8,510 research outputs found
Energy-momentum tensor in thermal strong-field QED with unstable vacuum
The mean value of the one-loop energy-momentum tensor in thermal QED with
electric-like background that creates particles from vacuum is calculated. The
problem differes essentially from calculations of effective actions (similar to
that of Heisenberg--Euler) in backgrounds that do not violate the stability of
vacuum. The role of a constant electric background in the violation of both the
stability of vacuum and the thermal character of particle distribution is
investigated. Restrictions on the electric field and its duration under which
one can neglect the back-reaction of created particles are established.Comment: 7 pages, Talk presented at Workshop "Quantum Field Theory under the
Influence of External Conditions", Leipzig, September 17-21, 2007;
introduction extended, version accepted for publication in J.Phys.
Arbitrarily slow, non-quasistatic, isothermal transformations
For an overdamped colloidal particle diffusing in a fluid in a controllable,
virtual potential, we show that arbitrarily slow transformations, produced by
smooth deformations of a double-well potential, need not be reversible. The
arbitrarily slow transformations do need to be fast compared to the barrier
crossing time, but that time can be extremely long. We consider two types of
cyclic, isothermal transformations of a double-well potential. Both start and
end in the same equilibrium state, and both use the same basic operations---but
in different order. By measuring the work for finite cycle times and
extrapolating to infinite times, we found that one transformation required no
work, while the other required a finite amount of work, no matter how slowly it
was carried out. The difference traces back to the observation that when time
is reversed, the two protocols have different outcomes, when carried out
arbitrarily slowly. A recently derived formula relating work production to the
relative entropy of forward and backward path probabilities predicts the
observed work average.Comment: 6 pages, 6 figure
Multiple testing of local maxima for detection of peaks in 1D
A topological multiple testing scheme for one-dimensional domains is proposed
where, rather than testing every spatial or temporal location for the presence
of a signal, tests are performed only at the local maxima of the smoothed
observed sequence. Assuming unimodal true peaks with finite support and
Gaussian stationary ergodic noise, it is shown that the algorithm with
Bonferroni or Benjamini--Hochberg correction provides asymptotic strong control
of the family wise error rate and false discovery rate, and is power
consistent, as the search space and the signal strength get large, where the
search space may grow exponentially faster than the signal strength.
Simulations show that error levels are maintained for nonasymptotic conditions,
and that power is maximized when the smoothing kernel is close in shape and
bandwidth to the signal peaks, akin to the matched filter theorem in signal
processing. The methods are illustrated in an analysis of electrical recordings
of neuronal cell activity.Comment: Published in at http://dx.doi.org/10.1214/11-AOS943 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Peak Detection as Multiple Testing
This paper considers the problem of detecting equal-shaped non-overlapping
unimodal peaks in the presence of Gaussian ergodic stationary noise, where the
number, location and heights of the peaks are unknown. A multiple testing
approach is proposed in which, after kernel smoothing, the presence of a peak
is tested at each observed local maximum. The procedure provides strong control
of the family wise error rate and the false discovery rate asymptotically as
both the signal-to-noise ratio (SNR) and the search space get large, where the
search space may grow exponentially as a function of SNR. Simulations assuming
a Gaussian peak shape and a Gaussian autocorrelation function show that desired
error levels are achieved for relatively low SNR and are robust to partial peak
overlap. Simulations also show that detection power is maximized when the
smoothing bandwidth is close to the bandwidth of the signal peaks, akin to the
well-known matched filter theorem in signal processing. The procedure is
illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: 37 pages, 8 figure
Optimal fast single pulse readout of qubits
The computer simulations of the process of single pulse readout from the
flux-biased phase qubit is performed in the frame of one-dimensional
Schroedinger equation. It has been demonstrated that the readout error can be
minimized by choosing the optimal pulse duration and the depth of a potential
well, leading to the fidelity of 0.94 for 2ns and 0.965 for 12ns sinusoidal
pulses.Comment: 4 pages, 6 figure
On "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field"
Recently the paper "Schwinger Mechanism for Gluon Pair Production in the
Presence of Arbitrary Time Dependent Chromo-Electric Field" by G. C. Nayak was
published [Eur. Phys. J. C 59, 715 (2009); arXiv:0708.2430]. Its aim is to
obtain an exact expression for the probability of non-perturbative gluon pair
production per unit time per unit volume and per unit transverse momentum in an
arbitrary time-dependent chromo-electric background field. We believe that the
obtained expression is open to question. We demonstrate its inconsistency on
some well-known examples. We think that this is a consequence of using the
so-called "shift theorem" [arXiv:hep-th/0609192] in deriving the expression for
the probability. We make some critical comments on the theorem and its
applicability to the problem in question.Comment: 4 page
Quantum scalar field in FRW Universe with constant electromagnetic background
We discuss massive scalar field with conformal coupling in
Friedmann-Robertson-Walker (FRW) Universe of special type with constant
electromagnetic field. Treating an external gravitational-electromagnetic
background exactly, at first time the proper-time representations for out-in,
in-in, and out-out scalar Green functions are explicitly constructed as
proper-time integrals over the corresponding (complex) contours. The
vacuum-to-vacuum transition amplitudes and number of created particles are
found and vacuum instability is discussed. The mean values of the current and
energy-momentum tensor are evaluated, and different approximations for them are
investigated. The back reaction of the particles created to the electromagnetic
field is estimated in different regimes. The connection between proper-time
method and effective action is outlined. The effective action in scalar QED in
weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic
field is found as derivative expansion over curvature and electromagnetic field
strength. Possible further applications of the results are briefly mentioned.Comment: 38 pages, LaTe
One-loop energy-momentum tensor in QED with electric-like background
We have obtained nonperturbative one-loop expressions for the mean
energy-momentum tensor and current density of Dirac's field on a constant
electric-like background. One of the goals of this calculation is to give a
consistent description of back-reaction in such a theory. Two cases of initial
states are considered: the vacuum state and the thermal equilibrium state.
First, we perform calculations for the vacuum initial state. In the obtained
expressions, we separate the contributions due to particle creation and vacuum
polarization. The latter contributions are related to the Heisenberg-Euler
Lagrangian. Then, we study the case of the thermal initial state. Here, we
separate the contributions due to particle creation, vacuum polarization, and
the contributions due to the work of the external field on the particles at the
initial state. All these contributions are studied in detail, in different
regimes of weak and strong fields and low and high temperatures. The obtained
results allow us to establish restrictions on the electric field and its
duration under which QED with a strong constant electric field is consistent.
Under such restrictions, one can neglect the back-reaction of particles created
by the electric field. Some of the obtained results generalize the calculations
of Heisenberg-Euler for energy density to the case of arbitrary strong electric
fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68)
corrected, results unchange
Comments on spin operators and spin-polarization states of 2+1 fermions
In this brief article we discuss spin polarization operators and spin
polarization states of 2+1 massive Dirac fermions and find a convenient
representation by the help of 4-spinors for their description. We stress that
in particular the use of such a representation allows us to introduce the
conserved covariant spin operator in the 2+1 field theory. Another advantage of
this representation is related to the pseudoclassical limit of the theory.
Indeed, quantization of the pseudoclassical model of a spinning particle in 2+1
dimensions leads to the 4-spinor representation as the adequate realization of
the operator algebra, where the corresponding operator of a first-class
constraint, which cannot be gauged out by imposing the gauge condition, is just
the covariant operator previously introduced in the quantum theory.Comment: 6 page
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