937 research outputs found
Trans-Planckian Tail in a Theory with a Cutoff
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a
tail of an exponentially large amplitude wave that is mostly hidden behind the
horizon. The present proposal requires implementing a final state condition.
This condition involves only frequencies below the cutoff scale. It may be
interpreted as a condition on the singularity. Despite the introduction of the
cutoff, the Hawking radiation is restored for static observers. Freely falling
observers see empty space outside the horizon, but are "heated" as they cross
the horizon.Comment: 17 pages, RevTe
Dynamics of Vortex Pair in Radial Flow
The problem of vortex pair motion in two-dimensional plane radial flow is
solved. Under certain conditions for flow parameters, the vortex pair can
reverse its motion within a bounded region. The vortex-pair translational
velocity decreases or increases after passing through the source/sink region,
depending on whether the flow is diverging or converging, respectively. The
rotational motion of two corotating vortexes in a quiescent environment
transforms into motion along a logarithmic spiral in the presence of radial
flow. The problem may have applications in astrophysics and geophysics.Comment: 13 pages, 9 figure
``Weighing'' a closed system and the time-energy uncertainty principle
A gedanken-experiment is proposed for `weighing'' the total mass of a closed
system from within the system. We prove that for an internal observer the time
, required to measure the total energy with accuracy , is
bounded according to . This time-energy uncertainty
principle for a closed system follows from the measurement back-reaction on the
system. We generally examine what other conserved observables are in principle
measurable within a closed system and what are the corresponding uncertainty
relations.Comment: 8 page
Quantum limitations on superluminal propagation
Unstable systems such as media with inverted atomic population have been
shown to allow the propagation of analytic wavepackets with group velocity
faster than that of light, without violating causality. We illuminate the
important role played by unstable modes in this propagation, and show that the
quantum fluctuations of these modes, and their unitary time evolution, impose
severe restrictions on the observation of superluminal phenomena.Comment: RevTeX 4 page
The Fermi Problem in Discrete Systems
The Fermi two-atom problem illustrates an apparent causality violation in
Quantum Field Theory which has to do with the nature of the built in
correlations in the vacuum. It has been a constant subject of theoretical
debate and discussions during the last few decades. Nevertheless, although the
issues at hand could in principle be tested experimentally, the smallness of
such apparent violations of causality in Quantum Electrodynamics prevented the
observation of the predicted effect. In the present paper we show that the
problem can be simulated within the framework of discrete systems that can be
manifested, for instance, by trapped atoms in optical lattices or trapped ions.
Unlike the original continuum case, the causal structure is no longer sharp.
Nevertheless, as we show, it is possible to distinguish between "trivial"
effects due to "direct" causality violations, and the effects associated with
Fermi's problem, even in such discrete settings. The ability to control
externally the strength of the atom-field interactions, enables us also to
study both the original Fermi problem with "bare atoms", as well as correction
in the scenario that involves "dressed" atoms. Finally, we show that in
principle, the Fermi effect can be detected using trapped ions.Comment: Second version - minor change
Temporal Ordering in Quantum Mechanics
We examine the measurability of the temporal ordering of two events, as well
as event coincidences. In classical mechanics, a measurement of the
order-of-arrival of two particles is shown to be equivalent to a measurement
involving only one particle (in higher dimensions). In quantum mechanics, we
find that diffraction effects introduce a minimum inaccuracy to which the
temporal order-of-arrival can be determined unambiguously. The minimum
inaccuracy of the measurement is given by dt=1/E where E is the total kinetic
energy of the two particles. Similar restrictions apply to the case of
coincidence measurements. We show that these limitations are much weaker than
limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more
accurately than time-of-arrival. To appear in Journal of Physics
Modes of Oscillation in Radiofrequency Paul Traps
We examine the time-dependent dynamics of ion crystals in radiofrequency
traps. The problem of stable trapping of general three-dimensional crystals is
considered and the validity of the pseudopotential approximation is discussed.
We derive analytically the micromotion amplitude of the ions, rigorously
proving well-known experimental observations. We use a method of infinite
determinants to find the modes which diagonalize the linearized time-dependent
dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')
transformation to coordinates of decoupled linear oscillators. We demonstrate
the utility of the method by analyzing the modes of a small `peculiar' crystal
in a linear Paul trap. The calculations can be readily generalized to
multispecies ion crystals in general multipole traps, and time-dependent
quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction
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