3,269 research outputs found
Combinatorics and geometry of finite and infinite squaregraphs
Squaregraphs were originally defined as finite plane graphs in which all
inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e.,
the vertices not incident with the outer face) have degrees larger than three.
The planar dual of a finite squaregraph is determined by a triangle-free chord
diagram of the unit disk, which could alternatively be viewed as a
triangle-free line arrangement in the hyperbolic plane. This representation
carries over to infinite plane graphs with finite vertex degrees in which the
balls are finite squaregraphs. Algebraically, finite squaregraphs are median
graphs for which the duals are finite circular split systems. Hence
squaregraphs are at the crosspoint of two dualities, an algebraic and a
geometric one, and thus lend themselves to several combinatorial
interpretations and structural characterizations. With these and the
5-colorability theorem for circle graphs at hand, we prove that every
squaregraph can be isometrically embedded into the Cartesian product of five
trees. This embedding result can also be extended to the infinite case without
reference to an embedding in the plane and without any cardinality restriction
when formulated for median graphs free of cubes and further finite
obstructions. Further, we exhibit a class of squaregraphs that can be embedded
into the product of three trees and we characterize those squaregraphs that are
embeddable into the product of just two trees. Finally, finite squaregraphs
enjoy a number of algorithmic features that do not extend to arbitrary median
graphs. For instance, we show that median-generating sets of finite
squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the
corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure
Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability
We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein
condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian
of Bose-Hubbard type: The corresponding mean-field system described by a
discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation)
instability due to chaotic dynamics and equipartition over the quasimomentum
modes. It is shown, that these phenomena are related to a depletion of the
Floquet-Bogoliubov states and a decoherence of the condensate in the
many-particle description. Three different types of dynamics are distinguished:
(i) decaying oscillations in the region of dynamical instability, and (ii)
persisting Bloch oscillations or (iii) periodic decay and revivals in the
region of stability.Comment: 12 pages, 14 figure
Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein
condensate in a tilted optical lattice is studied in a discrete mean-field
approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation.
If the static field is varied the system shows a plethora of dynamical
phenomena. In the strong field limit we demonstrate the existence of (almost)
non-spreading states which remain localized on the lattice region populated
initially and show coherent Bloch oscillations with fractional revivals in the
momentum space (so called quantum carpets). With decreasing field, the dynamics
becomes irregular, however, still confined in configuration space. For even
weaker fields we find sub-diffusive dynamics with a wave-packet width spreading
as .Comment: 4 pages, 5 figure
Pathological regional blood flow in opiate-dependent patients during withdrawal: A HMPAO-SPECT study
The aims of the present study were to investigate regional cerebral blood flow (rCBF) in heroin-dependent patients during withdrawal and to assess the relation between these changes and duration of heroin consumption and withdrawal data. The rCBF was measured using brain SPECT with Tc-99m-HMPAO in 16 heroin-dependent patients during heroin withdrawal. Thirteen patients received levomethadone at the time of the SPECT scans. The images were analyzed both visually and quantitatively, a total of 21 hypoperfused brain regions were observed in 11 of the 16 patients. The temporal lobes were the most affected area, hypoperfusions of the right and left temporal lobe were observed in 5 and 5 patients, respectively. Three of the patients had a hypoperfusion of the right frontal lobe, 2 patients showed perfusion defects in the left frontal lobe, right parietal lobe and left parietal lobe. The results of the quantitative assessments of the rCBF were consistent with the results of the qualitative findings. The stepwise regression analysis showed a significant positive correlation (r = 0.54) between the dose of levomethadone at the time of the SPECT scan and the rCBF of the right parietal lobe. Other significant correlations between clinical data and rCBF were not found. The present results suggest brain perfusion abnormalities during heroin withdrawal in heroin-dependent patients, which are not due to the conditions of withdrawal
Vibronic origin of long-lived coherence in an artificial molecular light harvester
Natural and artificial light harvesting processes have recently gained new
interest. Signatures of long lasting coherence in spectroscopic signals of
biological systems have been repeatedly observed, albeit their origin is a
matter of ongoing debate, as it is unclear how the loss of coherence due to
interaction with the noisy environments in such systems is averted. Here we
report experimental and theoretical verification of coherent
exciton-vibrational (vibronic) coupling as the origin of long-lasting coherence
in an artificial light harvester, a molecular J-aggregate. In this
macroscopically aligned tubular system, polarization controlled 2D spectroscopy
delivers an uncongested and specific optical response as an ideal foundation
for an in-depth theoretical description. We derive analytical expressions that
show under which general conditions vibronic coupling leads to prolonged
excited-state coherence
Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
Assuming the validity of random matrices for describing the statistics of a
closed chaotic quantum system, we study analytically some statistical
properties of the S-matrix characterizing scattering in its open counterpart.
In the first part of the paper we attempt to expose systematically ideas
underlying the so-called stochastic (Heidelberg) approach to chaotic quantum
scattering. Then we concentrate on systems with broken time-reversal invariance
coupled to continua via M open channels. By using the supersymmetry method we
derive:
(i) an explicit expression for the density of S-matrix poles (resonances) in
the complex energy plane
(ii) an explicit expression for the parametric correlation function of
densities of eigenphases of the S-matrix.
We use it to find the distribution of derivatives of these eigenphases with
respect to the energy ("partial delay times" ) as well as with respect to an
arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be
published in the special issue of the Journal of Mathematical Physic
How to measure spatial distances?
The use of time--like geodesics to measure temporal distances is better
justified than the use of space--like geodesics for a measurement of spatial
distances. We give examples where a ''spatial distance'' cannot be
appropriately determined by the length of a space--like geodesic.Comment: 4 pages, latex, no figure
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