Effective theory

There are two fundamental chromatography theories that deal with solute retention and solute dispersion and these are the Plate Theory and the Rate Theory, respectively. It is essential to be familiar with both these theories in order to understand the chromatographic process, the function of the column, and column design. The first effective theory to be developed was the plate theory, which revealed those factors that controlled chromatographic retention and allowed the... 

Kohlrausch s theory leaves quite unexplained the fact that no thermoelectric current is set up in a homogeneous wire along which a current of heat is flowing, whilst the theory of Lord Kelvin is difficult to reconcile with the fact that thermoelectric currents cannot be set up in a circuit of liquid metals, although these show the Thomson effect. The latter seems, therefore, to be to a certain extent independent of the Peltier effect. Theories intended to escape these difficulties have been proposed by Planck (1889), and Duhem, in which the conception of the entropy of electricity is introduced. 

Needless to say, tunneling is one of the most famous quantum mechanical effects. Theory of multidimensional tunneling, however, has not yet been completed. As is well known, in chemical dynamics there are the following three kinds of problems (1) energy splitting due to tunneling in symmetric double-well potential, (2) predissociation of metastable state through... 

As the trans effect theory indicates, there should be some relationship between lability of a ligand and its role as a labilizing group in another position in a complex. In an octahedral complex reacting via a dissociative mode of activation, the transition state has five strongly bound ligands. This state will be stabilized... 

FIGURE 6.12 Traditional application of the Mills-Nixon effect theory to a-tocopherol-type henzopyranols and benzofuranols, having an anullation angle sum of (a + (3). 

In Kadanoff s [130, 131] two-dimensional block-spin model four neighbouring spins are assumed to have identical spins, either up or down, near the critical point. The block of four then acts like a single effective spin. The lattice constant of the effective new lattice is double the original lattice constant. The coherence length measured in units of the new lattice constant will hence be at half of its original measure. Repetition of this procedure allows further reduction in by factors of two, until finally one has an effective theory with = 1. At each step it is convenient to define renormalized block spins such that their magnitude is 1 instead of 4. The energy of such blocked spins is... 

Tapia, O. Solvent effect theories quantum and classical formalisms and their applications in chemistry and biochemistry, J.Math. Chem., 10 (1992), 139-181... 

Angyan, J. Common theoretical framework for quantum chemical solvent effect theories,... 

The low energy effective theory supports solitonic excitations which can be identified with the baryonic sector of the theory at non-zero chemical potential. In order to obtain classically stable configurations, it is necessary to include at least a four-derivative term (containing two temporal derivatives) in addition to the usual two-derivative term. Such a term is the Skyrme term ... 

It is also interesting to note that the explicit dependence on the quark chemical potential is communicated to the Goldstone excitations via the coefficients of the effective Lagrangian (see [31] for a review). For example is proportional to fj, in the high chemical potential limit and the low energy effective theory is a good expansion in the number of derivatives which allows to consistently incorporate in the theory the Wess-Zumino-Witten term [32] and its corrections. 

COLOR SUPERCONDUCTIVITY AND HIGH DENSITY EFFECTIVE THEORY... 

Keywords effective theory, dense QCD, color superconductivity, sign problem... 

At low temperature or energy, most degrees of freedom of quark matter are irrelevant due to Pauli blocking. Only quasi-quarks near the Fermi surface are excited. Therefore, relevant modes for quark matter are quasi-quarks near the Fermi surface and the physical properties of quark matter like the symmetry of the ground state are determined by those modes. High density effective theory (HDET) [7, 8] of QCD is an effective theory for such modes to describe the low-energy dynamics of quark matter. 

Color superconductivity and high density effective theory... 

At low energy, the typical momentum transfer by quarks near the Fermi surface is much smaller than the Fermi momentum. Therefore, similarly to the heavy quark effective theory, we may decompose the momentum of quarks near the Fermi surface as... 

In order for the effective theory to be meaningful, it should have a consistent power-counting. We find the consistent counting in HDET to be for A j = A... 

To construct the low energy effective theory of the fermionic system, we rewrite the fermion fields as... 

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