365 research outputs found
Combinatorial identities for binary necklaces from exact ray-splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system,
we derive novel combinatorial identities for cyclic binary sequences (P\'olya
necklaces).Comment: 15 page
One-dimensional quantum chaos: Explicitly solvable cases
We present quantum graphs with remarkably regular spectral characteristics.
We call them {\it regular quantum graphs}. Although regular quantum graphs are
strongly chaotic in the classical limit, their quantum spectra are explicitly
solvable in terms of periodic orbits. We present analytical solutions for the
spectrum of regular quantum graphs in the form of explicit and exact periodic
orbit expansions for each individual energy level.Comment: 9 pages and 4 figure
Diagnostic criterion for crystallized beams
Small ion crystals in a Paul trap are stable even in the absence of laser
cooling. Based on this theoretically and experimentally well-established fact
we propose the following diagnostic criterion for establishing the presence of
a crystallized beam: Absence of heating following the shut-down of all cooling
devices. The validity of the criterion is checked with the help of detailed
numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR
Quantum Fractal Fluctuations
We numerically analyse quantum survival probability fluctuations in an open,
classically chaotic system. In a quasi-classical regime, and in the presence of
classical mixed phase space, such fluctuations are believed to exhibit a
fractal pattern, on the grounds of semiclassical arguments. In contrast, we
work in a classical regime of complete chaoticity, and in a deep quantum regime
of strong localization. We provide evidence that fluctuations are still
fractal, due to the slow, purely quantum algebraic decay in time produced by
dynamical localization. Such findings considerably enlarge the scope of the
existing theory.Comment: revtex, 4 pages, 5 figure
Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
We deduce the effects of quantum interference on the conductance of chaotic
cavities by using a statistical ansatz for the S matrix. Assuming that the
circular ensembles describe the S matrix of a chaotic cavity, we find that the
conductance fluctuation and weak-localization magnitudes are universal: they
are independent of the size and shape of the cavity if the number of incoming
modes, N, is large. The limit of small N is more relevant experimentally; here
we calculate the full distribution of the conductance and find striking
differences as N changes or a magnetic field is applied.Comment: 4 pages revtex 3.0 (2-column) plus 2 postscript figures (appended),
hub.pam.94.
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties
We show that reflection symmetry has a strong influence on quantum transport
properties. Using a random S-matrix theory approach, we derive the
weak-localization correction, the magnitude of the conductance fluctuations,
and the distribution of the conductance for three classes of reflection
symmetry relevant for experimental ballistic microstructures. The S-matrix
ensembles used fall within the general classification scheme introduced by
Dyson, but because the conductance couples blocks of the S-matrix of different
parity, the resulting conductance properties are highly non-trivial.Comment: 4 pages, includes 3 postscript figs, uses revte
Reducing multiphoton ionization in a linearly polarized microwave field by local control
We present a control procedure to reduce the stochastic ionization of
hydrogen atom in a strong microwave field by adding to the original Hamiltonian
a comparatively small control term which might consist of an additional set of
microwave fields. This modification restores select invariant tori in the
dynamics and prevents ionization. We demonstrate the procedure on the
one-dimensional model of microwave ionization.Comment: 8 page
How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities
We investigate the effects of phase-breaking events on electronic transport
through ballistic chaotic cavities. We simulate phase-breaking by a fictitious
lead connecting the cavity to a phase-randomizing reservoir and introduce a
statistical description for the total scattering matrix, including the
additional lead. For strong phase-breaking, the average and variance of the
conductance are calculated analytically. Combining these results with those in
the absence of phase-breaking, we propose an interpolation formula, show that
it is an excellent description of random-matrix numerical calculations, and
obtain good agreement with several recent experiments.Comment: 4 pages, revtex, 3 figures: uuencoded tar-compressed postscrip
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