35 research outputs found
Transport properties of continuous-time quantum walks on Sierpinski fractals
We model quantum transport, described by continuous-time quantum walks
(CTQW), on deterministic Sierpinski fractals, differentiating between
Sierpinski gaskets and Sierpinski carpets, along with their dual structures.
The transport efficiencies are defined in terms of the exact and the average
return probabilities, as well as by the mean survival probability when
absorbing traps are present. In the case of gaskets, localization can be
identified already for small networks (generations). For carpets, our numerical
results indicate a trend towards localization, but only for relatively large
structures. The comparison of gaskets and carpets further implies that,
distinct from the corresponding classical continuous-time random walk, the
spectral dimension does not fully determine the evolution of the CTQW.Comment: 10 pages, 6 figure
Slow transport by continuous time quantum walks
Continuous time quantum walks (CTQW) do not necessarily perform better than
their classical counterparts, the continuous time random walks (CTRW). For one
special graph, where a recent analysis showed that in a particular direction of
propagation the penetration of the graph is faster by CTQWs than by CTRWs, we
demonstrate that in another direction of propagation the opposite is true; In
this case a CTQW initially localized at one site displays a slow transport. We
furthermore show that when the CTQW's initial condition is a totally symmetric
superposition of states of equivalent sites, the transport gets to be much more
rapid.Comment: 5 pages, 7 figures, accepted for publication in Phys. Rev.
Slow Excitation Trapping in Quantum Transport with Long-Range Interactions
Long-range interactions slow down the excitation trapping in quantum
transport processes on a one-dimensional chain with traps at both ends. This is
counter intuitive and in contrast to the corresponding classical processes with
long-range interactions, which lead to faster excitation trapping. We give a
pertubation theoretical explanation of this effect.Comment: 4 pages, 3 figure
Dissipative Dynamics with Trapping in Dimers
The trapping of excitations in systems coupled to an environment allows to
study the quantum to classical crossover by different means. We show how to
combine the phenomenological description by a non-hermitian Liouville-von
Neumann Equation (LvNE) approach with the numerically exact path integral
Monte-Carlo (PIMC) method, and exemplify our results for a system of two
coupled two-level systems. By varying the strength of the coupling to the
environment we are able to estimate the parameter range in which the LvNE
approach yields satisfactory results. Moreover, by matching the PIMC results
with the LvNE calculations we have a powerful tool to extrapolate the
numerically exact PIMC method to long times.Comment: 5 pages, 2 figure
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
Quantum transport on small-world networks: A continuous-time quantum walk approach
We consider the quantum mechanical transport of (coherent) excitons on
small-world networks (SWN). The SWN are build from a one-dimensional ring of N
nodes by randomly introducing B additional bonds between them. The exciton
dynamics is modeled by continuous-time quantum walks and we evaluate
numerically the ensemble averaged transition probability to reach any node of
the network from the initially excited one. For sufficiently large B we find
that the quantum mechanical transport through the SWN is, first, very fast,
given that the limiting value of the transition probability is reached very
quickly; second, that the transport does not lead to equipartition, given that
on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request
The Origins of Phase Transitions in Small Systems
The identification and classification of phases in small systems, e.g.
nuclei, social and financial networks, clusters, and biological systems, where
the traditional definitions of phase transitions are not applicable, is
important to obtain a deeper understanding of the phenomena observed in such
systems. Within a simple statistical model we investigate the validity and
applicability of different classification schemes for phase transtions in small
systems. We show that the whole complex temperature plane contains necessary
information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see
http://www.smallsystems.d
Deceptive signals of phase transitions in small magnetic clusters
We present an analysis of the thermodynamic properties of small transition
metal clusters and show how the commonly used indicators of phase transitions
like peaks in the specific heat or magnetic susceptibility can lead to
deceptive interpretations of the underlying physics. The analysis of the
distribution of zeros of the canonical partition function in the whole complex
temperature plane reveals the nature of the transition. We show that signals in
the magnetic susceptibility at positive temperatures have their origin at zeros
lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see
http://www.smallsystems.d
Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
This paper reviews recent advances in continuous-time quantum walks (CTQW)
and their application to transport in various systems. The introduction gives a
brief survey of the historical background of CTQW. After a short outline of the
theoretical ideas behind CTQW and of its relation to classical continuous-time
random walks (CTRW) in Sec.~2, implications for the efficiency of the transport
are presented in Sec.~3. The fourth section gives an overview of different
types of networks on which CTQW have been studied so far. Extensions of CTQW to
systems with long-range interactions and with static disorder are discussed in
section V. Systems with traps, i.e., systems in which the walker's probability
to remain inside the system is not conserved, are presented in section IV.
Relations to similar approaches to the transport are studied in section VII.
The paper closes with an outlook on possible future directions.Comment: review article to appear in Physics Reports, 39 pages, 44 figure
Quantum transport on two-dimensional regular graphs
We study the quantum-mechanical transport on two-dimensional graphs by means
of continuous-time quantum walks and analyse the effect of different boundary
conditions (BCs). For periodic BCs in both directions, i.e., for tori, the
problem can be treated in a large measure analytically. Some of these results
carry over to graphs which obey open boundary conditions (OBCs), such as
cylinders or rectangles. Under OBCs the long time transition probabilities
(LPs) also display asymmetries for certain graphs, as a function of their
particular sizes. Interestingly, these effects do not show up in the marginal
distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.