27 research outputs found
Periodic orbit analysis of an elastodynamic resonator using shape deformation
We report the first definitive experimental observation of periodic orbits
(POs) in the spectral properties of an elastodynamic system. The Fourier
transform of the density of flexural modes show peaks that correspond to stable
and unstable POs of a clover shaped quartz plate. We change the shape of the
plate and find that the peaks corresponding to the POs that hit only the
unperturbed sides are unchanged proving the correspondence. However, an exact
match to the length of the main POs could be made only after a small rescaling
of the experimental results. Statistical analysis of the level dynamics also
shows the effect of the stable POs.Comment: submitted to Europhysics Letter
Resonance- and Chaos-Assisted Tunneling
We consider dynamical tunneling between two symmetry-related regular islands
that are separated in phase space by a chaotic sea. Such tunneling processes
are dominantly governed by nonlinear resonances, which induce a coupling
mechanism between ``regular'' quantum states within and ``chaotic'' states
outside the islands. By means of a random matrix ansatz for the chaotic part of
the Hamiltonian, one can show that the corresponding coupling matrix element
directly determines the level splitting between the symmetric and the
antisymmetric eigenstates of the pair of islands. We show in detail how this
matrix element can be expressed in terms of elementary classical quantities
that are associated with the resonance. The validity of this theory is
demonstrated with the kicked Harper model.Comment: 25 pages, 5 figure
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
The phase-space path-integral approach to the damped harmonic oscillator is
analyzed beyond the Markovian approximation. It is found that pairs of
nonclassical trajectories contribute to the path-integral representation of the
Wigner propagating function. Due to the linearity of the problem, the sum
coordinate of a pair still satisfies the classical equation of motion.
Furthermore, it is shown that the broadening of the Wigner propagating function
of the damped oscillator arises due to the time-nonlocal interaction mediated
by the heat bath.Comment: 8 pages, 3 figures, accepted for publication in Chemical Physic
Symplectic evolution of Wigner functions in markovian open systems
The Wigner function is known to evolve classically under the exclusive action
of a quadratic hamiltonian. If the system does interact with the environment
through Lindblad operators that are linear functions of position and momentum,
we show that the general evolution is the convolution of the classically
evolving Wigner function with a phase space gaussian that broadens in time. We
analyze the three generic cases of elliptic, hyperbolic and parabolic
Hamiltonians. The Wigner function always becomes positive in a definite time,
which is shortest in the hyperbolic case. We also derive an exact formula for
the evolving linear entropy as the average of a narrowing gaussian taken over a
probability distribution that depends only on the initial state. This leads to
a long time asymptotic formula for the growth of linear entropy.Comment: this new version treats the dissipative cas
Resonance-assisted tunneling in near-integrable systems
Dynamical tunneling between symmetry related invariant tori is studied in the
near-integrable regime. Using the kicked Harper model as an illustration, we
show that the exponential decay of the wave functions in the classically
forbidden region is modified due to coupling processes that are mediated by
classical resonances. This mechanism leads to a substantial deviation of the
splitting between quasi-degenerate eigenvalues from the purely exponential
decrease with 1 / hbar obtained for the integrable system. A simple
semiclassical framework, which takes into account the effect of the resonance
substructure on the KAM tori, allows to quantitatively reproduce the behavior
of the eigenvalue splittings.Comment: 4 pages, 2 figures, gzipped tar file, to appear in Phys. Rev. Lett,
text slightly condensed compared to first versio
A primer for resonant tunnelling
Resonant tunnelling is studied numerically and analytically with the help of
a three-well quantum one-dimensional time-independent model. The simplest cases
are considered where the three-well potential is polynomial or piecewise
constant.Comment: accepted to EJP, 19 pages, 8 figure
Tunneling dynamics in exactly-solvable models with triple-well potentials
Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein
condensate dynamics, we apply a general technique of N=4 extended
Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well
potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical
propagators, which take into account all states of the spectrum, are obtained,
within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian
of a harmonic oscillator, we obtain the explicit expressions of potentials,
wavefunctions and propagators. The obtained results are applied to tunneling
dynamics of localized states in triple-well potentials and for studying its
features. In particular, we observe a Josephson-type tunneling transition of a
wave packet, the effect of its partial trapping and a non-monotonic dependence
of tunneling dynamics on the shape of a three-well potential. We investigate,
among others, the possibility of controlling tunneling transport by changing
parameters of the central well, and we briefly discuss potential applications
of this aspect to atomtronic devices.Comment: Latex, 28 pages, 7 Figs, 2 Tables; minor presentation changes,
journal versio
Semiclassical Evolution of Dissipative Markovian Systems
A semiclassical approximation for an evolving density operator, driven by a
"closed" hamiltonian operator and "open" markovian Lindblad operators, is
obtained. The theory is based on the chord function, i.e. the Fourier transform
of the Wigner function. It reduces to an exact solution of the Lindblad master
equation if the hamiltonian operator is a quadratic function and the Lindblad
operators are linear functions of positions and momenta.
Initially, the semiclassical formulae for the case of hermitian Lindblad
operators are reinterpreted in terms of a (real) double phase space, generated
by an appropriate classical double Hamiltonian. An extra "open" term is added
to the double Hamiltonian by the non-hermitian part of the Lindblad operators
in the general case of dissipative markovian evolution. The particular case of
generic hamiltonian operators, but linear dissipative Lindblad operators, is
studied in more detail. A Liouville-type equivariance still holds for the
corresponding classical evolution in double phase, but the centre subspace,
which supports the Wigner function, is compressed, along with expansion of its
conjugate subspace, which supports the chord function.
Decoherence narrows the relevant region of double phase space to the
neighborhood of a caustic for both the Wigner function and the chord function.
This difficulty is avoided by a propagator in a mixed representation, so that a
further "small-chord" approximation leads to a simple generalization of the
quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.
A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields
Statistics of tunneling rates in the presence of chaotic classical dynamics
is discussed on a realistic example: a hydrogen atom placed in parallel uniform
static electric and magnetic fields, where tunneling is followed by ionization
along the fields direction. Depending on the magnetic quantum number, one may
observe either a standard Porter-Thomas distribution of tunneling rates or, for
strong scarring by a periodic orbit parallel to the external fields, strong
deviations from it. For the latter case, a simple model based on random matrix
theory gives the correct distribution.Comment: Submitted to Phys. Rev.
Quantifying decoherence in continuous variable systems
We present a detailed report on the decoherence of quantum states of
continuous variable systems under the action of a quantum optical master
equation resulting from the interaction with general Gaussian uncorrelated
environments. The rate of decoherence is quantified by relating it to the decay
rates of various, complementary measures of the quantum nature of a state, such
as the purity, some nonclassicality indicators in phase space and, for two-mode
states, entanglement measures and total correlations between the modes.
Different sets of physically relevant initial configurations are considered,
including one- and two-mode Gaussian states, number states, and coherent
superpositions. Our analysis shows that, generally, the use of initially
squeezed configurations does not help to preserve the coherence of Gaussian
states, whereas it can be effective in protecting coherent superpositions of
both number states and Gaussian wave packets.Comment: Review article; 36 pages, 19 figures; typos corrected, references
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