Quasianti-Hermitian Hamiltonians and quaternionic quantum systems

Alberto Blasi, G. Scolarici, Luigi Solombrino

Sergio Giardino

Giardino Filho, Sérgio Augusto

G. Scolarici

We characterize the subclass of quasianti-Hermitian quaternionic Hamiltonian dynamics such that their complex projections are one-parameter semigroup dynamics in the space of complex quasi-Hermitian density matrices.As an example, the complex projection of a spin-1 2 system in a constant quasianti-Hermitian quaternionic potential is considered.

Alberto Blasi, G. Scolarici, Luigi Solombrino

We characterize the quasianti-Hermitian quaternionic operators in quaternionic quantum mechanics by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum optical physical system, in the realm of quaternionic quantum mechanics, while no alternative can exist in complex quantum mechanics, and we discuss some differences between them.

G Scolarici, L Solombrino

We show that the complex projections of time-dependent η-quasianti-Hermitian quaternionic Hamiltonian dynamics are complex stochastic dynamics in the space of complex quasi-Hermitian density matrices if and only if a quasistationarity condition is fulfilled, i.e. if and only if η is an Hermitian positive time-independent complex operator. An example is also discussed.