The method exploits infinitesimal unitary transformation
steps, from which renormalization-group-like flow equations are derived to produce the effective Hamiltonian.
Following this idea, Huarng and Yeh  introduced an outstanding unitary transformation
for low-complexity DOA estimation with real-valued computation.
Alhaidari [11-13] applies a unitary transformation
to Dirac equation such that the resulting second-order differential equation becomes Schroodinger-like equation so that comparison with the well-known nonrelativistic problems is transparent.
The link consists of a (constant) unitary transformation
of the [[beta].sup.[mu]] matrices and a projection onto a lower-dimensional subspace.
We have shown via a careful error analysis that it is possible to do this deflation via a structure preserving real orthogonal or unitary transformation
as well as with a Schur complement approach.
QFT can be used in novel image encryption and decryption , where the quantum bit numbers of the quantum state |x) are m, [U.sub.QFT] is a unitary operator, and QFT is a [2.sup.m]-dimensional unitary transformation
In this formulation the real part of the dielectric constant [[epsilon].sup./] will lead to an expression for the change in Curie temperature ([T.sub.c]) by the presence of electric field.We make use of unitary transformation
discussed in previous studies  which render the most significant first order dipole moment to effect the Curie temperature ([T.sub.c]) with the applied electric field.
When anyons move around each other along braided paths, the motion changes the pattern of the anyons' interactions with each other--a change physicists call a unitary transformation
. This transformation alters what will happen if two anyons collide, so by bumping anyons into each other it's possible to tell that they have moved.
Assume that U is a unitary transformation
that clones, in that U(|a0>) = |aa> for all quantum states |a>.
For example, the unitary transformation
that inverts the amplitude of each basis state is modeled as follows:
The nonrelativistic approximation can be obtained by using the well-known Foldy-Wouthuysen unitary transformation
(FWUF)  and by neglecting the spin degree of freedom the nonrelativistic Hamiltonian is given as [25, 26]
He uses a unitary transformation
which yields wave functions which do not undergo Coulomb forces.