75 research outputs found
Invariants and Coherent States for Nonstationary Fermionic Forced Oscillator
The most general form of Hamiltonian that preserves fermionic coherent states
stable in time is found in the form of nonstationary fermion oscillator.
Invariant creation and annihilation operators and related Fock states and
coherent states are built up for the more general system of nonstationary
forced fermion oscillator.Comment: 13 pages, Latex, no figure
Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
A new class of non-Hermitian Hamiltonians with real spectrum, which are
written as a real linear combination of su(2) generators in the form , , is analyzed. The metrics
which allows the transition to the equivalent Hermitian Hamiltonian is
established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is
performed. They correspond to the pseudo-Hermitian supersymmetric systems of
the boson-phermion oscillators. We extend the supercoherent states formalism to
such supersymmetic systems via the pseudo-unitary supersymmetric displacement
operator method. The constructed family of these supercoherent states consists
of two dual subfamilies that form a bi-overcomplete and bi-normal system in the
boson-phermion Fock space. The states of each subfamily are eigenvectors of the
boson annihilation operator and of one of the two phermion lowering operators
On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems
In the context of non-Hermitian quantum mechanics, many systems are known to
possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related
to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a
derivation of pseudo PT symmetry and {\eta} -pseudo-Hermiticity simultaneously
for the time dependent non-Hermitian Hamiltonians by intoducing a new metric
{\eta}(t)=PT{\eta}(t) that not satisfy the time-dependent quasi-Hermiticity
relation but obeys the Heisenberg evolution equation. Here, we solve the
SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a
time-dependent solutions by employing this new metric and discuss a concrete
physical applications of our results.Comment: 11 pages, Minor correction in the list and name of authors in
reference
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