25,156 research outputs found
Efficient Diagonalization of Kicked Quantum Systems
We show that the time evolution operator of kicked quantum systems, although
a full matrix of size NxN, can be diagonalized with the help of a new method
based on a suitable combination of fast Fourier transform and Lanczos algorithm
in just N^2 ln(N) operations. It allows the diagonalization of matrizes of
sizes up to N\approx 10^6 going far beyond the possibilities of standard
diagonalization techniques which need O(N^3) operations. We have applied this
method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages
RevTex, 1 figur
The possibility of a metal insulator transition in antidot arrays induced by an external driving
It is shown that a family of models associated with the kicked Harper model
is relevant for cyclotron resonance experiments in an antidot array. For this
purpose a simplified model for electronic motion in a related model system in
presence of a magnetic field and an AC electric field is developed. In the
limit of strong magnetic field it reduces to a model similar to the kicked
Harper model. This model is studied numerically and is found to be extremely
sensitive to the strength of the electric field. In particular, as the strength
of the electric field is varied a metal -- insulator transition may be found.
The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p
Quantized Orbits and Resonant Transport
A tight binding representation of the kicked Harper model is used to obtain
an integrable semiclassical Hamiltonian consisting of degenerate "quantized"
orbits. New orbits appear when renormalized Harper parameters cross integer
multiples of . Commensurability relations between the orbit frequencies
are shown to correlate with the emergence of accelerator modes in the classical
phase space of the original kicked problem. The signature of this resonant
transport is seen in both classical and quantum behavior. An important feature
of our analysis is the emergence of a natural scaling relating classical and
quantum couplings which is necessary for establishing correspondence.Comment: REVTEX document - 8 pages + 3 postscript figures. Submitted to
Phys.Rev.Let
Quantum Computation of a Complex System : the Kicked Harper Model
The simulation of complex quantum systems on a quantum computer is studied,
taking the kicked Harper model as an example. This well-studied system has a
rich variety of dynamical behavior depending on parameters, displays
interesting phenomena such as fractal spectra, mixed phase space, dynamical
localization, anomalous diffusion, or partial delocalization, and can describe
electrons in a magnetic field. Three different quantum algorithms are presented
and analyzed, enabling to simulate efficiently the evolution operator of this
system with different precision using different resources. Depending on the
parameters chosen, the system is near-integrable, localized, or partially
delocalized. In each case we identify transport or spectral quantities which
can be obtained more efficiently on a quantum computer than on a classical one.
In most cases, a polynomial gain compared to classical algorithms is obtained,
which can be quadratic or less depending on the parameter regime. We also
present the effects of static imperfections on the quantities selected, and
show that depending on the regime of parameters, very different behaviors are
observed. Some quantities can be obtained reliably with moderate levels of
imperfection, whereas others are exponentially sensitive to imperfection
strength. In particular, the imperfection threshold for delocalization becomes
exponentially small in the partially delocalized regime. Our results show that
interesting behavior can be observed with as little as 7-8 qubits, and can be
reliably measured in presence of moderate levels of internal imperfections
Proposal of a cold-atom realization of quantum maps with Hofstadter's butterfly spectrum
Quantum systems with Hofstadter's butterfly spectrum are of fundamental interest to many research areas. Based upon slight modifications of existing cold-atom experiments, a cold-atom realization of quantum maps with Hofstadter's butterfly spectrum is proposed. Connections and differences between our realization and the kicked Harper model are identified. This work also exposes, for the first time, a simple connection between the kicked Harper model and the kicked rotor model, the two paradigms of classical and quantum chaos
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