Jiri's Home Page


My name is Jiri Vanicek (or Jirka). I am a Ph.D. student of physics and specialize in semiclassical physics and quantum chaos. Presently I am working on semiclassical approaches to evaluating quantum fidelity (Loschmidt echo). Other areas of my interest are mesoscopic and atomic physics. I have worked on problems of photodissocation of carbon dioxide, uniformization of a full homoclinic tangle, quasiresonant energy transfer in adiabatic atom-diatom collisions. I also studied generalizations of semiclassical methods in situations where usual stationary-phase approximations or even standard (e.g., Airy) uniformizations fail.


Publications

Jiri Vanicek and Eric J. Heller
Semiclassical evaluation of fidelity in the Fermi-golden-rule and Lyapunov regimes
[preprint at quant-ph/0302192 ]

We present a numerically feasible semiclassical (SC) method to evaluate fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Remarkably, it also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than a post facto comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation (CPA) and show that within this approximation,``diagonal approximation'' of Jalabert and Pastawski [1] is automatic and does not require ensemble averaging.


Jiri Vanicek and Doron Cohen
Survival probability and the local density of states for one-dimensional Hamiltonian systems
[preprint at quant-ph/0303103 ]

For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes, and to the observation that semiclassical tools are useful in the latter case. We discuss what is "left" from this theory in the case of one-dimensional systems. We demonstrate that the remarkably accurate uniform semiclassical approximation captures the physics of all the different regimes, though it cannot take into account the effect of strong localization.


Jiri Vanicek and Eric J. Heller
Uniform semiclassical wave function for coherent two-dimensional electron flow
[ Phys. Rev. E 67, 016211 (2003) , preprint at nlin.CD/0209001 ]

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.


Jiri Vanicek and Eric J. Heller
Replacement manifolds: A method to uniformize semiclassical wave functions
[ Phys. Rev. E 64, 026215 (2001) , preprint at nlin.CD/0101055 ]

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.


Maxim Ol'shanii, Jiri Vanicek and Mara Prentiss
Atomic beamsplitter based on multiple adiabatic passage in the optical interference pattern
[ Quantum Semiclass. Opt. 8, 655 (1996) ]

We describe a simple and robust method of creating an efficient large-angle adiabatic passage beamsplitter that does not require the light fields to be pulsed. We present simulations that show momentum splittings of , where more than 60% of the atoms in the initial distribution are in the final momentum peaks at $\pm 40 \hbar k$.


You can contact me at jiri@tsunami.harvard.edu.