Non-self-adjoint Hamiltonians with complex eigenvalues

Fabio Bagarello, Bagarello

Risultato della ricerca: Article

7 Citazioni (Scopus)

Abstract

Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.
Lingua originaleEnglish
pagine (da-a)-
Numero di pagine17
RivistaJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume49
Stato di pubblicazionePublished - 2016

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Hamiltonians
Living Systems
Quantum theory
Hilbert spaces
Hilbert space
Transition Probability
transition probabilities
Quantum Mechanics
quantum mechanics
eigenvalues
Eigenvalue
operators
Computing
Operator
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics
  • Modelling and Simulation
  • Statistics and Probability

Cita questo

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AB - Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.

KW - antilinear operators; intertwining relations; PT-quantum mechanics; Mathematical Physics; Physics and Astronomy (all); Statistical and Nonlinear Physics; Modeling and Simulation; Statistics and Probability

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