1,298 research outputs found
Minimal Brownian Ratchet: An Exactly Solvable Model
We develop an exactly-solvable three-state discrete-time minimal Brownian
ratchet (MBR), where the transition probabilities between states are
asymmetric. By solving the master equations we obtain the steady-state
probabilities. Generally the steady-state solution does not display detailed
balance, giving rise to an induced directional motion in the MBR. For a reduced
two-dimensional parameter space we find the null-curve on which the net current
vanishes and detailed balance holds. A system on this curve is said to be
balanced. On the null-curve, an additional source of external random noise is
introduced to show that a directional motion can be induced under the zero
overall driving force. We also indicate the off-balance behavior with biased
random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be
appeared in Phys. Rev. Let
New paradoxical games based on Brownian ratchets
Based on Brownian ratchets, a counter-intuitive phenomenon has recently
emerged -- namely, that two losing games can yield, when combined, a
paradoxical tendency to win. A restriction of this phenomenon is that the rules
depend on the current capital of the player. Here we present new games where
all the rules depend only on the history of the game and not on the capital.
This new history-dependent structure significantly increases the parameter
space for which the effect operates.Comment: 4 pages, 3 eps figures, revte
Quantum field theory on quantum graphs and application to their conductance
We construct a bosonic quantum field on a general quantum graph. Consistency
of the construction leads to the calculation of the total scattering matrix of
the graph. This matrix is equivalent to the one already proposed using
generalized star product approach. We give several examples and show how they
generalize some of the scattering matrices computed in the mathematical or
condensed matter physics litterature.
Then, we apply the construction for the calculation of the conductance of
graphs, within a small distance approximation. The consistency of the
approximation is proved by direct comparison with the exact calculation for the
`tadpole' graph.Comment: 32 pages; misprints in tree graph corrected; proofs of consistency
and unitarity adde
Boundary condition at the junction
The quantum graph plays the role of a solvable model for a two-dimensional
network. Here fitting parameters of the quantum graph for modelling the
junction is discussed, using previous results of the second author.Comment: Replaces unpublished draft on related researc
Non-Weyl asymptotics for quantum graphs with general coupling conditions
Inspired by a recent result of Davies and Pushnitski, we study resonance
asymptotics of quantum graphs with general coupling conditions at the vertices.
We derive a criterion for the asymptotics to be of a non-Weyl character. We
show that for balanced vertices with permutation-invariant couplings the
asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions,
while for graphs without permutation numerous examples of non-Weyl behaviour
can be constructed. Furthermore, we present an insight helping to understand
what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance
point of view. Finally, we demonstrate a generalization to quantum graphs with
nonequal edge weights.Comment: minor changes, to appear in Pierre Duclos memorial issue of J. Phys.
A: Math. Theo
Bosonization and Scale Invariance on Quantum Wires
We develop a systematic approach to bosonization and vertex algebras on
quantum wires of the form of star graphs. The related bosonic fields propagate
freely in the bulk of the graph, but interact at its vertex. Our framework
covers all possible interactions preserving unitarity. Special attention is
devoted to the scale invariant interactions, which determine the critical
properties of the system. Using the associated scattering matrices, we give a
complete classification of the critical points on a star graph with any number
of edges. Critical points where the system is not invariant under wire
permutations are discovered. By means of an appropriate vertex algebra we
perform the bosonization of fermions and solve the massless Thirring model. In
this context we derive an explicit expression for the conductance and
investigate its behavior at the critical points. A simple relation between the
conductance and the Casimir energy density is pointed out.Comment: LaTex 31+1 pages, 2 figures. Section 3.6 and two references added. To
appear in J. Phys. A: Mathematical and Theoretica
Spectral simplicity and asymptotic separation of variables
We describe a method for comparing the real analytic eigenbranches of two
families of quadratic forms that degenerate as t tends to zero. One of the
families is assumed to be amenable to `separation of variables' and the other
one not. With certain additional assumptions, we show that if the families are
asymptotic at first order as t tends to 0, then the generic spectral simplicity
of the separable family implies that the eigenbranches of the second family are
also generically one-dimensional. As an application, we prove that for the
generic triangle (simplex) in Euclidean space (constant curvature space form)
each eigenspace of the Laplacian is one-dimensional. We also show that for all
but countably many t, the geodesic triangle in the hyperbolic plane with
interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure
Optical and Infrared Spectroscopy of the type IIn SN 1998S : Days 3-127
We present contemporary infrared and optical spectroscopic observations of
the type IIn SN 1998S for the period between 3 and 127 days after discovery. In
the first week the spectra are characterised by prominent broad emission lines
with narrow peaks superimposed on a very blue continuum(T~24000K). In the
following two weeks broad, blueshifted absorption components appeared in the
spectra and the temperature dropped. By day 44, broad emission components in H
and He reappeared in the spectra. These persisted to 100-130d, becoming
increasingly asymmetric. We agree with Leonard et al. (2000) that the broad
emission lines indicate interaction between the ejecta and circumstellar
material (CSM) and deduce that progenitor of SN 1998S appears to have gone
through at least two phases of mass loss, giving rise to two CSM zones.
Examination of the spectra indicates that the inner zone extended to <90AU,
while the outer CSM extended from 185AU to over 1800AU. Analysis of high
resolution spectra shows that the outer CSM had a velocity of 40-50 km/s.
Assuming a constant velocity, we can infer that the outer CSM wind commenced
more than 170 years ago, and ceased about 20 years ago, while the inner CSM
wind may have commenced less than 9 years ago. During the era of the outer CSM
wind the outflow was high, >2x10^{-5}M_{\odot}/yr corresponding to a mass loss
of at least 0.003M_{\odot} and suggesting a massive progenitor. We also model
the CO emission observed in SN 1998S. We deduce a CO mass of ~10^{-3} M_{\odot}
moving at ~2200km/s, and infer a mixed metal/He core of ~4M_{\odot}, again
indicating a massive progenitor.Comment: 22 pages, 14 figures, accepted in MNRA
Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching
We propose a new mechanism for pattern formation based on the global
alternation of two dynamics neither of which exhibits patterns. When driven by
either one of the separate dynamics, the system goes to a spatially homogeneous
state associated with that dynamics. However, when the two dynamics are
globally alternated sufficiently rapidly, the system exhibits stationary
spatial patterns. Somewhat slower switching leads to oscillatory patterns. We
support our findings by numerical simulations and discuss the results in terms
of the symmetries of the system and the ratio of two relevant characteristic
times, the switching period and the relaxation time to a homogeneous state in
each separate dynamics.Comment: REVTEX preprint: 12 pages including 1 (B&W) + 3 (COLOR) figures (to
appear in Physical Review Letters
- …