Erratum: Unitary expansion of the time evolution operator [Phys. Rev. A82, 042110 (2010)]

Abstract

Erratum: Unitary expansion of the time evolution operator [Phys. Rev. A 82, 042110 (2010)]

Interaction-free evolution in the presence of time-dependent Hamiltonians

“…In general Eq. (1) is untractable and, except for some lucky cases [14][15][16], it requires special assumptions, such as for example the adiabatic one [17], or suitable approximations, like in the perturbative treatment [18,19]. Therefore, even the partial resolution of a class of timedependent problems in the presence of time-dependent Hamiltonians is of interest itself.…”

New BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras

“…Alternatively, these relations can also be deduced by using the unitary expansion method of Ref. [23].…”

Resonant Transitions Due to Changing Boundaries

“…Once the problem of one particle in a 2D box with moving walls is transformed into the problem of a particle in a static box, we get the Hamiltonian in Eq. (6).…”

“…In fact, exact resolutions are rare and limited to specific classes of problems [1][2][3][4]. On the contrary, in most of the cases one can solve the dynamical problem only under special assumptions and with some approximations, as it happens in the presence of weak interactions which legitimate the use of a perturbative approach [5][6][7], or when specific commutation relations are satisfied [8][9][10]. An important class of time-dependent hamiltonians is that of slowly changing ones, since they lead to adiabatic evolutions [11], with very important applications in quantum system manipulation spanning from Landau-Zener model [12][13][14][15] and its generalizations [16][17][18][19][20] to STIRAP protocols [21][22][23][24][25][26][27] to the 'fast counterpart' of adiabatic evolutions, i.e., the shortcuts to adiabaticity [28][29][30].…”