Here, we investigate the connection between the spectral properties of the quantum-mechanical scattering matrix and its semiclassical equivalent based on the semiclassical zeta-function of Gutzwiller and Voros. Our quantum-mechanical calculation is well-defined at every step, as the on-shell T-matrix ...
40 (a). In general, the transmission (or scattering-matrix elements) will exhibit characteristically enhanced fluctuations in relativistic than in nonrelativistic quantum mechanics. Sign in to download hi-res image Fig. 40. Quantum pointer states as a cause of various transmission resonances. Quantum...
The phase matrix, and in particular its large impact parameter expression, plays an important role in extracting physical observ- ables, as we review in the following. In order to simplify the notation we restrict hereafter to the case of m1 = m3 and m2 = m4. In this case, initial and ...
Should the charge densities in the two frameworks be the same, we expect the S-matrix elements to agree. In what follows, we show that this is indeed true. In the quantum-mechanics case, the v-component of the current density, in a given partial, can be directly read off from eq. (...
That is, the determinant of the scattering matrix is unity. In analogy with the spectral problem for the KdV equation, (which is the Schro¨dinger equation from quantum mechanics) [36], one can introduce a reflection coefficient, R(k, σ) = b(k, σ)/a(k, σ). (2.19) The matrix ...
As a result, the solutions often have a spectrum that can be identified with a Hilbert space, and scattering is described by a certain map, the S matrix, on Hilbert spaces. Spaces with a discrete spectrum correspond to bound states in quantum mechanics, while a continuous spectrum is ...
Namely, it was shown in [34] that, for any off-shell amplitude one can construct its gauge invariant extension, using matrix elements which involve straight infinite Wilson lines. As it turns out, those Wilson lines also encode certain recursion which turns out to be identical to the ...
In the time-dependent formulation, the key quantity describing the result of the collision is not the transition matrix, as in SST, but rather the collision-complex momentum-space wave function. We begin by showing that the generalization of a result known as the “imaging theorem” (IT) ...
But what is the “unperturbed” wave function of the NΔ, which has yet to be computed to get this matrix element? This is a problem in old perturbation calculations such as Ref. [44], which can reproduce the total cross section of pp→dπ+ well by straightforward substitution of the ...
It is easy to verify that the determinant of this matrix is equal to the squared norm of the associated 4-vector: detp=pμpμ=p2 (4) Now, in order to describe the scattering of n-gluons we need to specify n momentum vectors: {pμ1,pμ2,…,pμn}. Since gluons are massless,...