Bloch vector

To verify the theory of PIP, a computer program using C language was developed. It can be used to directly calculate the excitation profiles by PIPs or any other RF pulses. The calculation is based on the Bloch vector model for a non-interacting spin-1/2 system, where the spin-lattice relaxation during the pulse is neglected. The basic idea of the program is discussed as follows. 

If at the Fermi level, the only surface Bloch wave of the material is a sinusoidal function with Bloch vector q. 

APPENDIX B BLOCH VECTOR ANALOG OF STOKES VECTOR... 

The definition of the Stokes vector in terms of bilinear products of field amplitudes is analogous to the definition of the two-state Bloch vector r = [u, v, iv] from products of probability amplitudes. The conventional numbering of the two vectors differs the connection is... 

The torque equation (5.18) is the analog of the Feynman-Vernon-Helwarth torque equation for the Bloch vector [9],... 

Fig. 9 2 Bloch vector view of time evolution of b (t) and h2(t) complex coefficients of the V J (t)exp(— iE t+ b2(t) exp(—f 2t/S) 2) superposition state. Two complex coeffi-3f% jients are constrained by normalization and therefore can be represented as a point on a firee-dmiensional sphere, shown here as a function of twice the mixing angle 6 and the izimuthal angle x of Eq. (9.22). In this space the z axis corresponds to the 6t 2 — fi2 2 ation difference, the x axis to Re h />2, and the y axis to hn 6J62 - In case of two-h Qton resonance (A, — A2 = 0) and when phases of two lasers fields are the same...

The Bloch vector k which may be used to label the one-electron states is conveniently viewed as a vector in reciprocal space. A lattice vector G in... 

In addition to the Bloch vector, a complete description of the electronic states in a crystal requires a band index j, which may be defined such that... 

Formally the energy-band structure for an infinite crystal is defined to be the eigenvalues Ej(k) of the one-electron Schrodinger equation (1.4) obtained as functions of the Bloch vector k. Physically, this definition is of course not very illuminating and I shall therefore now give the simplest possible derivation of a condition for the formation of energy bands, which has a very appealing physical interpretation. 

The centre of gravity of a canonical band with i > 0 is zero at each value of the Bloch vector k, i.e. 

Figure Al.6.4. FVH diagram, showing the concept of adiabatic following. The Bloch vector, /, precesses in a narrow cone about the rotating frame torque vector, S . As the detuning. A, changes from negative to positive, the field vector, fi, becomes inverted. If the change in is adiabatic the Bloch vector follows the...

Sg = trg(ff/Og0 is the QuANTON S initial Bloch vector. The z-axis is chosen for quantization the eigenstates z) of this z-basis are pure states corresponding to... 

The PS introduces a phase difference of effect rotations about the y-axis by +90° and -90°, respectively, thereby unmixing and remixing the amplitudes for taking these paths. The total effect is equivalent to a rotation of the Bloch vector by -0g about the x-axis ... 

Entanglement with a Detector will cause sg to decrease and the linear entropy Qg to increase. The square of the Quanton s Bloch vector can thus be taken as a measure of the total information content of pg. In hght of Eqs. (2), (8), (11), and (13)-(14), Sg satisfies... 

The information content of the Quanton resides in the initial Bloch vector sg related to Vq and Vqo through Eqs. (11)-(15). The final Bloch vector given by Eqs. (29)-(31) is seen to decrease for a nontrivial detector [11] ... 

We consider here a particular model for the Detector which fulfills several purposes. A 2-state Detector, or Detecton, is the simplest possible quantal device that can probe which-way information of the Quanton. The DETECTON can then be viewed as a QUANTON itself, likewise describable by a predictability Vd and a fringe visiblity Vdq-Its initial state can also be described by a Bloch vector which can, if necessary, be... 

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