The doublet representation of non-Hilbert eigenstates of the Hamiltonian

Laura

1997

Phys. Rev. A

It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable states that vanish when t → ∞. These "Gamov vectors" have zero norm, in such a way that the norm and the energy of the physical states remain constant. The evolution operator has no inverse, showing that we are really dealing with a time-asymmetric theory. Using Friedrichs model reasonable physical results are obtained, e. g. : the remaining of an unstable decaying state reappears, in the continuous spectrum of the model, with its primitive energy.•PACS Nrs. 05.20-y, 03.65. BZ, 05.30-d.•

Section: Generalized Expansions In the Literaturementioning

confidence: 99%

Minimal irreversible quantum mechanics: Pure-state formalism

Laura

1997

Phys. Rev. A

“…In this case we have lost the particle number operator corresponding to the discrete part of the spectrum of H and we do not have the correct form of H when λ → 0 [30]. This problem can be solved promoting the energy (or frequency) ω to be a complex variable z.…”

Section: Continuationmentioning

confidence: 99%

Minimal irreversible quantum mechanics. The decay of unstable states

Arbó

Physica A: Statistical Mechanics and its Applications

Gaioli

et al. 2000

Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution that is used to study the time evolution of the reduced density operator. It is derived in a closed form, in the one-particle sector of the model. The irreversible behavior of the Brownian particle is described by a reduced density matrix.

“…(see also [38] and paper [34], where the Nakanishi trick is explain). From its own definition it is evident that |n− >, |z− >, | ω− >∈ φ × −,out , since these vectors are functionals over |ϕ >∈ φ −,out and that |n+ >, |z+ >, | ω+ >∈ φ × +,in since these vectors are functionals over |ψ >∈ φ +,in .…”

Section: The Modelmentioning

confidence: 99%

Mathematical structure of quantum superspace as a consequence of time asymmetry

1998

Phys. Rev. D

It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace of the wave functions of the universe, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields directly an irreversible evolution, in the classical ͑and semiclassical͒ phase of the universe, where decoherence and correlations take place and therefore give origin to a classical universe, the second law of thermodynamics is demonstrated, connection with the Reichenbach branch system idea can be implemented, some rough coincidences with observational data are obtained, the arrows of time can be correlated, and time asymmetry can be explained as a state space asymmetry ͑e.g., like a spontaneous symmetry breaking͒. All these facts solve the problem of time asymmetry and show that it is time asymmetry itself that defines the most important features of the mathematical structure of superspace.