1,664 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
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junction is discussed, using previous results of the second author.Comment: Replaces unpublished draft on related researc
Brownian ratchets and Parrondo's games
Parrondo's games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player's current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of "noise" that is rectified by game B to produce overall positive drift-as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo's games is that they are physically motivated and were originally derived by considering a Brownian ratchet-the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research. (c) 2001 American Institute of Physics.Gregory P. Harmer, Derek Abbott, Peter G. Taylor, and Juan M. R. Parrond
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
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
Recommended from our members
'Landlocked'
The nautical imagery within my work derives directly from my involvement with the Canadian Navy, from exposure to coastal communities and my constantly transitory lifestyle.
The images which form my woodcuts are simply bold and stark. They contain a presence that is large, cold and denies the use of colour, much like the diagrams found in everday exposure within our society, as well as academic and military institutional textbooks. These woodcuts were created with the potential of having a multiple edtion of prints made of them. The reality of these woodcuts is that they will most likely never be printed. The decision in not printing them c_reates a perverse idea of waste; of time, energy and never knowing of the second existence that they may have obtained as coloured prints. The beauty of these woodcuts is apparent within the finished product. The experience of chiseling, carving and routoring the image out of the wood forms a parallel to the idea of map making and navigation.
The exposure to the Great Lakes of Canada and to some of the oceans and seas of the world created a strong bond between myself and the sea. This bond eventually led me to join the Canadian Navy. My experiences, and the close friends that I made while I was with the navy, strengthened my desire to be around the sea as much as I could. It also made me realize how painfully lonely and misplaced one could be at sea, how minute and insignificant I was on such a large body of open water. In those situations, thoughts of having been adopted and not knowing the identity of my birth parents, of moving from city to city and always being at sea created an uneasiness in me. This 'uneasiness' could be described as a void, that at times felt cold and empty, much like some of the derelict ships I've seen on beaches and along wharfs. These ships lie lifeless and still, only at times reminding society of a time and era gone by. Thus creating a nostalgic atmosphere.
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