I conjecture that the nearsightedness of component electronic matter largely determines the size of a virus. These two length scales, one from physics and one from biochemistry, are in fact the same dimension which connects our quantum and everyday worlds. Learning how viruses interact with microscopic molecules and macroscopic biological cells might help us understand the quantum-to-classical transition in general cases of multiscale phenomena.
I conjecture that the nearsightedness of component electronic matter largely determines the size of a virus. These two length scales, one from physics and one from biochemistry, are in fact the same dimension which connects our quantum and everyday worlds. Learning how viruses interact with microscopic molecules and macroscopic biological cells might help us understand the quantum-to-classical transition in general cases of multiscale phenomena.
In an earlier paper, W. Kohn had qualitatively introduced the concept of "nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's "chemical bond," "transferability," and Yang's computational principle of "divide and conquer." It describes the fact that, for fixed chemical potential, local electronic properties, such as the density n(r), depend significantly on the effective external potential only at nearby points. Changes of that potential, no matter how large, beyond a distance R have limited effects on local electronic properties, which rapidly tend to zero as a function of R. In the present paper, the concept is first sharpened for representative models of uncharged fermions moving in external potentials, and then the effects of electron-electron interactions and of perturbing external charges are discussed.
When the revolutionary conceptual structure for the description of the physical world which we know as quantum mechanics was first formulated nearly 90 years ago, and its predictions tested in the laboratory, most of the experiments in question were on systems which were both very well characterized and reasonably well isolated from their environments, such as single electrons and atoms, small molecules and near-perfect crystalline solids. While from the very start most physicists have taken it for granted that the formalism of quantum mechanics, when combined with appropriate system-specific information, can “in principle” account for all phenomena occurring in the physical world, including those usually regarded as the subject-matter of biology, until quite recently the overwhelmingly majority opinion has been that in a biological context the role of quantum theory is confined to elucidating the equilibrium structures of the relevant molecules and their reaction processes, and that subtle phenomena such as superposition and entanglement, of which we can now routinely exhibit spectacular effects at the level of a few well-isolated photons or atoms, play at most a very indirect role in any phenomena of biological interest. A major reason conventionally given for this view has been that biological systems, at least working ones, are by their very nature “warm and wet” – a phrase which in the physicist's lexicon translates to “prone to massive decoherence”; it looks as though any interesting superposition, say of different energy eigenstates of one's system, would be rapidly decohered by the ever-present, and usually microscopically very complex, environment.
With the advent of nanoscience, scientists are creating nanosys- tems with ever reducing size scales. In some cases, such as quantum dots with a diameter of a few nanometres, the num- ber of atoms in these systems falls in the range of 100 to 100,000 atoms. As we approach the atomic scale, the quantum nature of the nanosystems becomes dominant. Quantum physics encom- passes those laws of physics we use to describe and predict the properties of matter at the length scales of atoms and electrons. An understanding of quantum physics is therefore important for understanding the behaviour of the nanomaterials and nanode- vices as their dimensions are reduced towards atomic sizes. The main focus of this chapter is to describe some of the basic concepts of quantum physics.
Both classical and quantum principles coexist in the mesoscopic world, something between the microscopic and the macroscopic worlds.More precisely, mesoscopic physics studies how the "coherence", which governs the wave property and especially the interference effect of matter, disappear gradually as the scale increases from the microscopic to the macroscopic scale.Another important issue in mesoscopic physics is many-body effects, which originate from the interaction among electrons.Many-body effects are a fundamental issue in all modern physics, but mesoscopic physics is particularly well adopted for their study because mesoscopic systems allow for tunability of various parameters, which is not possible in bulk systems.Further, the interplay between coherence and many-body effects leads to rich physical phe-
Quantum fluids are fluids, indeed. We have seen in the previous chapter what it means from a classical physics point of view. But quantum fluids are by definition ruled by quantum physics, as well. The goal of this chapter is to introduce some key concepts of quantum physics necessary to understand what makes a fluid a quantum one or rather what quantum property makes an ensemble of particles a quantum fluid. We are here precisely at the edge of our basic intuition of quantum physics. Indeed, one usually associates the notion of quantum object to a microscopic nature and it may thus a priori seem paradoxical to link the word quantum to a macroscopic object, such as the notion of fluid. Thinking it over a bit deeper, quantum physics is certainly present at all scales and we are confronted with quantum mechanics through the many electronic devices which have invaded our everyday life. And it actually turns out that, as we will see later on, most of these quantum devices are directly connected to the notion of quantum fluids, the case of electron fluids being certainly the most common one in such devices. Quantum physics has for sure deeply modified our everyday life. But it has also changed our perception of the world, and as we shall see in this chapter, it is precisely this new vision of the world which allows us to understand the concept of quantum fluids underlying so many physical systems.