1,490 research outputs found
Bound states in the continuum driven by AC fields
We report the formation of bound states in the continuum driven by AC fields.
This system consists of a quantum ring connected to two leads. An AC side-gate
voltage controls the interference pattern of the electrons passing through the
system. We model the system by two sites in parallel connected to two
semi-infinite lattices. The energy of these sites change harmonically with
time. We obtain the transmission probability and the local density of states at
the ring sites as a function of the parameters that define the system. The
transmission probability displays a Fano profile when the energy of the
incoming electron matches the driving frequency. Correspondingly, the local
density of states presents a narrow peak that approaches a Dirac delta function
in the weak coupling limit. We attribute these features to the presence of
bound states in the continuum.Comment: 5 pages, 3 figure
Ricci flow, quantum mechanics and gravity
It has been argued that, underlying any given quantum-mechanical model, there
exists at least one deterministic system that reproduces, after
prequantisation, the given quantum dynamics. For a quantum mechanics with a
complex d-dimensional Hilbert space, the Lie group SU(d) represents classical
canonical transformations on the projective space CP^{d-1} of quantum states.
Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and
let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then
the underlying deterministic model we propose here is the Lie group SU(d),
acted on by the operation PR. Finally we comment on some possible consequences
that our model may have on a quantum theory of gravity.Comment: 8 page
Remarks on the representation theory of the Moyal plane
We present an explicit construction of a unitary representation of the
commutator algebra satisfied by position and momentum operators on the Moyal
plane.Comment: 10 pages, minor changes, refs. adde
Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability
The existence of a Lagrangian description for the second-order Riccati
equation is analyzed and the results are applied to the study of two different
nonlinear systems both related with the generalized Riccati equation. The
Lagrangians are nonnatural and the forces are not derivable from a potential.
The constant value of a preserved energy function can be used as an
appropriate parameter for characterizing the behaviour of the solutions of
these two systems. In the second part the existence of two--dimensional
versions endowed with superintegrability is proved. The explicit expressions of
the additional integrals are obtained in both cases. Finally it is proved that
the orbits of the second system, that represents a nonlinear oscillator, can be
considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure
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