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 $\alpha$. The current operator, defined as the derivative of the Hamiltonian with respect to $\alpha$, 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 $\alpha$ 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 $\Z^d$ 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 $\Z^d$ 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 $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, 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 $\Z^d$ 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 $\Z^d$ 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