Frohlich field

External electric field vector (absolute value), Frohlich field... 

TABLE 1. Conversion Factors (g, gj) for Spherical Molecules, Relating Internal Field (Ei t), Directing Field (E ir), and Frohlich Field (Ep = E ir) to the (measured) Maxwell Field (E)"... 

The actual field working as the directing field is the Frohlich field which is given by... 

The imaginary part of the dielectric function of SiC at its Frohlich frequency in the infrared (about 932 cm- ) is close to that of aluminum at 8.8 eV. So Fig. 2Aa also shows the field lines of the Poynting vector around a small SiC sphere illuminated by light of frequency 932 cm-1. At nearby frequencies, 900... 

Two - particle energy correction correction to electron - electron correlation energy due to the phonon field. This non-adiabatic term represents full attractive contribution, and can be compared to the reduced form of Frohlich effective Hamiltonian which maximizes attractive contribution of electron - electron interaction and that can be either attractive or repulsive (interaction term of the BCS theory). For superconducting state transition at the non-adiabatic conditions, the two-particle correction is unimportant - see [2],... 

However, beyond this overt similarity, there are differences. For example, Covalon by the nature of covalency would have to operate under a much more stringent correlation than that existing in the Frohlich s model between one paired n-electron and all other such pairs along the chain. This is a natural consequence of distortion in the alternating single double bonds. This treatment also differs from that of self-consistent field treatment [19] of a linear chain and that of Little [20] in our inclusion of bond vibration. Covalon also differs from polaron treatments [21] in the consideration of the movement of spin-paired correlated electrons in a covalent bond, instead of movement of spin-uncorrelated electrons in the zeroth order. 

Sauer FA (1983) Forces on suspended particles in the electromagnetic field. In Frohlich H, Kremer F (eds) Coherent Excitations in Biological Systems. Springer, Berlin Heidelberg New York, p 134... 

Next, use is made of the simple hypothesis that all the positions of the molecules and segments are equally probable, and, following tradition, we shall formulate an expression for the internal field as a field within a spherical cavity (Vleck 1932 Frohlich 1958)... 

One can see that, to a first approximation, as it is well known (Vleck 1932 Frohlich 1958), allowance for the internal field by the Lorentz procedure is equivalent to multiplication by the factor... 

Figure 7. Formal representation of the interaction of an external EM field with the dissipative subsystem in the Frohlich vibrational model (n is the nonlinear coupling parameter (Equation 17) the other quantities have the same meaning as...

On the basis of Frohlich s suggestions and the properties of biological systems (vid. models 2, 3) one may take into account the following possible interactions of an electromagnetic field with biological systems (16, 17) ... 

Vol. 1542 J.Frohlich, Th.Kerler, Quantum Groups, Quantum Categories and Quantum Field Theory. VII, 431 pages. 1993. 

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

Frohlich (1947) based his calculations on the hypothesis of the energy-level scheme shown in Fig. 6.1, where conduction electrons are derived from impurity levels lying deep (V = 1 eV or more) in the forbidden zone. There is also a set of shallow traps spread below the conduction-band edge (F> AF> kT). In outline, the theory of breakdown is then as follows. In an applied electric field E, energy is transferred directly to the conduction electrons (charge e, mass m) at a rate A = jE, where j is the current density. If we suppose that each electron is accelerated in the field direction for an average time 2r between collisions at which its energy is completely randomised, then the mean drift velocity of the conduction electrons in the field direction... 

Fig. 6.2 Energy-transfer curves for increasing applied fields, showing the onset of electron temperature runaway. After Frohlich (1947), by courtesy of the Royal Society.

However, the most recent discussions favour these high values of g although values of the order of 20% lower had ori nally been favoured. This is because the Frohlich equation [equation (1)] differs from the earlier version of Kirkwood, and treats the inner field in a more nearly correct manner. It is no longer necessary to make a calculation of the HjO dipole moment in its surroundings in the liquid, as had been necessary in the application of the Kirkwood equation. The dipole moment of the free molecule, /i = 1.84D, is used in equation (1), together with = 1.80 at 293 K. This leads to a value of = 2.82, which is sufficiently close to that calculated from the computer dynamics model to warrant optimism for future calculations. The exact choice of will continue to present difficulties until the far-i.r. data are complete over a wide range of temperature. 

Reversible pole. There is an interesting additional asymmetry in a system first discussed by Frohlich. We consider a linear molecule constrained by strong local forces due to its neighbours, which in the absence of an external field permit it to oscillate with frequency v about two oppositely oriented equilibrium positions, making comparatively infrequent jumps from one equilibrium attitude to the other. 

There are two views about the fate of the secondary electron. Samuel and Magee assume that the electron does not leave the field of the parent ion, and that it eventually forms a hydrogen atom by charge-neutralization with HaO . Platzmann and Frohlich - and Baxendale and Hughes, on the other hand, favor the idea that the hydrogen atom is created at a considerable distance from the parent ion, mainly by subexcitation electrons. These electrons come principally from the primary ionization of wa-... 

However, recalculating the value of y using the method described in the paper for the field factors, gives the value in brackets. The unbracketed value, for the overall microscopic nonlinearity, converts to 2859 au. In the case of associating liquids the authors argue that equation (7) can be used in modified form with the inclusion of a factor, g, which they deduce from the Kirkwood-Frohlich modification of the Onsager theory,... 

Anomalous rotational diffusion in a potential may be treated by using the fractional equivalent of the diffusion equation in a potential [7], This diffusion equation allows one to include explicitly in Frohlich s model as generalized to fractional dynamics (i) the influence of the dissipative coupling to the heat bath on the Arrhenius (overbarrier) process and (ii) the influence of the fast (high-frequency) intrawell relaxation modes on the relaxation process. The fractional translational diffusion in a potential is discussed in detail in Refs. 7 and 31. Here, just as the fractional translational diffusion treated in Refs. 7 and 31, we consider fractional rotational subdiffusion (0rotation about fixed axis in a potential Vo(< >)- We suppose that a uniform field Fi (having been applied to the assembly of dipoles at a time t = oo so that equilibrium conditions prevail by the time t = 0) is switched off at t = 0. In addition, we suppose that the field is weak (i.e., pFj linear response condition). 

If the nanocrystal permittivity is greater than the host permittivity, snc > Shost, the screening factor S describes depression of the decay due to screening of the radiation field inside the nanocrystal. Frohlich was the first to note that for a metal nanocrystal with the complex frequency-dependent dielectric function... 

Further developments in the theory of the structure of polar liquids included estimates of the correlation of a given dipole to its neighbors. Important contributions were made in this direction by Kirkwood [22] and Frohlich [23]. In Kirkwood s model, the field Ej is calculated by considering all possible orientations of surrounding dipoles in a spherical cavity for a fixed orientation of the central dipole. By averaging over these orientations, Kirkwood obtained an improved estimate of the polarization of the medium. For the case of non-polarizable dipoles the result is... 

The one-dimensional Frohlich model is investigated for kgT S0 Eg with the mean field Peierls gap at T = 0. Treating the ions classically... 

It was proposed to picture TQ in terms of a Peierls-Frohlich condensation of the conduction electron with a high mean field temperature /3o/, with electronic properties dominated by CDW fluctuations in the domain Tp T Tpm ... 

J. Frohlich, in Applications of Field Theory to Statistical Mechanics, L. Garrido, Ed., Lecture Notes in Physics 216, Springer-Verlag, Berlin, 1985. The Statistical Mechanics of Surfaces. 

Here, p and v denote the magnitude of molecular dipole and the number density of those dipoles, respectively is the Boltzmann constant and T is the absolute temperature, f is a correction factor for a difference between the applied and internal electric fields (f = (Sq + 2) /9 in the Onsager form for nonpolar low-M molecules), and g is the Kirkwood-Frohlich factor that represents the magnitude of the motional correlation of the dipoles (i.e., of the dipole-carrying molecules). 

H. Frohlich, Collective Behaviour of Non-Linearly Coupled Oscillating Fields, J. Collect. Phenom. 1, 101-109 (1973). 

ABSTRACT We present a dynamical scheme for biological systems. We use methods and techniques of quantum field theory since our analysis is at a microscopic molecular level. Davydov solitons on biomolecular chains and coherent electric dipole waves are described as collective dynamical modes. Electric polarization waves predicted by Frohlich are identified with the Goldstone massless modes of the theory with spontaneous breakdown of the dipole-rotational symmetry. Self-organization, dissipativity, and stability of biological systems appear as observable manifestations of the microscopic quantum dynamics. 

H. Pohl, Natural Oscillating Fields of Cells, in Coherent Excitations in Biological Systems (H. Frohlich and F. Kremer, eds.). Springer, Berhn (1983), pp. 199-210. 

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