16,605 research outputs found
Quantum Algorithms Revisited
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. A common pattern underpinning quantum algorithms can be
identified when quantum computation is viewed as multi-particle interference.
We use this approach to review (and improve) some of the existing quantum
algorithms and to show how they are related to different instances of quantum
phase estimation. We provide an explicit algorithm for generating any
prescribed interference pattern with an arbitrary precision.Comment: 18 pages, LaTeX, 7 figures. Submitted to Proc. Roy. Soc. Lond.
A Laplace transform approach to the quantum harmonic oscillator
The one-dimensional quantum harmonic oscillator problem is examined via the
Laplace transform method. The stationary states are determined by requiring
definite parity and good behaviour of the eigenfunction at the origin and at
infinity
The Cerenkov effect revisited: from swimming ducks to zero modes in gravitational analogs
We present an interdisciplinary review of the generalized Cerenkov emission
of radiation from uniformly moving sources in the different contexts of
classical electromagnetism, superfluid hydrodynamics, and classical
hydrodynamics. The details of each specific physical systems enter our theory
via the dispersion law of the excitations. A geometrical recipe to obtain the
emission patterns in both real and wavevector space from the geometrical shape
of the dispersion law is discussed and applied to a number of cases of current
experimental interest. Some consequences of these emission processes onto the
stability of condensed-matter analogs of gravitational systems are finally
illustrated.Comment: Lecture Notes at the IX SIGRAV School on "Analogue Gravity" in Como,
Italy from May 16th-21th, 201
The scar mechanism revisited
Unstable periodic orbits are known to originate scars on some eigenfunctions
of classically chaotic systems through recurrences causing that some part of an
initial distribution of quantum probability in its vicinity returns
periodically close to the initial point. In the energy domain, these
recurrences are seen to accumulate quantum density along the orbit by a
constructive interference mechanism when the appropriate quantization (on the
action of the scarring orbit) is fulfilled. Other quantized phase space
circuits, such as those defined by homoclinic tori, are also important in the
coherent transport of quantum density in chaotic systems. The relationship of
this secondary quantum transport mechanism with the standard mechanism for
scarring is here discussed and analyzed.Comment: 6 pages, 6 figure
Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
We show that the -product for , group Fourier transform and
effective action arising in [1] in an effective theory for the integer spin
Ponzano-Regge quantum gravity model are compatible with the noncommutative
bicovariant differential calculus, quantum group Fourier transform and
noncommutative scalar field theory previously proposed for 2+1 Euclidean
quantum gravity using quantum group methods in [2]. The two are related by a
classicalisation map which we introduce. We show, however, that noncommutative
spacetime has a richer structure which already sees the half-integer spin
information. We argue that the anomalous extra `time' dimension seen in the
noncommutative geometry should be viewed as the renormalisation group flow
visible in the coarse-graining in going from to . Combining our
methods we develop practical tools for noncommutative harmonic analysis for the
model including radial quantum delta-functions and Gaussians, the Duflo map and
elements of `noncommutative sampling theory'. This allows us to understand the
bandwidth limitation in 2+1 quantum gravity arising from the bounded
momentum and to interpret the Duflo map as noncommutative compression. Our
methods also provide a generalised twist operator for the -product.Comment: 53 pages latex, no figures; extended the intro for this final versio
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