16 research outputs found
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
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
Quantum features of a charged particle in ionized plasma controlled by a time-dependent magnetic field
Quantum characteristics of a charged particle traveling under the influence of an external time-dependent magnetic field in ionized plasma are investigated using the invariant operator method. The Hamiltonian that gives the radial part of the classical equation of motion for the charged particle is dependent on time. The corresponding invariant operator that satisfies Liouville-von Neumann equation is constructed using fundamental relations. The exact radial wave functions are derived by taking advantage of the eigenstates of the invariant operator. Quantum properties of the system is studied using these wave functions. Especially, the time behavior of the radial component of the quantized energy is addressed in detail
A new symmetry theory for non-Hermitian Hamiltonians
The {\eta} pseudo PT symmetry theory, denoted by the symbol {\eta}, explores
the conditions under which non-Hermitian Hamiltonians can possess real spectra
despite the violation of PT symmetry, that is the adjoint of H, denoted
H^{{\dag}} is expressed as H^{{\dag}}=PTHPT. This theory introduces a new
symmetry operator, {\eta}=PT{\eta}, which acts on the Hilbert space. The {\eta}
pseudo PT symmetry condition requires the Hamiltonian to commute with the
{\eta} operator, leading to real eigenvalues. We discuss some general
implications of our results for the coupled non hermitian harmonic oscillator.Comment: Section 4 (end of page 7 until page 8 before the conclusion in this
new version) has been rewritten , minor typos corrected , 10 page
Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic field
The dynamics of time-dependent coupled oscillator model for the charged
particle motion subjected to a time-dependent external magnetic field is
investigated. We used canonical transformation approach for the classical
treatment of the system, whereas unitary transformation approach is used when
managing the system in the framework of quantum mechanics. For both approaches,
the original system is transformed to a much more simple system that is the sum
of two independent harmonic oscillators which have time-dependent frequencies.
We therefore easily identified the wave functions in the transformed system
with the help of invariant operator of the system. The full wave functions in
the original system is derived from the inverse unitary transformation of the
wave functions associated to the transformed system.Comment: 16 page