J. C. Garrison and R. Y. Chiao
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198508861
- eISBN:
- 9780191708640
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508861.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter shows that the interaction of photons with a passive, linear device can be described by the scattering matrix of classical optics. Combining this with the paraxial approximation leads to ...
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This chapter shows that the interaction of photons with a passive, linear device can be described by the scattering matrix of classical optics. Combining this with the paraxial approximation leads to a quantum description of lenses, mirrors, beam splitters, optical isolators, Y-junctions, optical circulators, and stops. In this way, each device is described by means of scattering channels together with input and output ports. Studying quantum noise in the transmitted and reflected signals from a beam splitter or a stop leads to the idea of partition noise, which is ascribed to vacuum fluctuations entering through a classically unused port. This effect is avoided in an optical circulator by arranging for destructive interference of vacuum fluctuation waves traveling in opposite senses of circulation around a ferrite pill containing a static magnetic field.Less
This chapter shows that the interaction of photons with a passive, linear device can be described by the scattering matrix of classical optics. Combining this with the paraxial approximation leads to a quantum description of lenses, mirrors, beam splitters, optical isolators, Y-junctions, optical circulators, and stops. In this way, each device is described by means of scattering channels together with input and output ports. Studying quantum noise in the transmitted and reflected signals from a beam splitter or a stop leads to the idea of partition noise, which is ascribed to vacuum fluctuations entering through a classically unused port. This effect is avoided in an optical circulator by arranging for destructive interference of vacuum fluctuation waves traveling in opposite senses of circulation around a ferrite pill containing a static magnetic field.
ANGELO GAVEZZOTTI
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570806
- eISBN:
- 9780191718779
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570806.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Everyday objects display an almost incredible variety of properties that may be felt with animal senses and that human intellect wishes to apprehend, categorise, understand, and — possibly — predict. ...
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Everyday objects display an almost incredible variety of properties that may be felt with animal senses and that human intellect wishes to apprehend, categorise, understand, and — possibly — predict. We have gaseous bodies such as the Earth's atmosphere, liquid bodies such as a drop of water, solid bodies such as glasses or crystals, semi-solid bodies such as gels, or even such exotic states of condensation as liquid crystals. The distribution of electric charges in a molecule plays a central role in all discussions of intermolecular interactions. This chapter discusses the physical nature and computer simulations of the intermolecular potential, the representation of the molecular charge distribution and of the electric potential, full electron density, central multipoles and distributed multipoles, point charges, Coulombic potential energy, polarisation (electrostatic induction) energy, dispersion energy, Pauli (exchange) repulsion energy, total energies versus partitioned energies, intermolecular hydrogen bonding, simulation methods, and force field fitting from ab initio calculations.Less
Everyday objects display an almost incredible variety of properties that may be felt with animal senses and that human intellect wishes to apprehend, categorise, understand, and — possibly — predict. We have gaseous bodies such as the Earth's atmosphere, liquid bodies such as a drop of water, solid bodies such as glasses or crystals, semi-solid bodies such as gels, or even such exotic states of condensation as liquid crystals. The distribution of electric charges in a molecule plays a central role in all discussions of intermolecular interactions. This chapter discusses the physical nature and computer simulations of the intermolecular potential, the representation of the molecular charge distribution and of the electric potential, full electron density, central multipoles and distributed multipoles, point charges, Coulombic potential energy, polarisation (electrostatic induction) energy, dispersion energy, Pauli (exchange) repulsion energy, total energies versus partitioned energies, intermolecular hydrogen bonding, simulation methods, and force field fitting from ab initio calculations.
ANGELO GAVEZZOTTI
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570806
- eISBN:
- 9780191718779
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570806.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, ...
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Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, one is never confronted with a single water molecule, but rather with bodies composed of a very large number of molecules. Chemical systems do not tend to equilibrium by minimising their internal energy. Another driving force is provided by spontaneous randomisation of the position of molecules in space and of the distribution of energies among available energy levels. This fundamental fact is embodied in the macroscopic property called entropy. Temperature, pressure, internal energy, and entropy are the basic functions of chemical thermodynamics. This chapter discusses calorimetry and thermodynamic measurements of the molecular structure and properties of macroscopic systems, partition function and calculation of molecular energies, measurement of heat capacity and entropy, calculation of entropy for chemical systems, free energy and chemical equilibrium, and thermodynamic measurements of melting enthalpies and sublimation enthalpies.Less
Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, one is never confronted with a single water molecule, but rather with bodies composed of a very large number of molecules. Chemical systems do not tend to equilibrium by minimising their internal energy. Another driving force is provided by spontaneous randomisation of the position of molecules in space and of the distribution of energies among available energy levels. This fundamental fact is embodied in the macroscopic property called entropy. Temperature, pressure, internal energy, and entropy are the basic functions of chemical thermodynamics. This chapter discusses calorimetry and thermodynamic measurements of the molecular structure and properties of macroscopic systems, partition function and calculation of molecular energies, measurement of heat capacity and entropy, calculation of entropy for chemical systems, free energy and chemical equilibrium, and thermodynamic measurements of melting enthalpies and sublimation enthalpies.
Niels Engholm Henriksen and Flemming Yssing Hansen
- Published in print:
- 2018
- Published Online:
- November 2018
- ISBN:
- 9780198805014
- eISBN:
- 9780191843129
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805014.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode ...
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This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.Less
This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.
