519 research outputs found
Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings
We formulate an adiabatic theorem adapted to models that present an
instantaneous eigenvalue experiencing an infinite number of crossings with the
rest of the spectrum. We give an upper bound on the leading correction terms
with respect to the adiabatic limit. The result requires only differentiability
of the considered spectral projector, and some geometric hypothesis on the
local behaviour of the eigenvalues at the crossings
Abstract adiabatic charge pumping
This paper is devoted to the analysis of an abstract formula describing
quantum adiabatic charge pumping in a general context. We consider closed
systems characterized by a slowly varying time-dependent Hamiltonian depending
on an external parameter . The current operator, defined as the
derivative of the Hamiltonian with respect to , once integrated over
some time interval, gives rise to a charge pumped through the system over that
time span. We determine the first two leading terms in the adiabatic parameter
of this pumped charge under the usual gap hypothesis. In particular, in case
the Hamiltonian is time periodic and has discrete non-degenerate spectrum, the
charge pumped over a period is given to leading order by the derivative with
respect to of the corresponding dynamical and geometric phases
Non-abelian superconducting pumps
Cooper pair pumping is a coherent process. We derive a general expression for
the adiabatic pumped charge in superconducting nanocircuits in the presence of
level degeneracy and relate it to non-Abelian holonomies of Wilczek and Zee. We
discuss an experimental system where the non-Abelian structure of the adiabatic
evolution manifests in the pumped charge.Comment: 5 pages, 3 figure
Smooth adiabatic evolutions with leaky power tails
Adiabatic evolutions with a gap condition have, under a range of
circumstances, exponentially small tails that describe the leaking out of the
spectral subspace. Adiabatic evolutions without a gap condition do not seem to
have this feature in general. This is a known fact for eigenvalue crossing. We
show that this is also the case for eigenvalues at the threshold of the
continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure
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
Superadiabatic transitions in quantum molecular dynamics
We study the dynamics of a molecule’s nuclear wave function near an avoided crossing of two electronic energy levels for one nuclear degree of freedom. We derive the general form of the Schrödinger equation in the nth superadiabatic representation for all n є N. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace when a wave packet travels through the transition region. In the optimal superadiabatic representation, which we define, this component builds up monotonically. Finally, we give an explicit formula for the transition wave function away from the avoided crossing, which is in excellent agreement with high-precision numerical calculations
Localization Properties of the Chalker-Coddington Model
The Chalker Coddington quantum network percolation model is numerically
pertinent to the understanding of the delocalization transition of the quantum
Hall effect. We study the model restricted to a cylinder of perimeter 2M. We
prove firstly that the Lyapunov exponents are simple and in particular that the
localization length is finite; secondly that this implies spectral
localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov
exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the
Lyapunov spectrum and finiteness of the localization length are proven. To
appear in Annales Henri Poincar
Fetal sex and the relative reactivity of human umbilical vein and arteries are key determinants in potential beneficial effects of phosphodiesterase inhibitors.
Intrauterine growth restriction (IUGR) is a common complication of pregnancy. We previously demonstrated that IUGR is associated with an impaired nitric oxide (NO)-induced relaxation in the human umbilical vein (HUV) of growth-restricted females compared to appropriate for gestational age (AGA) newborns. We found that phosphodiesterase (PDE) inhibition improved NO-induced relaxation in HUV, suggesting that PDEs could represent promising targets for therapeutic intervention. This study aimed to investigate the effects of PDE inhibition on human umbilical arteries (HUAs) compared to HUV. Umbilical vessels were collected in IUGR and AGA term newborns. NO-induced relaxation was studied using isolated vessel tension experiments in the presence or absence of the nonspecific PDE inhibitor 3-isobutyl-1-methylxanthine (IBMX). PDE1B, PDE1C, PDE3A, PDE4B, and PDE5A were investigated by Western blot. NO-induced vasodilation was similar between IUGR and AGA HUAs. In HUAs precontracted with serotonin, IBMX enhanced NO-induced relaxation only in IUGR females, whereas in HUV IBMX increased NO-induced relaxation in all groups except IUGR males. In umbilical vessels preconstricted with the thromboxane A2 analog U46619, IBMX improved NO-induced relaxation in all groups to a greater extent in HUV than HUAs. However, the PDE protein content was higher in HUAs than HUV in all study groups. Therefore, the effects of PDE inhibition depend on the presence of IUGR, fetal sex, vessel type, and vasoconstrictors implicated. Despite a higher PDE protein content, HUAs are less sensitive to IBMX than HUV, which could lead to adverse effects of PDE inhibition in vivo by impairment of the fetoplacental hemodynamics.NEW & NOTEWORTHY The effects of phosphodiesterase inhibition on the umbilical circulation depend on the presence of intrauterine growth restriction, the fetal sex, vessel type, and vasoconstrictors implicated. The human umbilical vascular tone regulation is complex and depends on the amount and activity of specific proteins but also probably on the subcellular organization mediating protein interactions. Therefore, therapeutic interventions using phosphodiesterase inhibitors to improve the placental-fetal circulation should consider fetal sex and both umbilical vein and artery reactivity
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
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