233 research outputs found
Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided
We define a measuring device (detector) of the coordinate of quantum particle
as an absorbing wall that cuts off the particle's wave function. The wave
function in the presence of such detector vanishes on the detector. The trace
the absorbed particles leave on the detector is identifies as the absorption
current density on the detector. This density is calculated from the solution
of Schr\"odinger's equation with a reflecting boundary at the detector. This
current density is not the usual Schr\"odinger current density. We define the
probability distribution of the time of arrival to a detector in terms of the
absorption current density. We define coordinate measurement by an absorbing
wall in terms of 4 postulates. We postulate, among others, that a quantum
particle has a trajectory. In the resulting theory the quantum mechanical
collapse of the wave function is replaced with the usual collapse of the
probability distribution after observation. Two examples are presented, that of
the slit experiment and the slit experiment with absorbing boundaries to
measure time of arrival. A calculation is given of the two dimensional
probability density function of a free particle from the measurement of the
absorption current on two planes.Comment: 20 pages, latex, no figure
A Path Intergal Approach to Current
Discontinuous initial wave functions or wave functions with discontintuous
derivative and with bounded support arise in a natural way in various
situations in physics, in particular in measurement theory. The propagation of
such initial wave functions is not well described by the Schr\"odinger current
which vanishes on the boundary of the support of the wave function. This
propagation gives rise to a uni-directional current at the boundary of the
support. We use path integrals to define current and uni-directional current
and give a direct derivation of the expression for current from the path
integral formulation for both diffusion and quantum mechanics. Furthermore, we
give an explicit asymptotic expression for the short time propagation of
initial wave function with compact support for both the cases of discontinuous
derivative and discontinuous wave function. We show that in the former case the
probability propagated across the boundary of the support in time is
and the initial uni-directional current is . This recovers the Zeno effect for continuous detection of a particle
in a given domain. For the latter case the probability propagated across the
boundary of the support in time is and the
initial uni-directional current is . This is an anti-Zeno
effect. However, the probability propagated across a point located at a finite
distance from the boundary of the support is . This gives a decay
law.Comment: 17 pages, Late
Quantum particle displacement by a moving localized potential trap
We describe the dynamics of a bound state of an attractive -well
under displacement of the potential. Exact analytical results are presented for
the suddenly moved potential. Since this is a quantum system, only a fraction
of the initially confined wavefunction remains confined to the moving
potential. However, it is shown that besides the probability to remain confined
to the moving barrier and the probability to remain in the initial position,
there is also a certain probability for the particle to move at double speed. A
quasi-classical interpretation for this effect is suggested. The temporal and
spectral dynamics of each one of the scenarios is investigated.Comment: 5 pages, 6 figure
Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells
The experimental results obtained for the magneto-transport in the
InGaAs/InAlAs double quantum wells (DQW) structures of two different shapes of
wells are reported. The beating-effect occurred in the Shubnikov-de Haas (SdH)
oscillations was observed for both types of the structures at low temperatures
in the parallel transport when magnetic field was perpendicular to the layers.
An approach to the calculation of the Landau levels energies for DQW structures
was developed and then applied to the analysis and interpretation of the
experimental data related to the beating-effect. We also argue that in order to
account for the observed magneto-transport phenomena (SdH and Integer Quantum
Hall effect), one should introduce two different quasi-Fermi levels
characterizing two electron sub-systems regarding symmetry properties of their
states, symmetric and anti-symmetric ones which are not mixed by
electron-electron interaction.Comment: 20 pages, 20 figure
A quantum decay model with exact explicit analytical solution
A simple decay model is introduced. The model comprises of a point potential
well, which experiences an abrupt change. Due to the temporal variation the
initial quantum state can either escape from the well or stay localized as a
new bound state. The model allows for an exact analytical solution while having
the necessary features of a decay process. The results show that the decay is
never exponential, as classical dynamics predicts. Moreover, at short times the
decay has a \textit{fractional} power law, which differs from perturbation
quantum methods predictions.Comment: 4 pages, 3 figure
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