Magnetic physical quantities

The physical quantities essential to understand the magnetic properties of materials are briefly described in the following paragraphs. 

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The long range of the dipole-dipole interaction leads to a sample shape dependence of the physical quantities dependent on an external magnetic field [32,33]. In the expressions obtained for the susceptibility, this sample shape dependence is home by the slowly convergent lattice sums 5, and If we consider sufficiently isotropic lattices, in the sense of fulfilhng =... 

In an actual experiment, two different physical quantities connected with electric (or magnetic) dipole transitions are accessible via optical studies, on the one hand the intensities of the... 

Statistical Perturbation Calculus.—Statistical Mean Value. Let Q denote some physical quantity (electric polarization, magnetic polarization, exs,t%y), in general a function of the continuously varying canonic variables F (generalized momeita, generalized co-orclassical statistical mechanics, the mean value of Q is defined as ... 

The interaction between the orbital magnetic moment of the electrons and the nuclear moment can also be separated into an isotropic part (the chemical shift) and a traceless symmetric part (the shift anisotropy). The equation for the shift tensor contains two terms, usually called the dia- and paramagnetic contribution, but only the sum of the two corresponds to a physical quantity. Actually, the theory (76) is concerned with the shielding important difference between the two... 

The second-order expansion given in eqn (6.96) recovers all of the physical quantities needed to describe a quantum system and determine its properties the charge density p and its gradient vector field Vp define atoms and determine many of their properties in a stationary state the current density determines the system s magnetic properties and the change in p in a time-dependent system and, finally, the stress tensor determines the local and average mechanical properties of the system. Thus, one does not need all the... 

The study of chemical shifts in NMR provides an example of the sort of physical quantities to which one may refer. As is well known, the total magnetic field to which a nucleus of a molecule is subject is the sum of the external field ext and of the induced field created by the electrons surrounding the nucleus under study. The latter field is proportional to the external field and of opposite sign. The effective fidd thus acting on the nucleus is ... 

The properties of Eqs. (1.62) and (1.67) can be examined from a different viewpoint. We already understand that the electromagnetic potentials introduced, A and , lead to the physical quantities, E and B, but in practice we measure the electric field, E, or the magnetic flux density, B. That is to say, there exist innumerable pairs of functions, A and differential operations. Hence, it is very difficult to choose a physically-reasonable pair of A and 0 among all the possible pairs. For example, A and can be transformed to A and , respectively, as in Eq. (1.68) by using an arbitrary scalar function, ip(x,y, t). 

The interaction bet veen electromagnetic vaves and matter is quantified by the two complex physical quantities - the dielectric permittivity, s, and the magnetic susceptibility, fi. The electric components of electromagnetic waves can induce currents of free charges (electric conduction that can be of electronic or ionic origin). 

Under the condition that there is a nontrivial MAB effect, let us ask what is its physical nature in relation to the standard AB effect Let us first address the issue of locality. As already indicated, the standard AB effect, which may occur when a charged particle encircles a line of magnetic flux, is nonlocal as it fulfills the criteria (Nl) and (N2) the effect arises although the particle experiences no physical field and no exchange of physical quantity takes place along the particle s path. Could the same be said about the MAB effect One way to address this question is to note that since the electronic Born-Oppenheimer states are eigenstates of it may be tempting to... 

Recently the question of the number of basic units necessary to describe any physical system has been revisited and reviewed [26], In the Gaussian system, three basic dimensions are still necessary and sufficient to express the dimension of any physical quantity. These correspond to space (L), time (T), and matter (M). The number of units do not depend on the number and the nature of fundamental interactions in world. For example the basic units would be consistent with a world without gravity. Even electric and magnetic phenomena can be expressed based on space, time, and matter. In 1870, Stoney, associated another meaning to the fundamental units ... 

The order that is represented by a tensorial term in the distribution function is reflected in its influence on the macroscopic tensorial physical quantities, such as the magnetic susceptibility. 

Consider a dielectric sphere (medium 1) of radius a embedded in an external medium (medium 2). The physical quantities pertaining to the two media will be labeled with suffixes 1 and 2 respectively. Let a circularly polarized plane wave of angular frequency wq be incident on the sphere along the z-axis with electric and magnetic fields given by... 

All above means that the ferroics can be regarded as a general notation for the materials, where at T < (so-called low-temperature phase) some reorientable physical quantities (order parameters) spontaneously appear. Latter order parameters can be of vector (spontaneous electric polarization, spontaneous magnetization) or tensor (second order tensor like spontaneous deformation or higher order tensors like elastic moduli and piezoelectric coefficients) nature. In low-temperature phase ferroics can usually split into domains, their switching being possible by the external fields. 

Consider a time-dependent external field h(t) (magnetic field, electric field, or velocity gradient field) applied to a system in equilibrium. In general, the field perturbs the system, and changes the average values of physical quantities from those in the equflibrium state. If the field is weak, the change in any physical quantity is a linear functional of the field, and is written as... 

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