On the dynamics created by a time--dependent Aharonov-Bohm flux

We study the dynamics of classical and quantum particles moving in a punctured plane under the influence of a homogeneous magnetic field and driven by a time-dependent singular flux tube through the hole

Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical Physic

Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux

We study the dynamics of a classical particle moving in a punctured plane under the influence of a strong homogeneous magnetic field, an electrical background, and driven by a time-dependent singular flux tube through the hole. We exhibit a striking classical (de)localization effect: in the far past the trajectories are spirals around a bound center; the particle moves inward towards the flux tube loosing kinetic energy. After hitting the puncture it becomes ``conducting'': the motion is a cycloid around a center whose drift is outgoing, orthogonal to the electric field, diffusive, and without energy loss

Weakly regular Floquet Hamiltonians with pure point spectrum

We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on the parameter omega. We assume that the spectrum of H is discrete, {h_m (m = 1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m - h_n)^(-sigma) < infinity where mu_{mn} = sqrt(min{M_m,M_n)) M_m M_n. We show that in that case there exist a suitable norm to measure the regularity of V, denoted epsilon, and positive constants, epsilon_* & delta_*, such that: if epsilon |Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure point spectrum for all omega in Omega_infinity.Comment: 35 pages, Latex with AmsAr

On the harmonic oscillator on the Lobachevsky plane

We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential $V(r)=(a^2\omega^2/4)sinh(r/a)^2$ where $a$ is the curvature radius and $r$ is the geodesic distance from a fixed center. Thus the potential is rotationally symmetric and unbounded likewise as in the Euclidean case. The eigenvalue equation leads to the differential equation of spheroidal functions. We provide a basic numerical analysis of eigenvalues and eigenfunctions in the case when the value of the angular momentum, $m$, equals 0.Comment: to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler

Stem cell bioprocessing: The bioengineering of lung epithelium in 3D from embryonic stem cells

Stem cell therapies and tissue engineering strategies are required for the clinical treatment of respiratory diseases. Previous studies have established protocols for the differentiation of airway epithelium from stem cells but have involved costly and laborious culture methods. The aim of this thesis was to achieve efficient and reproducible maintenance and differentiation of embryonic stem cells to airway epithelium, in 2D and 3D culture, by developing appropriate bioprocessing technology. Firstly, the 2D differentiation process of human and murine ES cells into pulmonary epithelial cells was addressed. The main finding in was that the proportion of type II pneumocytes, the major epithelial component of the gas-exchange area of lung, differentiated with this method was higher than that obtained in previous sudies, 33% of resultant cell expressed the specific marker surfactant protein C (SPC) compared with up to 10%. Secondly, the maintenance and differentiation was carried out in 3D. A protocol was devised that maintained undifferentiated human ES cells in culture for more than 200 days encapsulated in alginate without any feeder layer or growth factors. For ES cell differentiation in 3D, a method was devised to provide a relatively cheap and simple means of culture and use medium conditioned by a human pneumocyte tumour cell line (A549). The differentiation of human and murine ES cells into pulmonary epithelial cells, particularly type II pneumocytes, was found to be upregulated by culture in this conditioned medium, with or without embryoid body formation. The third step was to test whether this differentiation protocol was amenable to scale-up and automation in a bioreactor using cell encapsulation. It was possible to show that encapsulated murine ES cells cultured in static, co-culture or rotating wall bioreactor (HARV) systems, differentiate into endoderm and, predominantly, type I and II pneumocytes. Flow cytometry revealed that the mean yield of differentiated type II pneumocytes was around 50% at day 10 of cultivation. The final stage of the work was to design and produce a perfusion system airlift bioreactor to mimic the pulmonary microenvironment in order to achieve large scale production of biologically functional tissue. The results of these studies thus provide new protocols for the maintenance of ES cells and their differentiation towards pulmonary phenotypes that are relatively simple and cheap and can be applied in bioreactor systems that provide for the kind of scale up of differentiated cell production needed for future clinical applications

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories

Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry

We consider an invariant quantum Hamiltonian $H=-\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a countable discrete symmetry group $\Gamma$. Typically, $\tilde{M}$ is the universal covering space of a multiply connected Riemannian manifold $M$ and $\Gamma$ is the fundamental group of $M$. On the one hand, following the basic step of the Bloch analysis, one decomposes the $L^{2}$ space over $\tilde{M}$ into a direct integral of Hilbert spaces formed by equivariant functions on $\tilde{M}$. The Hamiltonian $H$ decomposes correspondingly, with each component $H_{\Lambda}$ being defined by a quasi-periodic boundary condition. The quasi-periodic boundary conditions are in turn determined by irreducible unitary representations $\Lambda$ of $\Gamma$. On the other hand, fixing a quasi-periodic boundary condition (i.e., a unitary representation $\Lambda$ of $\Gamma$) one can express the corresponding propagator in terms of the propagator associated to the Hamiltonian $H$. We discuss these procedures in detail and show that in a sense they are mutually inverse

Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit

We show that for any Hilbert-space dimension, the optimal universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states whose states are related by generalized phase-space displacements.Comment: 10 revtex pages, no figure