183 research outputs found
Public attitudes towards a European minimum income benefit:How (perceived) welfare state performance and expectations shape popular support
Sources of quantum waves
Due to the space and time dependence of the wave function in the time
dependent Schroedinger equation, different boundary conditions are possible.
The equation is usually solved as an ``initial value problem'', by fixing the
value of the wave function in all space at a given instant. We compare this
standard approach to "source boundary conditions'' that fix the wave at all
times in a given region, in particular at a point in one dimension. In contrast
to the well-known physical interpretation of the initial-value-problem
approach, the interpretation of the source approach has remained unclear, since
it introduces negative energy components, even for ``free motion'', and a
time-dependent norm. This work provides physical meaning to the source method
by finding the link with equivalent initial value problems.Comment: 12 pages, 7 inlined figures; typos correcte
EU health solidarity in times of crisis: Explaining public preferences for EU-risk pooling for medicines
A measurement-based approach to quantum arrival times
For a quantum-mechanically spread-out particle we investigate a method for
determining its arrival time at a specific location. The procedure is based on
the emission of a first photon from a two-level system moving into a
laser-illuminated region. The resulting temporal distribution is explicitly
calculated for the one-dimensional case and compared with axiomatically
proposed expressions. As a main result we show that by means of a deconvolution
one obtains the well known quantum mechanical probability flux of the particle
at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.
Transient response of a quantum wave to an instantaneous potential step switching
The transient response of a stationary state of a quantum particle in a step
potential to an instantaneous change in the step height (a simplified model for
a sudden bias switch in an electronic semiconductor device) is solved exactly
by means of a semianalytical expression. The characteristic times for the
transient process up to the new stationary state are identified. A comparison
is made between the exact results and an approximate method.Comment: 8 pages, 8 figures, Revtex
Quantum times of arrival for multiparticle states
Using the concept of crossing state and the formalism of second quantization,
we propose a prescription for computing the density of arrivals of particles
for multiparticle states, both in the free and the interacting case. The
densities thus computed are positive, covariant in time for time independent
hamiltonians, normalized to the total number of arrivals, and related to the
flux. We investigate the behaviour of this prescriptions for bosons and
fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure
Generalizations of Kijowski's time-of-arrival distribution for interaction potentials
Several proposals for a time-of-arrival distribution of ensembles of
independent quantum particles subject to an external interaction potential are
compared making use of the ``crossing state'' concept. It is shown that only
one of them has the properties expected for a classical distribution in the
classical limit. The comparison is illustrated numerically with a collision of
a Gaussian wave packet with an opaque square barrier.Comment: 5 inlined figures: some typo correction
Towards a time-reversal mirror for quantum systems
The reversion of the time evolution of a quantum state can be achieved by
changing the sign of the Hamiltonian as in the polarization echo experiment in
NMR. In this work we describe an alternative mechanism inspired by the acoustic
time reversal mirror. By solving the inverse time problem in a discrete space
we develop a new procedure, the perfect inverse filter. It achieves the exact
time reversion in a given region by reinjecting a prescribed wave function at
its periphery.Comment: 6 pages, 4 figures. Introduction modified, references added, one
figure added to improve the discussio
Quantum-wave evolution in a step potential barrier
By using an exact solution to the time-dependent Schr\"{o}dinger equation
with a point source initial condition, we investigate both the time and spatial
dependence of quantum waves in a step potential barrier. We find that for a
source with energy below the barrier height, and for distances larger than the
penetration length, the probability density exhibits a {\it forerunner}
associated with a non-tunneling process, which propagates in space at exactly
the semiclassical group velocity. We show that the time of arrival of the
maximum of the {\it forerunner} at a given fixed position inside the potential
is exactly the traversal time, . We also show that the spatial evolution
of this transient pulse exhibits an invariant behavior under a rescaling
process. This analytic property is used to characterize the evolution of the
{\it forerunner}, and to analyze the role played by the time of arrival,
, found recently by Muga and B\"{u}ttiker [Phys. Rev. A {\bf 62},
023808 (2000)].Comment: To be published in Phys. Rev. A (2002
Simulation of wavepacket tunneling of interacting identical particles
We demonstrate a new method of simulation of nonstationary quantum processes,
considering the tunneling of two {\it interacting identical particles},
represented by wave packets. The used method of quantum molecular dynamics
(WMD) is based on the Wigner representation of quantum mechanics. In the
context of this method ensembles of classical trajectories are used to solve
quantum Wigner-Liouville equation. These classical trajectories obey
Hamilton-like equations, where the effective potential consists of the usual
classical term and the quantum term, which depends on the Wigner function and
its derivatives. The quantum term is calculated using local distribution of
trajectories in phase space, therefore classical trajectories are not
independent, contrary to classical molecular dynamics. The developed WMD method
takes into account the influence of exchange and interaction between particles.
The role of direct and exchange interactions in tunneling is analyzed. The
tunneling times for interacting particles are calculated.Comment: 11 pages, 3 figure
- âŠ