1,577 research outputs found
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
The Effects of Additives on the Physical Properties of Electroformed Nickel and on the Stretch of Photoelectroformed Nickel Components
The process of nickel electroforming is becoming increasingly important in
the manufacture of MST products, as it has the potential to replicate complex
geometries with extremely high fidelity. Electroforming of nickel uses
multi-component electrolyte formulations in order to maximise desirable product
properties. In addition to nickel sulphamate (the major electrolyte component),
formulation additives can also comprise nickel chloride (to increase nickel
anode dissolution), sulphamic acid (to control pH), boric acid (to act as a pH
buffer), hardening/levelling agents (to increase deposit hardness and lustre)
and wetting agents (to aid surface wetting and thus prevent gas bubbles and
void formation). This paper investigates the effects of some of these variables
on internal stress and stretch as a function of applied current density.Comment: Submitted on behalf of TIMA Editions
(http://irevues.inist.fr/tima-editions
Curved planar quantum wires with Dirichlet and Neumann boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional curved strip. We impose the Dirichlet
and Neumann boundary conditions on opposite sides of the strip. The existence
of the discrete eigenvalue below the essential spectrum threshold depends on
the sign of the total bending angle for the asymptotically straight strips.Comment: 7 page
Bound States in Mildly Curved Layers
It has been shown recently that a nonrelativistic quantum particle
constrained to a hard-wall layer of constant width built over a geodesically
complete simply connected noncompact curved surface can have bound states
provided the surface is not a plane. In this paper we study the weak-coupling
asymptotics of these bound states, i.e. the situation when the surface is a
mildly curved plane. Under suitable assumptions about regularity and decay of
surface curvatures we derive the leading order in the ground-state eigenvalue
expansion. The argument is based on Birman-Schwinger analysis of Schroedinger
operators in a planar hard-wall layer.Comment: LaTeX 2e, 23 page
A constant of quantum motion in two dimensions in crossed magnetic and electric fields
We consider the quantum dynamics of a single particle in the plane under the
influence of a constant perpendicular magnetic and a crossed electric potential
field. For a class of smooth and small potentials we construct a non-trivial
invariant of motion. Do to so we proof that the Hamiltonian is unitarily
equivalent to an effective Hamiltonian which commutes with the observable of
kinetic energy.Comment: 18 pages, 2 figures; the title was changed and several typos
corrected; to appear in J. Phys. A: Math. Theor. 43 (2010
On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum
of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha,
with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay
as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously
differentiable in the strong sense and such that the matrix entries with
respect to the spectral decomposition of H obey the estimate
|V(t)_{m,n}|0,
p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be
arbitrarily small provided p is sufficiently large and \epsilon is small
enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the
diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where
\sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the
Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was
discussed earlier in the literature by Howland
Pulse-driven quantum dynamics beyond the impulsive regime
We review various unitary time-dependent perturbation theories and compare
them formally and numerically. We show that the Kolmogorov-Arnold-Moser
technique performs better owing to both the superexponential character of
correction terms and the possibility to optimize the accuracy of a given level
of approximation which is explored in details here. As an illustration, we
consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure
H^+_2$ in a strong magnetic field described via a solvable model
We consider the hydrogen molecular ion in the presence of a strong
homogeneous magnetic field. In this regime, the effective Hamiltonian is almost
one dimensional with a potential energy which looks like a sum of two Dirac
delta functions. This model is solvable, but not close enough to our exact
Hamiltonian for relevant strenght of the magnnetic field. However we show that
the correct values of the equilibrium distance as well as the binding energy of
the ground state of the ion, can be obtained when incorporating perturbative
corrections up to second order. Finally, we show that exists for
sufficiently large magnetic fields
H2 molecule in strong magnetic fields
The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant
magnetic field is asymptotic, in norm-resolvent sense, to an effective
Hamiltonian which has the form of a multi-particle Schr\"odinger operator with
interactions given by one-dimensional \delta-potentials. We study this
effective Hamiltonian in the case of the H2 -molecule and establish existence
of the ground state. We also show that the inter-nuclear equilibrium distance
tends to 0 as the field-strength tends to infinity
Bound states in straight quantum waveguides with combined boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional straight strip. We impose the combined
Dirichlet and Neumann boundary conditions on different parts of the boundary.
Several statements on the existence or the absence of the discrete spectrum are
proven for two models with combined boundary conditions. Examples of
eigenfunctions and eigenvalues are computed numerically.Comment: 24 pages, LaTeX 2e with 4 eps figure
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