1,404 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
Fast Decoders for Topological Quantum Codes
We present a family of algorithms, combining real-space renormalization
methods and belief propagation, to estimate the free energy of a topologically
ordered system in the presence of defects. Such an algorithm is needed to
preserve the quantum information stored in the ground space of a topologically
ordered system and to decode topological error-correcting codes. For a system
of linear size L, our algorithm runs in time log L compared to L^6 needed for
the minimum-weight perfect matching algorithm previously used in this context
and achieves a higher depolarizing error threshold.Comment: 4 pages, 4 figure
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
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
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
Universal topological phase of 2D stabilizer codes
Two topological phases are equivalent if they are connected by a local
unitary transformation. In this sense, classifying topological phases amounts
to classifying long-range entanglement patterns. We show that all 2D
topological stabilizer codes are equivalent to several copies of one universal
phase: Kitaev's topological code. Error correction benefits from the
corresponding local mappings.Comment: 4 pages, 3 figure
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
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
Emergence of a confined state in a weakly bent wire
In this paper we use a simple straightforward technique to investigate the
emergence of a bound state in a weakly bent wire. We show that the bend behaves
like an infinitely shallow potential well, and in the limit of small bending
angle and low energy the bend can be presented by a simple 1D delta function
potential.Comment: 4 pages, 3 Postscript figures (uses Revtex); added references and
rewritte
Polymers in Curved Boxes
We apply results derived in other contexts for the spectrum of the Laplace
operator in curved geometries to the study of an ideal polymer chain confined
to a spherical annulus in arbitrary space dimension D and conclude that the
free energy compared to its value for an uncurved box of the same thickness and
volume, is lower when , stays the same when , and is higher when
\mbox{}. Thus confining an ideal polymer chain to a cylindrical shell,
lowers the effective bending elasticity of the walls, and might induce
spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned
results show that {\em {any}} shell in induces this effect, except for
a spherical shell). We compute the contribution of this effect to the bending
rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule
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