quantum theory/ finite-difference methodsclassical evolution problemsquantum evolution problemssymplectic natureclassical mechanicsunitarityWe show that the symmetrically split-operator technique provides a use
The connection only at limiting value of the coin operator and the need to invoke null coordinates or the rotational invariance to recover DH could not completely resolve the connection between the the QW-DCA-DH. Resolving the difference between the DCA and QW will make QW a suitable method ...
Let us recall the principle of the Mermin and Peres11,12 operator-based proofs of quantum contextuality. Consider the configuration of two-qubit observables depicted in Fig. 1 and known as a Peres–Mermin magic square. Figure 1 The Peres–Mermin magic square: all two-qubit observables on the...
To this end, we define the operator∂j:=(pT−pj)⋅∇,j=1,…,s+1. Step 0. Let us split f in (19) into two sums, We show that λ(i;0)=0 for all (i;0)∈Is,0d, and start by studying the terms of the above sums restricted to the facet Fs,s+1. From Proposition...
We show that the symmetrically split-operator technique provides a useful method to study evolution problems in classical and quantum mechanics. It is shown that it leads to a finite-difference scheme naturally preserving the symplectic nature of the problem in classical mechanics and the unitarity ...