivated from different quantum phenomena, Siegert [30] was the first to introduce the idea of solving the TISE with outgoing BCs, also known as Siegert boundary conditions or radiation boundary conditions. In one dimension, these outgoing BCs read... 

The rate coefficient of a reactive process is a transport coefficient of interest in chemical physics. It has been shown from linear response theory that this coefficient can be obtained from the reactive flux correlation function of the system of interest. This quantity has been computed extensively in the literature for systems such as proton and electron transfer in solvents as well as clusters [29,32,33,56,71-76], where the use of the QCL formalism has allowed one to consider quantum phenomena such as the kinetic isotope effect in proton transfer [31], Here, we will consider the problem of formulating an expression for a reactive rate coefficient in the framework of the QCL theory. Results from a model calculation will be presented including a comparison to the approximate methods described in Sec. 4. 

We have presented some of the most recent developments in the computation and modeling of quantum phenomena in condensed phased systems in terms of the quantum-classical Liouville equation. In this approach we consider situations where the dynamics of the environment can be treated as if it were almost classical. This description introduces certain non-classical features into the dynamics, such as classical evolution on the mean of two adiabatic surfaces. Decoherence is naturally incorporated into the description of the dynamics. Although the theory involves several levels of approximation, QCL dynamics performs extremely well when compared to exact quantum calculations for some important benchmark tests such as the spin-boson system. Consequently, QCL dynamics is an accurate theory to explore the dynamics of many quantum condensed phase systems. 

---