First-harmonic approximation in nonlinear chirped-driven oscillators

Abstract

Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon.

The role of singular values in single copy entanglement manipulations and unambiguous state discrimination

“…If an inconclusive result is obtained, the state of the system is always the same regardless of the input. This case naturally appears in the embedding scheme when the ancilla has only one level [19]. This is consistent with the fact that no information can be encoded in a single quantum level.…”

“…Positive K operators have a special property. In [19] it was shown that the positivity is a necessary condition for minimizing the time-energy resources needed for unitary embedding of the desired USD. Note that if K is not positive, it can be made positive by applying a unitary from the left.…”

On the equivalence of lossy evolution and POVM generalized quantum measurements

“…and as a result further USD is possible. However in [35] there is an argument that explains why this is impossible.…”

“…Otherwise, by controlling the signal amplification, the detection probability can be effectively increased. A lossy evolution can also be realized by embedding in a larger unitary system [8,30,31,32,33]. When only some part of Hilbert space is measured it appears as if the evolution is non-unitary.…”

“…Yet, in this regime the spectral norm is larger than one and the evolution operator is not passive anymore. In particular non-passive systems cannot be embedded in a unitary evolution as suggested in [8,31,32,33]. The necessary and sufficient equivalence condition K sp ≤ 1 does implies that the moduli of the eigenvalues of K are smaller than one, but the converse is not true.…”