Quasistationary quaternionic Hamiltonians and complex stochastic maps

G. Scolarici, L. Solombrino

Published Jan 1, 2008• 1 citation

Abstract

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. 1

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Quasistationary quaternionic Hamiltonians and complex stochastic maps

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Oct 28, 20163 citations

Quasistationary quaternionic Hamiltonians and complex stochastic maps

G. Scolarici, L. Solombrino

Published Jan 1, 2008• 1 citation

OpenAlex

Abstract

Related papers

Quasistationary quaternionic Hamiltonians and complex stochastic maps

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.

arXiv:0711.1244Journal of Physics A Mathematical and TheoreticalJun 3, 20081 citation

Complex Projection of Quasianti-Hermitian Quaternionic Hamiltonian Dynamics

G. Scolarici

arXiv:0709.1198Symmetry Integrability and Geometry Methods and ApplicationsSep 8, 20072 citations

Complex positive maps and quaternionic unitary evolution

M. Asorey, G. Scolarici

Journal of Physics A Mathematical and GeneralJul 19, 200611 citations

Quaternionic versus complex maps

M. Asorey, G. Scolarici, Luigi Solombrino

Journal of Physics Conference SeriesNov 1, 20070 citations

Alternative descriptions in quaternionic quantum mechanics

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.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.

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Oct 28, 20163 citations

We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators

H(t)

that generate a real phase in their time-evolution. This involves the use of invariant operators

I_{PH}(t)

that are pseudo-Hermitian with respect to the time-dependent metric operator and which implies that the dynamics is governed by unitary time evolution. Furthermore,

H(t)

is not generally quasi-Hermitian and does not define an observable of the system but

I_{PH}(t)

obeys a quasi-hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.