Non-classical oscillator model for persistent fluctuations in stock markets

2008 ◽  
Vol 387 (5-6) ◽  
pp. 1255-1263 ◽  
Author(s):  
C. Ye ◽  
J.P. Huang
Keyword(s):  
Stock Markets ◽  
Oscillator Model ◽  
Classical Oscillator

Dielectric Loss of Adsorbed Polar Molecules

1973 ◽  
Vol 51 (24) ◽  
pp. 4038-4047 ◽  
Author(s):  
T. McMullen
Keyword(s):  
Exact Solution ◽  
Dielectric Loss ◽  
Oscillator Model ◽  
Dielectric Susceptibility ◽  
Lattice Vibrations ◽  
Linear Coupling ◽  
Classical Oscillator ◽  
Ionic Solids ◽  
Density Of Phonon States ◽  
Diagrammatic Perturbation Theory

A theory of the dielectric susceptibility of polar gases adsorbed on ionic solids is presented. The rotational oscillator model of an adsorbed polar molecule is used, and dielectric loss is assumed to occur by phonon emission and absorption. For linear coupling of the rotational oscillator to the lattice vibrations, an exact solution is found using diagrammatic perturbation theory at finite temperature. In this model, appreciable loss is only found if the density of phonon states near the classical oscillator frequency is reasonably large, and it is suggested that this is to be expected in situations where the rotational oscillator model is valid. The method can be extended to more complex adsorbate–lattice interactions.

Electrodynamics I: Macroscopic Interaction of Light and Matter

2006 ◽  
Author(s):  
Michael E. Thomas
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Oscillator Model ◽  
Energy Structure ◽  
Coupling Mechanism ◽  
Classical Oscillator ◽  
Force Relation ◽  
Propagation Media

Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.

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