Biomedical subjects

Holger Schanz

Publications and source records attributed to Holger Schanz.

8 recordsLinked to original sources

PubMed2006

Signature of directed chaos in the conductance of a nanowire.

We study the conductance of chaotic or disordered wires in a situation where equilibrium transport decomposes into biased diffusion and a countermoving regular current. A possible realization is a semiconductor nanostructure with a transversal magnetic field and suitably patterned surfaces. We find a nontrivial dependence of the conductance on the wire length. It differs qualitatively from Ohm's law by the existence of a characteristic length scale and a finite saturation value.

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PubMed2005

Phase-space correlations of chaotic eigenstates.

It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in configuration space, they persist in the semiclassical limit. A quantitative theory is developed on the basis of Gaussian wave packet dynamics and random-matrix arguments. The role of symmetries is discussed for the example of time-reversal invariance.

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PubMed2005

Quantum pumping: the charge transported due to a translation of a scatterer.

The amount of charge that is pushed by a moving scatterer is dQ= -GdX , where dX is the displacement of the scatterer. The question is: what is G ?. Does it depend on the transmission g(0) of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case what are the implications of having "quantum chaos" and/or coupling to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.

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PubMed2005

Directed chaotic transport in Hamiltonian ratchets.

We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport like a mixed classical phase space. A sum rule is derived which connects the contributions of different phase-space components to transport. We show that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems. For quantized Hamiltonian ratchets we study transport in terms of the evolution of wave packets and derive a semiclassical expression for the distribution of level velocities which encode the quantum transport in the Floquet band spectra. We discuss the role of dynamical tunneling between transporting islands and the chaotic sea and the breakdown of transport in quantum ratchets with broken spatial periodicity.

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PubMed2003

Shot noise in chaotic cavities from action correlations.

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system, we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.

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PubMed2003

Scars on quantum networks ignore the Lyapunov exponent.

We show that enhanced wave function localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical stability. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation numbers.

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PubMed2002

Eigenstates ignoring regular and chaotic phase-space structures.

We report the failure of the semiclassical eigenfunction hypothesis if regular classical transport coexists with chaotic dynamics. All eigenstates, instead of being restricted to either a regular island or the chaotic sea, ignore these classical phase-space structures. We argue that this is true even in the semiclassical limit for extended systems with transporting regular islands such as the standard map with accelerator modes.

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PubMed2002

Leading off-diagonal correction to the form factor of large graphs.

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, K(tau), of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We calculate the contribution from pairs of self-intersecting orbits that differ from each other only in the orientation of a single loop. In the limit of large graphs, these pairs produce a contribution -2tau(2) to the form factor which agrees with random-matrix theory.

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