2,758 research outputs found
Continuous-Time Quantum Walks and Trapping
Recent findings suggest that processes such as the electronic energy transfer
through the photosynthetic antenna display quantal features, aspects known from
the dynamics of charge carriers along polymer backbones. Hence, in modeling
energy transfer one has to leave the classical, master-equation-type formalism
and advance towards an increasingly quantum-mechanical picture, while still
retaining a local description of the complex network of molecules involved in
the transport, say through a tight-binding approach.
Interestingly, the continuous time random walk (CTRW) picture, widely
employed in describing transport in random environments, can be mathematically
reformulated to yield a quantum-mechanical Hamiltonian of tight-binding type;
the procedure uses the mathematical analogies between time-evolution operators
in statistical and in quantum mechanics: The result are continuous-time quantum
walks (CTQWs). However, beyond these formal analogies, CTRWs and CTQWs display
vastly different physical properties. In particular, here we focus on trapping
processes on a ring and show, both analytically and numerically, that distinct
configurations of traps (ranging from periodical to random) yield strongly
different behaviours for the quantal mean survival probability, while
classically (under ordered conditions) we always find an exponential decay at
long times.Comment: 8 pages, 6 figures; to be published in International Journal of
Bifurcation and Chao
Survival of classical and quantum particles in the presence of traps
We present a detailed comparison of the motion of a classical and of a
quantum particle in the presence of trapping sites, within the framework of
continuous-time classical and quantum random walk. The main emphasis is on the
qualitative differences in the temporal behavior of the survival probabilities
of both kinds of particles. As a general rule, static traps are far less
efficient to absorb quantum particles than classical ones. Several lattice
geometries are successively considered: an infinite chain with a single trap, a
finite ring with a single trap, a finite ring with several traps, and an
infinite chain and a higher-dimensional lattice with a random distribution of
traps with a given density. For the latter disordered systems, the classical
and the quantum survival probabilities obey a stretched exponential asymptotic
decay, albeit with different exponents. These results confirm earlier
predictions, and the corresponding amplitudes are evaluated. In the
one-dimensional geometry of the infinite chain, we obtain a full analytical
prediction for the amplitude of the quantum problem, including its dependence
on the trap density and strength.Comment: 35 pages, 10 figures, 2 tables. Minor update
One- and two-dimensional quantum walks in arrays of optical traps
We propose a novel implementation of discrete time quantum walks for a
neutral atom in an array of optical microtraps or an optical lattice. We
analyze a one-dimensional walk in position space, with the coin, the additional
qubit degree of freedom that controls the displacement of the quantum walker,
implemented as a spatially delocalized qubit, i.e., the coin is also encoded in
position space. We analyze the dependence of the quantum walk on temperature
and experimental imperfections as shaking in the trap positions. Finally,
combining a spatially delocalized qubit and a hyperfine qubit, we also give a
scheme to realize a quantum walk on a two-dimensional square lattice with the
possibility of implementing different coin operators.Comment: 10 pages, 8 figures; v2: some comments added and other minor change
Coined quantum walks on percolation graphs
Quantum walks, both discrete (coined) and continuous time, form the basis of
several quantum algorithms and have been used to model processes such as
transport in spin chains and quantum chemistry. The enhanced spreading and
mixing properties of quantum walks compared with their classical counterparts
have been well-studied on regular structures and also shown to be sensitive to
defects and imperfections in the lattice. As a simple example of a disordered
system, we consider percolation lattices, in which edges or sites are randomly
missing, interrupting the progress of the quantum walk. We use numerical
simulation to study the properties of coined quantum walks on these percolation
lattices in one and two dimensions. In one dimension (the line) we introduce a
simple notion of quantum tunneling and determine how this affects the
properties of the quantum walk as it spreads. On two-dimensional percolation
lattices, we show how the spreading rate varies from linear in the number of
steps down to zero, as the percolation probability decreases to the critical
point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after
referee comments, added extra figur
Limits of quantum speedup in photosynthetic light harvesting
It has been suggested that excitation transport in photosynthetic light
harvesting complexes features speedups analogous to those found in quantum
algorithms. Here we compare the dynamics in these light harvesting systems to
the dynamics of quantum walks, in order to elucidate the limits of such quantum
speedups. For the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria,
we show that while there is indeed speedup at short times, this is short lived
(70 fs) despite longer lived (ps) quantum coherence. Remarkably, this time
scale is independent of the details of the decoherence model. More generally,
we show that the distinguishing features of light-harvesting complexes not only
limit the extent of quantum speedup but also reduce rates of diffusive
transport. These results suggest that quantum coherent effects in biological
systems are optimized for efficiency or robustness rather than the more elusive
goal of quantum speedup.Comment: 9 pages, 6 figures. To appear in New Journal Physics, special issue
on "Quantum Effects and Noise in Biomolecules." Updated to accepted versio
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