53 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
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
Zitterbewegung of optical pulses in nonlinear frequency conversion
Pulse walk-off in the process of sum frequency generation in a nonlinear
crystal is shown to be responsible for pulse jittering which is
reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely
moving Dirac particle. An analytical expression for the pulse center of mass
trajectory is derived in the no-pump-depletion limit, and numerical examples of
Zitterbewegung are presented for sum frequency generation in periodically-poled
lithium niobate. The proposed quantum-optical analogy indicates that frequency
conversion in nonlinear optics could provide an experimentally accessible
simulator of the Dirac equation.Comment: to be published in Journal of Physics B: Atomic, Molecular & Optical
Physic
Comment on: "Quantum dynamics of a general time-dependent coupled oscillator"
By using dynamical invariants theory, Hassoul et al. [1,2] investigate the
quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled
oscillators. They claim that, in the 2D case, introducing two pairs of
annihilation and creation operators uncouples the original invariant operator
so that it becomes the one that describes two independent subsystems. For the
3D case, the authors pretend that they have obtained a diagonalized invariant
which is exactly the sum of three simple harmonic oscillators. We show that
their investigations suffer from basic errors and therefore the found results
are not valid .Comment: 11 page
Ermakov-Lewis angles for one-parameter supersymmetric families of Newtonian free damping modes
We apply the Ermakov-Lewis procedure to the one-parameter damped modes
\tilde{y} recently introduced by Rosu and Reyes, which are related to the
common Newtonian free damping modes y by the general Riccati solution [H.C.
Rosu and M. Reyes, Phys. Rev. E 57, 4850 (1998), physics/9707019]. In
particular, we calculate and plot the angle quantities of this approach that
can help to distinguish these modes from the common y modesComment: 6 pages, twocolumn, 18 figs embedded, only first 9 publishe
A geometric approach to time evolution operators of Lie quantum systems
Lie systems in Quantum Mechanics are studied from a geometric point of view.
In particular, we develop methods to obtain time evolution operators of
time-dependent Schrodinger equations of Lie type and we show how these methods
explain certain ad hoc methods used in previous papers in order to obtain exact
solutions. Finally, several instances of time-dependent quadratic Hamiltonian
are solved.Comment: Accepted for publication in the International Journal of Theoretical
Physic
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