16,752 research outputs found
Regularity of weak minimizers of the K-energy and applications to properness and K-stability
Let be a compact K\"ahler manifold and the space of
K\"ahler metrics cohomologous to . If a cscK metric exists in , we show that all finite energy minimizers of the extended K-energy are
smooth cscK metrics, partially confirming a conjecture of Y.A. Rubinstein and
the second author. As an immediate application, we obtain that existence of a
cscK metric in implies J-properness of the K-energy, thus
confirming one direction of a conjecture of Tian. Exploiting this properness
result we prove that an ample line bundle admitting a cscK metric in
is -polystable.Comment: v1 Comments welcome v2 New introduction and references added v3 Final
version. Preliminaries section added. Some notation changed. No other change
General-Purpose Parallel Simulator for Quantum Computing
With current technologies, it seems to be very difficult to implement quantum
computers with many qubits. It is therefore of importance to simulate quantum
algorithms and circuits on the existing computers. However, for a large-size
problem, the simulation often requires more computational power than is
available from sequential processing. Therefore, the simulation methods using
parallel processing are required.
We have developed a general-purpose simulator for quantum computing on the
parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We
have performed Shor's factorization and Grover's database search by using the
simulator, and we analyzed robustness of the corresponding quantum circuits in
the presence of decoherence and operational errors. The corresponding results,
statistics and analyses are presented.Comment: 15 pages, 15 figure
On the role of coupling in mode selective excitation using ultrafast pulse shaping in stimulated Raman spectroscopy
The coherence of two, coupled two-level systems, representing vibrational
modes in a semiclassical model, is calculated in weak and strong fields for
various coupling schemes and for different relative phases between initial
state amplitudes. A relative phase equal to projects the system into a
dark state. The selective excitation of one of the two, two-level systems is
studied as a function of coupling strength and initial phases.Comment: 7 pages, 4 figure
Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise
A promising technique for measuring single electron spins is magnetic
resonance force microscopy (MRFM), in which a microcantilever with a permanent
magnetic tip is resonantly driven by a single oscillating spin. If the quality
factor of the cantilever is high enough, this signal will be amplified over
time to the point that it can be detected by optical or other techniques. An
important requirement, however, is that this measurement process occur on a
time scale short compared to any noise which disturbs the orientation of the
measured spin. We describe a model of spin noise for the MRFM system, and show
how this noise is transformed to become time-dependent in going to the usual
rotating frame. We simplify the description of the cantilever-spin system by
approximating the cantilever wavefunction as a Gaussian wavepacket, and show
that the resulting approximation closely matches the full quantum behavior. We
then examine the problem of detecting the signal for a cantilever with thermal
noise and spin with spin noise, deriving a condition for this to be a useful
measurement.Comment: 12 pages, 8 figures in EPS format, RevTeX 4.
Non-Hermitian description of a superconducting phase qubit measurement
We present an approach based on a non-Hermitian Hamiltonian to describe the
process of measurement by tunneling of a phase qubit state. We derive simple
analytical expressions which describe the dynamics of measurement, and compare
our results with those experimentally available.Comment: 8 pages, 4 figure
Intrinsic Cavity QED and Emergent Quasi-Normal Modes for Single Photon
We propose a special cavity design that is constructed by terminating a
one-dimensional waveguide with a perfect mirror at one end and doping a
two-level atom at the other. We show that this atom plays the intrinsic role of
a semi-transparent mirror for single photon transports such that quasi-normal
modes (QNM's) emerge spontaneously in the cavity system. This atomic mirror has
its reflection coefficient tunable through its level spacing and its coupling
to the cavity field, for which the cavity system can be regarded as a two-end
resonator with a continuously tunable leakage. The overall investigation
predicts the existence of quasi-bound states in the waveguide continuum. Solid
state implementations based on a dc-SQUID circuit and a defected line resonator
embedded in a photonic crystal are illustrated to show the experimental
accessibility of the generic model.Comment: 4 pages,5 figures, Comments welcom
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