Strong external fields

Instruments with a balanced input circuit are available for measurements where both input terminals are normally at a potential other than earth. Further problems arise due to common-mode interference arising from the presence of multiple earth loops in the circuits. In these cases the instrument may need to be isolated from the mains earth. Finally, high-frequency instruments, unless properly screened, may be subject to radiated electromagnetic interference arising from strong external fields. 

In the absence of further limit conditions which may hold in the case of the electron (see later), we can now think of an electron spin and a nuclear spin anchored at points A and B, both aligned along the external magnetic field Bo, as shown in Fig. 1.5. Since the two magnetic moments are forced to be parallel by the strong external field, the energy of the interaction between them, given by Eq. (1.1), simplifies to... 

Stable states can be found, for example, by graphical solution of the equation 1 /x(4> — 4>o) = 7(potential minima [42,65], and it can be shown immediately that OB arises only if the system is biased by a sufficiently strong external field, that is, when it is far away from thermal equilibrium. If the noise intensity is weak, the system, when placed initially in an arbitrary state, will, with an overwhelming probability, approach the nearest potential minimum and will fluctuate near this minimum. Both the fluctuations and relaxation... 

Many-electron Sturmians applied to atoms and ions in strong external fields... 

In many cases the continuum may have structures that are narrower than the bandwidth of the pulse. Such structures may be due to either the natural spectrum of the molecular Hamiltonian [327, 328] or to the interaction with the strong external field [195, 197-199, 329]. Under such circumstances we expect the SVCA approximation to break down, yielding nonmonotonic decay dynamics. 

Chaos does not only wreak havoc in otherwise orderly atomic spectra, it also provides a natural framework, indeed a common language, in which one can discuss such seemingly unrelated systems as, e.g., ballistic electrons in mesoscopic semiconductor structures, the hehum atom, and Rydberg atoms in strong external fields. All these systems have one feature in common their classical counterparts are chaotic. Chaos imprints its presence on their spectra and manifests itself in spectral features which are very similar for all these systems (universahty). 

By employing a very strong external field, a gedankexperiment may be set up whereby the natural thermal motion of the molecules is put in competition with the aligning effect of the field. This method reveals some properties of the molecular liquid state which are otherwise hidden. In order to explain the observable effects of the applied fields, it is necessary to use equations of motion more generally valid than those of Benoit. These equations may be incorporated within the general structure of reduced model theory " (RMT) and illustrate the use of RMT in the context of liquid-state molecular dynamics. (Elsewhere in this volume RMT is applied to problems in other fields of physics where consideration of stochastic processes is necessary.) In this chapter modifications to the standard methods are described which enable the detailed study of field-on molecular dynamics. 

The effect of the strong external field is to accentuate this difference— using the method first developed for achiral molecules described earlier in this review—that of aligning the molecules in the molecular dynamics cube with an externally applied torque.This may be used to simulate the effect of an electric field on an assembly of dipolar molecules using second-order... 

A Strong external field acting on a non-Markovian system tends to decouple that system from its thermal bath, thereby rendering smaller its effective damping. 

We believe that the arguments above should convince the reader that the interesting phenomenon detected by Carmeli and Nitzan is another manifestation of the decoupling effect, well understood at least since 1976 (see ref. 86). The only physical systems, the dissipative properties of which are completely independent of whether or not an external field is present, are the purely ideal Markovian ones. Non-Markovian systems in the presence of a strong external field provoking them to exhibit fast oscUlations are characterized by field-dependent dissipation properties. These decoupling effects have also been found in the field of molecular dynamics in the liquid state studied via computer simulation (see Evans, Chapter V in this volume). 

On performing in (187a) an averaging with the statistical function (100) for the perturbation (188), we obtain by equation (187) and the general expression for the mean macroscopic field Et within a dielectric sphere of permittivity placed in a strong external field E, viz. 

A much more important technique is electron spin resonance (esr), also called electron paramagnetic resonance (epr). ° The principle of esr is similar to that of nmr, except that electron spin is involved rather than nuclear spin. The two electron spin states (m = and m = are ordinarily of equal energy, but in a magnetic field the energies are different. As in NMR, a strong external field is apphed and electrons are caused to flip from the lower state to the higher by the application of an appropriate radio-frequency (rf) signal. Inasmuch as two electrons paired in one orbital must have opposite spins which cancel, an esr spectrum arises only from species that have one or more unpaired electrons (i.e., free radicals). 

As long as n and remain good quantum numbers, the independent particle model and the central field approximation both apply, and quantum chaos does not arise. We can thus identify two situations where chaos could emerge the first is a complete breakdown in the independent electron approximation (due, for example, to strong correlations) and the second is a distortion of the central field approximation (due, for example, to a strong external field). 

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