728 research outputs found
The Generalized Hartle-Hawking Initial State: Quantum Field Theory on Einstein Conifolds
Recent arguments have indicated that the sum over histories formulation of
quantum amplitudes for gravity should include sums over conifolds, a set of
histories with more general topology than that of manifolds. This paper
addresses the consequences of conifold histories in gravitational functional
integrals that also include scalar fields. This study will be carried out
explicitly for the generalized Hartle-Hawking initial state, that is the
Hartle-Hawking initial state generalized to a sum over conifolds. In the
perturbative limit of the semiclassical approximation to the generalized
Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds
is recovered. In particular, the quantum field theory of a scalar field on de
Sitter spacetime with spatial topology is derived from the generalized
Hartle-Hawking initial state in this approximation. This derivation is carried
out for a scalar field of arbitrary mass and scalar curvature coupling.
Additionally, the generalized Hartle-Hawking boundary condition produces a
state that is not identical to but corresponds to the Bunch-Davies vacuum on
de Sitter spacetime. This result cannot be obtained from the original
Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein
manifold with round boundary.Comment: Revtex 3, 31 pages, 4 epsf figure
Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses
We report on the successful operation of an analogue computer designed to
factor numbers. Our device relies solely on the interference of classical light
and brings together the field of ultrashort laser pulses with number theory.
Indeed, the frequency component of the electric field corresponding to a
sequence of appropriately shaped femtosecond pulses is determined by a Gauss
sum which allows us to find the factors of a number
Measuring microwave quantum states: tomogram and moments
Two measurable characteristics of microwave one-mode photon states are
discussed: a rotated quadrature distribution (tomogram) and
normally/antinormally ordered moments of photon creation and annihilation
operators. Extraction of these characteristics from amplified microwave signal
is presented. Relations between the tomogram and the moments are found and can
be used as a cross check of experiments. Formalism of the ordered moments is
developed. The state purity and generalized uncertainty relations are
considered in terms of moments. Unitary and non-unitary time evolution of
moments is obtained in the form of linear differential equations in contrast to
partial differential equations for quasidistributions. Time evolution is
specified for the cases of a harmonic oscillator and a damped harmonic
oscillator, which describe noiseless and decoherence processes, respectively.Comment: 10 pages, 1 figure, to appear in Phys. Rev.
Quantum tunneling of semifluxons
We consider a system of two semifluxons of opposite polarity in a 0-pi-0 long
Josephson junction, which classically can be in one of two degenerate states:
up-down or down-up. When the distance between the 0-pi boundaries
(semifluxon's centers) is a bit larger than the crossover distance , the
system can switch from one state to the other due to thermal fluctuations or
quantum tunneling. We map this problem to the dynamics of a single particle in
a double well potential and estimate parameters for which quantum effects
emerge. We also determine the classical-to-quantum crossover temperature as
well as the tunneling rate (energy level splitting) between the states up-down
and down-up.Comment: submitted to PRB, comments/questions are welcom
Depletion of a Bose-Einstein condensate by laser-iduced dipole-dipole interactions
We study a gaseous Bose-Einstein condensate with laser-induced dipole-dipole
interactions using the Hartree-Fock-Bogoliubov theory within the Popov
approximation. The dipolar interactions introduce long-range atom-atom
correlations, which manifest themselves as increased depletion at momenta
similar to that of the laser wavelength, as well as a "roton" dip in the
excitation spectrum. Surprisingly, the roton dip and the corresponding peak in
the depletion are enhanced by raising the temperature above absolute zero.Comment: 10 pages, 6 figure
A tunable macroscopic quantum system based on two fractional vortices
We propose a tunable macroscopic quantum system based on two fractional
vortices. Our analysis shows that two coupled fractional vortices pinned at two
artificially created \kappa\ discontinuities of the Josephson phase in a long
Josephson junction can reach the quantum regime where coherent quantum
oscillations arise. For this purpose we map the dynamics of this system to that
of a single particle in a double-well potential. By tuning the \kappa\
discontinuities with injector currents we are able to control the parameters of
the effective double-well potential as well as to prepare a desired state of
the fractional vortex molecule. The values of the parameters derived from this
model suggest that an experimental realisation of this tunable macroscopic
quantum system is possible with today's technology.Comment: We updated our manuscript due to a change of the focus from qubit to
macroscopic quantum effect
WKB Propagation of Gaussian Wavepackets
We analyze the semiclassical evolution of Gaussian wavepackets in chaotic
systems. We prove that after some short time a Gaussian wavepacket becomes a
primitive WKB state. From then on, the state can be propagated using the
standard TDWKB scheme. Complex trajectories are not necessary to account for
the long-time propagation. The Wigner function of the evolving state develops
the structure of a classical filament plus quantum oscillations, with phase and
amplitude being determined by geometric properties of a classical manifold.Comment: 4 pages, 4 figures; significant improvement
Extending Hudson's theorem to mixed quantum states
According to Hudson's theorem, any pure quantum state with a positive Wigner
function is necessarily a Gaussian state. Here, we make a step towards the
extension of this theorem to mixed quantum states by finding upper and lower
bounds on the degree of non-Gaussianity of states with positive Wigner
functions. The bounds are expressed in the form of parametric functions
relating the degree of non-Gaussianity of a state, its purity, and the purity
of the Gaussian state characterized by the same covariance matrix. Although our
bounds are not tight, they permit us to visualize the set of states with
positive Wigner functions.Comment: 4 pages, 2 figure
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