8,128 research outputs found
Schwinger's Propagator Is Only A Green's Function
Schwinger used an analytic continuation of the effective action to correctly
compute the particle production rate per unit volume for QED in a uniform
electric field. However, if one simply evaluates the one loop expectation value
of the current operator using his propagator, the result is zero! We analyze
this curious fact from the context of a canonical formalism of operators and
states. The explanation turns out to be that Schwinger's propagator is not
actually the expectation value of the time-ordered product of field operators
in the presence of a time-independent state, although it is of course a Green's
function. We compute the true propagator in the presence of a state which is
empty at where is the lightcone
evolution parameter. Our result can be generalized to electric fields which
depend arbitrarily on .Comment: 18 pages, LaTeX 2 epsilo
Method of complex paths and general covariance of Hawking radiation
We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semi-classical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation. This also shows
that there is no correspondence between the particles detected by the model
detector and the particle spectrum obtained by the quantum field theoretic
analysis -- a result known in other contexts as well.Comment: 9 pages, uses MPLA Style file, Accepted for publication in Mod. Phys.
Letts.
Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system
A fiber taper waveguide is used to perform direct optical spectroscopy of a
microdisk-quantum-dot system, exciting the system through the photonic (light)
channel rather than the excitonic (matter) channel. Strong coupling, the regime
of coherent quantum interactions, is demonstrated through observation of vacuum
Rabi splitting in the transmitted and reflected signals from the cavity. The
fiber coupling method also allows the examination of the system's steady-state
nonlinear properties, where saturation of the cavity-QD response is observed
for less than one intracavity photon.Comment: adjusted references, added minor clarification
Particle production and complex path analysis
This paper discusses particle production in Schwarzschild-like spacetimes and in a uniform electric field. Both problems are approached using the method of complex path analysis which is used to describe tunnelling processes in semiclassical quantum mechanics. Particle production in Schwarzschild-like spacetimes with a horizon is obtained here by a new and simple semiclassical method based on the method of complex paths. Hawking radiation is obtained in the (t,r) coordinate system of the standard Schwarzschild metric without requiring the Kruskal extension. The coordinate singularity present at the horizon manifests itself as a singularity in the expression for the semiclassical propagator for a scalar field. We give a prescription whereby this singularity is regularized with Hawking's result being recovered. The equation satisfied by a scalar field is also reduced to solving a one-dimensional effective Schrodinger equation with a potential (-1/x2) near the horizon. Constructing the action for a fictitious nonrelativistic particle moving in this potential and applying the above mentioned prescription, one again recovers Hawking radiation. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely time-dependent gauge. In a purely space-dependent gauge, however, the tunnelling interpretation has to be resorted to in order to recover the previous result. We attempt, in this paper, to provide a tunnelling description using the formal method of complex paths for both the time and space dependent gauges. The usefulness of such a common description becomes evident when "mixed" gauges, which are functions of both space and time variables, are analyzed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of elementary functions unlike the standard modes which are transcendental parabolic cylinder functions. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime
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