402 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
Exact trace formulae for a class of one-dimensional ray-splitting systems
Based on quantum graph theory we establish that the ray-splitting trace
formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992))
is exact for a class of one-dimensional ray-splitting systems. Important
applications in combinatorics are suggested.Comment: 14 pages, 3 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
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
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
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.
Goos-Haenchen induced vector eigenmodes in a dome cavity
We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome
cavity resonator that owe their shape and character entirely to the
Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM
polarization, are well described by a 2D billiard map with the Goos-Haenchen
shift included. A phase space plot of this augmented billiard map reveals a
saddle-node bifurcation; the stable periodic orbit that is created in the
bifurcation corresponds to the numerically calculated eigenmode, dictating the
angle of its "V". A transition from a fundamental Gaussian to a TM V mode has
been observed as the cavity is lengthened to become nearly hemispherical.Comment: 4 pages, 4 figure
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
Correlations and pair emission in the escape dynamics of ions from one-dimensional traps
We explore the non-equilibrium escape dynamics of long-range interacting ions
in one-dimensional traps. The phase space of the few ion setup and its impact
on the escape properties are studied. As a main result we show that an
instantaneous reduction of the trap's potential depth leads to the synchronized
emission of a sequence of ion pairs if the initial configurations are close to
the crystalline ionic configuration. The corresponding time-intervals of the
consecutive pair emission as well as the number of emitted pairs can be tuned
by changing the final trap depth. Correlations between the escape times and
kinetic energies of the ions are observed and analyzed.Comment: 17 pages, 9 figure
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