379 research outputs found
Correlated Markov Quantum Walks
We consider the discrete time unitary dynamics given by a quantum walk on
performed by a particle with internal degree of freedom, called coin
state, according to the following iterated rule: a unitary update of the coin
state takes place, followed by a shift on the lattice, conditioned on the coin
state of the particle. We study the large time behavior of the quantum
mechanical probability distribution of the position observable in for
random updates of the coin states of the following form. The random sequences
of unitary updates are given by a site dependent function of a Markov chain in
time, with the following properties: on each site, they share the same
stationnary Markovian distribution and, for each fixed time, they form a
deterministic periodic pattern on the lattice.
We prove a Feynman-Kac formula to express the characteristic function of the
averaged distribution over the randomness at time in terms of the nth power
of an operator . By analyzing the spectrum of , we show that this
distribution posesses a drift proportional to the time and its centered
counterpart displays a diffusive behavior with a diffusion matrix we compute.
Moderate and large deviations principles are also proven to hold for the
averaged distribution and the limit of the suitably rescaled corresponding
characteristic function is shown to satisfy a diffusion equation.
An example of random updates for which the analysis of the distribution can
be performed without averaging is worked out. The random distribution displays
a deterministic drift proportional to time and its centered counterpart gives
rise to a random diffusion matrix whose law we compute. We complete the picture
by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with
arXiv:1010.400
Continuous deformations of the Grover walk preserving localization
The three-state Grover walk on a line exhibits the localization effect
characterized by a non-vanishing probability of the particle to stay at the
origin. We present two continuous deformations of the Grover walk which
preserve its localization nature. The resulting quantum walks differ in the
rate at which they spread through the lattice. The velocities of the left and
right-traveling probability peaks are given by the maximum of the group
velocity. We find the explicit form of peak velocities in dependence on the
coin parameter. Our results show that localization of the quantum walk is not a
singular property of an isolated coin operator but can be found for entire
families of coins
Localization of the Grover walks on spidernets and free Meixner laws
A spidernet is a graph obtained by adding large cycles to an almost regular
tree and considered as an example having intermediate properties of lattices
and trees in the study of discrete-time quantum walks on graphs. We introduce
the Grover walk on a spidernet and its one-dimensional reduction. We derive an
integral representation of the -step transition amplitude in terms of the
free Meixner law which appears as the spectral distribution. As an application
we determine the class of spidernets which exhibit localization. Our method is
based on quantum probabilistic spectral analysis of graphs.Comment: 32 page
Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing
In an adiabatic rapid passage experiment, the Bloch vector of a two-level
system (qubit) is inverted by slowly inverting an external field to which it is
coupled, and along which it is initially aligned. In twisted rapid passage, the
external field is allowed to twist around its initial direction with azimuthal
angle at the same time that it is inverted. For polynomial twist:
. We show that for , multiple avoided crossings
can occur during the inversion of the external field, and that these crossings
give rise to strong interference effects in the qubit transition probability.
The transition probability is found to be a function of the twist strength ,
which can be used to control the time-separation of the avoided crossings, and
hence the character of the interference. Constructive and destructive
interference are possible. The interference effects are a consequence of the
temporal phase coherence of the wavefunction. The ability to vary this
coherence by varying the temporal separation of the avoided crossings renders
twisted rapid passage with adjustable twist strength into a temporal
interferometer through which qubit transitions can be greatly enhanced or
suppressed. Possible application of this interference mechanism to construction
of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
Random Time-Dependent Quantum Walks
We consider the discrete time unitary dynamics given by a quantum walk on the
lattice performed by a quantum particle with internal degree of freedom,
called coin state, according to the following iterated rule: a unitary update
of the coin state takes place, followed by a shift on the lattice, conditioned
on the coin state of the particle. We study the large time behavior of the
quantum mechanical probability distribution of the position observable in
when the sequence of unitary updates is given by an i.i.d. sequence of
random matrices. When averaged over the randomness, this distribution is shown
to display a drift proportional to the time and its centered counterpart is
shown to display a diffusive behavior with a diffusion matrix we compute. A
moderate deviation principle is also proven to hold for the averaged
distribution and the limit of the suitably rescaled corresponding
characteristic function is shown to satisfy a diffusion equation. A
generalization to unitary updates distributed according to a Markov process is
also provided. An example of i.i.d. random updates for which the analysis of
the distribution can be performed without averaging is worked out. The
distribution also displays a deterministic drift proportional to time and its
centered counterpart gives rise to a random diffusion matrix whose law we
compute. A large deviation principle is shown to hold for this example. We
finally show that, in general, the expectation of the random diffusion matrix
equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in
Mathematical Physic
Detecting early myocardial ischemia in rat heart by MALDI imaging mass spectrometry.
Diagnostics of myocardial infarction in human post-mortem hearts can be achieved only if ischemia persisted for at least 6-12 h when certain morphological changes appear in myocardium. The initial 4 h of ischemia is difficult to diagnose due to lack of a standardized method. Developing a panel of molecular tissue markers is a promising approach and can be accelerated by characterization of molecular changes. This study is the first untargeted metabolomic profiling of ischemic myocardium during the initial 4 h directly from tissue section. Ischemic hearts from an ex-vivo Langendorff model were analysed using matrix assisted laser desorption/ionization imaging mass spectrometry (MALDI IMS) at 15 min, 30 min, 1 h, 2 h, and 4 h. Region-specific molecular changes were identified even in absence of evident histological lesions and were segregated by unsupervised cluster analysis. Significantly differentially expressed features were detected by multivariate analysis starting at 15 min while their number increased with prolonged ischemia. The biggest significant increase at 15 min was observed for m/z 682.1294 (likely corresponding to S-NADHX-a damage product of nicotinamide adenine dinucleotide (NADH)). Based on the previously reported role of NAD <sup>+</sup> /NADH ratio in regulating localization of the sodium channel (Na <sub>v</sub> 1.5) at the plasma membrane, Na <sub>v</sub> 1.5 was evaluated by immunofluorescence. As expected, a fainter signal was observed at the plasma membrane in the predicted ischemic region starting 30 min of ischemia and the change became the most pronounced by 4 h. Metabolomic changes occur early during ischemia, can assist in identifying markers for post-mortem diagnostics and improve understanding of molecular mechanisms
Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder
We consider an electron constrained to move on a surface with revolution
symmetry in the presence of a constant magnetic field parallel to the
surface axis. Depending on and the surface geometry the transverse part of
the spectrum typically exhibits many crossings which change to avoided
crossings if a weak symmetry breaking interaction is introduced. We study the
effect of such perturbations on the quantum propagation. This problem admits a
natural reformulation to which tools from molecular dynamics can be applied. In
turn, this leads to the study of a perturbation theory for the time dependent
Born-Oppenheimer approximation
Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
Quantum walks subject to decoherence generically suffer the loss of their
genuine quantum feature, a quadratically faster spreading compared to classical
random walks. This intuitive statement has been verified analytically for
certain models and is also supported by numerical studies of a variety of
examples. In this paper we analyze the long-time behavior of a particular class
of decoherent quantum walks, which, to the best of our knowledge, was only
studied at the level of numerical simulations before. We consider a local coin
operation which is randomly and independently chosen for each time step and
each lattice site and prove that, under rather mild conditions, this leads to
classical behavior: With the same scaling as needed for a classical diffusion
the position distribution converges to a Gaussian, which is independent of the
initial state. Our method is based on non-degenerate perturbation theory and
yields an explicit expression for the covariance matrix of the asymptotic
Gaussian in terms of the randomness parameters
Dissipation and Decoherence in Nanodevices: a Generalized Fermi's Golden Rule
We shall revisit the conventional adiabatic or Markov approximation, which
--contrary to the semiclassical case-- does not preserve the positive-definite
character of the corresponding density matrix, thus leading to highly
non-physical results. To overcome this serious limitation, originally pointed
out and partially solved by Davies and co-workers almost three decades ago, we
shall propose an alternative more general adiabatic procedure, which (i) is
physically justified under the same validity restrictions of the conventional
Markov approach, (ii) in the semiclassical limit reduces to the standard
Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus
providing a reliable/robust treatment of energy-dissipation and dephasing
processes in electronic quantum devices. Unlike standard master-equation
formulations, the dependence of our approximation on the specific choice of the
subsystem (that include the common partial trace reduction) does not threaten
positivity, and quantum scattering rates are well defined even in case the
subsystem is infinitely extended/has continuous spectrum.Comment: 6 pages, 0 figure
- …