259 research outputs found
Point perturbations of circle billiards
The spectral statistics of the circular billiard with a point-scatterer is
investigated. In the semiclassical limit, the spectrum is demonstrated to be
composed of two uncorrelated level sequences. The first corresponds to states
for which the scatterer is located in the classically forbidden region and its
energy levels are not affected by the scatterer in the semiclassical limit
while the second sequence contains the levels which are affected by the
point-scatterer. The nearest neighbor spacing distribution which results from
the superposition of these sequences is calculated analytically within some
approximation and good agreement with the distribution that was computed
numerically is found.Comment: 9 pages, 2 figure
Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
We study the spectral statistics of the Dirac operator on a rose-shaped
graph---a graph with a single vertex and all bonds connected at both ends to
the vertex. We formulate a secular equation that generically determines the
eigenvalues of the Dirac rose graph, which is seen to generalise the secular
equation for a star graph with Neumann boundary conditions. We derive
approximations to the spectral pair correlation function at large and small
values of spectral spacings, in the limit as the number of bonds approaches
infinity, and compare these predictions with results of numerical calculations.
Our results represent the first example of intermediate statistics from the
symplectic symmetry class.Comment: 26 pages, references adde
On the eigenvalue spacing distribution for a point scatterer on the flat torus
We study the level spacing distribution for the spectrum of a point scatterer
on a flat torus. In the 2-dimensional case, we show that in the weak coupling
regime the eigenvalue spacing distribution coincides with that of the spectrum
of the Laplacian (ignoring multiplicties), by showing that the perturbed
eigenvalues generically clump with the unperturbed ones on the scale of the
mean level spacing. We also study the three dimensional case, where the
situation is very different.Comment: 25 page
Lower bounds on dissipation upon coarse graining
By different coarse-graining procedures we derive lower bounds on the total
mean work dissipated in Brownian systems driven out of equilibrium. With
several analytically solvable examples we illustrate how, when, and where the
information on the dissipation is captured.Comment: 11 pages, 8 figure
Time independent description of rapidly oscillating potentials
The classical and quantum dynamics in a high frequency field are found to be
described by an effective time independent Hamiltonian. It is calculated in a
systematic expansion in the inverse of the frequency () to order
. The work is an extension of the classical result for the Kapitza
pendulum, which was calculated in the past to order . The analysis
makes use of an implementation of the method of separation of time scales and
of a quantum gauge transformation in the framework of Floquet theory. The
effective time independent Hamiltonian enables one to explore the dynamics in
presence of rapidly oscillating fields, in the framework of theories that were
developed for systems with time independent Hamiltonians. The results are
relevant, in particular, for exploration of the dynamics of cold atoms.Comment: 4 pages, 1 figure. Revised versio
Fluctuation relations and coarse-graining
We consider the application of fluctuation relations to the dynamics of
coarse-grained systems, as might arise in a hypothetical experiment in which a
system is monitored with a low-resolution measuring apparatus. We analyze a
stochastic, Markovian jump process with a specific structure that lends itself
naturally to coarse-graining. A perturbative analysis yields a reduced
stochastic jump process that approximates the coarse-grained dynamics of the
original system. This leads to a non-trivial fluctuation relation that is
approximately satisfied by the coarse-grained dynamics. We illustrate our
results by computing the large deviations of a particular stochastic jump
process. Our results highlight the possibility that observed deviations from
fluctuation relations might be due to the presence of unobserved degrees of
freedom.Comment: 19 pages, 6 figures, very minor change
Semiclassical theory of a quantum pump
In a quantum charge pump, the periodic variation of two parameters that
affect the phase of the electronic wavefunction causes the flow of a direct
current. The operating mechanism of a quantum pump is based on quantum
interference, the phases of interfering amplitudes being modulated by the
external parameters. In a ballistic quantum dot, there is a minimum time before
which quantum interference can not occur: the Ehrenfest time. Here we calculate
the current pumped through a ballistic quantum dot when the Ehrenfest time is
comparable to the mean dwell time. Remarkably, we find that the pumped current
has a component that is not suppressed if the Ehrenfest time is much larger
than the mean dwell time.Comment: 14 pages, 8 figures. Revised version, minor change
Planktonic Aggregates as Hotspots for Heterotrophic Diazotrophy: The Plot Thickens
Biological dinitrogen (N-2) fixation is performed solely by specialized bacteria and archaea termed diazotrophs, introducing new reactive nitrogen into aquatic environments. Conventionally, phototrophic cyanobacteria are considered the major diazotrophs in aquatic environments. However, accumulating evidence indicates that diverse non-cyanobacterial diazotrophs (NCDs) inhabit a wide range of aquatic ecosystems, including temperate and polar latitudes, coastal environments and the deep ocean. NCDs are thus suspected to impact global nitrogen cycling decisively, yet their ecological and quantitative importance remain unknown. Here we review recent molecular and biogeochemical evidence demonstrating that pelagic NCDs inhabit and thrive especially on aggregates in diverse aquatic ecosystems. Aggregates are characterized by reduced-oxygen microzones, high C:N ratio (above Redfield) and high availability of labile carbon as compared to the ambient water. We argue that planktonic aggregates are important loci for energetically-expensive N-2 fixation by NCDs and propose a conceptual framework for aggregate-associated N-2 fixation. Future studies on aggregate-associated diazotrophy, using novel methodological approaches, are encouraged to address the ecological relevance of NCDs for nitrogen cycling in aquatic environments
Semiclassical Approach to Chaotic Quantum Transport
We describe a semiclassical method to calculate universal transport
properties of chaotic cavities. While the energy-averaged conductance turns out
governed by pairs of entrance-to-exit trajectories, the conductance variance,
shot noise and other related quantities require trajectory quadruplets; simple
diagrammatic rules allow to find the contributions of these pairs and
quadruplets. Both pure symmetry classes and the crossover due to an external
magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version
reaction at intermediate energies
The reaction is considered at the energies between 200 MeV and
520 MeV. The Alt-Grassberger-Sandhas equations are iterated up to the lowest
order terms over the nucleon-nucleon t-matrix. The parameterized wave
function including five components is used. The angular dependence of the
differential cross section and energy dependence of tensor analyzing power
at the zero scattering angle are presented in comparison with the
experimental data
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