161 research outputs found
Theory of scanning gate microscopy
A systematic theory of the conductance measurements of non-invasive (weak
probe) scanning gate microscopy is presented that provides an interpretation of
what precisely is being measured. A scattering approach is used to derive
explicit expressions for the first and second order conductance changes due to
the perturbation by the tip potential in terms of the scattering states of the
unperturbed structure. In the case of a quantum point contact, the first order
correction dominates at the conductance steps and vanishes on the plateaus
where the second order term dominates. Both corrections are non-local for a
generic structure. Only in special cases, such as that of a centrally symmetric
quantum point contact in the conductance quantization regime, can the second
order correction be unambiguously related with the local current density. In
the case of an abrupt quantum point contact we are able to obtain analytic
expressions for the scattering eigenfunctions and thus evaluate the resulting
conductance corrections.Comment: 19 pages, 7 figure
A Uniform Approximation for the Fidelity in Chaotic Systems
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve
in highly complex, yet deterministic ways. A slight perturbation of the system,
though, will cause the evolution to diverge from its original behavior
increasingly with time. This divergence can be measured by the fidelity, which
is defined as the squared overlap of the two time evolved states. For chaotic
systems, two main decay regimes of either Gaussian or exponential behavior have
been identified depending on the strength of the perturbation. For perturbation
strengths intermediate between the two regimes, the fidelity displays both
forms of decay. By applying a complementary combination of random matrix and
semiclassical theory, a uniform approximation can be derived that covers the
full range of perturbation strengths. The time dependence is entirely fixed by
the density of states and the so-called transition parameter, which can be
related to the phase space volume of the system and the classical action
diffusion constant, respectively. The accuracy of the approximations are
illustrated with the standard map.Comment: 16 pages, 4 figures, accepted in J. Phys. A, special edition on
Random Matrix Theor
Localization properties of groups of eigenstates in chaotic systems
In this paper we study in detail the localized wave functions defined in
Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect
of unstable periodic orbits in highly chaotic Hamiltonian system. These
functions appear highly localized not only along periodic orbits but also on
the associated manifolds. Moreover, they show in phase space the hyperbolic
structure in the vicinity of the orbit, something which translates in
configuration space into the structure induced by the corresponding self--focal
points. On the other hand, the quantum dynamics of these functions are also
studied. Our results indicate that the probability density first evolves along
the unstable manifold emanating from the periodic orbit, and localizes
temporarily afterwards on only a few, short related periodic orbits. We believe
that this type of studies can provide some keys to disentangle the complexity
associated to the quantum mechanics of these kind of systems, which permits the
construction of a simple explanation in terms of the dynamics of a few
classical structures.Comment: 9 pages, 8 Postscript figures (low resolution). For high resolution
versions of figs http://www.tandar.cnea.gov.ar/~wisniack/ To appear in Phys.
Rev.
Entanglement production by interaction quenches of quantum chaotic subsystems
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate rescaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the nonperturbative regime is performed using a recursively embedded perturbation theory to produce the full transition and the saturation values. The analytical results are found to be in good agreement with numerical results for random matrix computations and a dynamical system given by a pair of coupled kicked rotors
First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
We report on first experimental signatures for chaos-assisted tunneling in a
two-dimensional annular billiard. Measurements of microwave spectra from a
superconducting cavity with high frequency resolution are combined with
electromagnetic field distributions experimentally determined from a normal
conducting twin cavity with high spatial resolution to resolve eigenmodes with
properly identified quantum numbers. Distributions of so-called quasi-doublet
splittings serve as basic observables for the tunneling between whispering
gallery type modes localized to congruent, but distinct tori which are coupled
weakly to irregular eigenstates associated with the chaotic region in phase
space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures:
http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published
in Phys. Rev. Let
On resumming periodic orbits in the spectra of integrable systems
Spectral determinants have proven to be valuable tools for resumming the periodic orbits in the Gutzwiller trace formula of chaotic systems. We investigate these tools in the context of integrable systems to which these techniques have not been previously applied. Our specific model is a stroboscopic map of an integrable Hamiltonian system with quadratic action dependence, for which each stage of the semiclassical approximation can be controlled. It is found that large errors occur in the semiclassical traces due to edge corrections which may be neglected if the eigenvalues are obtained by Fourier transformation over the long time dynamics. However, these errors cause serious harm to the spectral approximations of an integrable system obtained via the spectral determinants. The symmetry property of the spectral determinant does not generally alleviate the error, since it sometimes sheds a pair of eigenvalues from the unit circle. By taking into account the leading order asymptotics of the edge corrections, the spectral determinant method makes a significant recovery
Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator
Numerous experimental and theoretical studies have established that
intramolecular vibrational energy redistribution (IVR) in isolated molecules
has a heirarchical tier structure. The tier structure implies strong
correlations between the energy level motions of a quantum system and its
intensity-weighted spectrum. A measure, which explicitly accounts for this
correaltion, was first introduced by one of us as a sensitive probe of phase
space localization. It correlates eigenlevel velocities with the overlap
intensities between the eigenstates and some localized state of interest. A
semiclassical theory for the correlation is developed for systems that are
classically integrable and complements earlier work focusing exclusively on the
chaotic case. Application to a model two dimensional effective spectroscopic
Hamiltonian shows that the correlation measure can provide information about
the terms in the molecular Hamiltonian which play an important role in an
energy range of interest and the character of the dynamics. Moreover, the
correlation function is capable of highlighting relevant phase space structures
including the local resonance features associated with a specific bright state.
In addition to being ideally suited for multidimensional systems with a large
density of states, the measure can also be used to gain insights into the phase
space transport and localization. It is argued that the overlap intensity-level
velocity correlation function provides a novel way of studying vibrational
energy redistribution in isolated molecules. The correlation function is
ideally suited to analyzing the parametric spectra of molecules in external
fields.Comment: 16 pages, 13 figures (low resolution
Complexity, Tunneling and Geometrical Symmetry
It is demonstrated in the context of the simple one-dimensional example of a
barrier in an infinite well, that highly complex behavior of the time evolution
of a wave function is associated with the almost degeneracy of levels in the
process of tunneling. Degenerate conditions are obtained by shifting the
position of the barrier. The complexity strength depends on the number of
almost degenerate levels which depend on geometrical symmetry. The presence of
complex behavior is studied to establish correlation with spectral degeneracy.Comment: 9 revtex pages, 6 Postscript figures (uuencoded
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