24,925 research outputs found
Note on the derivative of the hyperbolic cotangent
In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we
presented a formula for the derivative of the hyperbolic cotangent that differs
from the standard one in the literature by an additional term proportional to
the Dirac delta function. Since our letter was necessarily brief, shortly after
its appearance we prepared a more extensive unpublished note giving a detailed
explanation of our argument. Since this note has been referenced in a recent
article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we
think it appropriate that it now appear in print. We have made no alteration to
the original note
Does the Third Law of Thermodynamics hold in the Quantum Regime?
The first in a long series of papers by John T. Lewis,
G. W. Ford and the present author, considered the problem of the most general
coupling of a quantum particle to a linear passive heat bath, in the course of
which they derived an exact formula for the free energy of an oscillator
coupled to a heat bath in thermal equilibrium at temperature T. This formula,
and its later extension to three dimensions to incorporate a magnetic field,
has proved to be invaluable in analyzing problems in quantum thermodynamics.
Here, we address the question raised in our title viz. Nernst's third law of
thermodynamics
Relativistic Elastic Differential Cross Sections for Equal Mass Nuclei
The effects of relativistic kinematics are studied for nuclear collisions of
equal mass nuclei. It is found that the relativistic and non-relativistic
elastic scattering amplitudes are nearly indistinguishable, and, hence, the
relativistic and non-relativistic differential cross sections become
indistinguishable. These results are explained by analyzing the
Lippmann-Schwinger equation with the first order optical potential that was
employed in the calculatio
The Effects of Stress Tensor Fluctuations upon Focusing
We treat the gravitational effects of quantum stress tensor fluctuations. An
operational approach is adopted in which these fluctuations produce
fluctuations in the focusing of a bundle of geodesics. This can be calculated
explicitly using the Raychaudhuri equation as a Langevin equation. The physical
manifestation of these fluctuations are angular blurring and luminosity
fluctuations of the images of distant sources. We give explicit results for the
case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices
B and
Decoherence in Phase Space
Much of the discussion of decoherence has been in terms of a particle moving
in one dimension that is placed in an initial superposition state (a
Schr\"{o}dinger "cat" state) corresponding to two widely separated wave
packets. Decoherence refers to the destruction of the interference term in the
quantum probability function. Here, we stress that a quantitative measure of
decoherence depends not only on the specific system being studied but also on
whether one is considering coordinate, momentum or phase space. We show that
this is best illustrated by considering Wigner phase space where the measure is
again different. Analytic results for the time development of the Wigner
distribution function for a two-Gaussian Schrodinger "cat" state have been
obtained in the high-temperature limit (where decoherence can occur even for
negligible dissipation) which facilitates a simple demonstration of our
remarks.Comment: in press in Laser Phys.13(2003
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
Building on a pair of earlier papers, I investigate the various point-wise
and averaged energy conditions for the quantum stress-energy tensor
corresponding to a conformally-coupled massless scalar field in the in the
(1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors
are analytically known, I can get exact results for the Hartle--Hawking,
Boulware, and Unruh vacua. This exactly solvable model serves as a useful
sanity check on my (3+1)-dimensional investigations wherein I had to resort to
a mixture of analytic approximations and numerical techniques. Key results in
(1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the
Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC
is violated everywhere in the spacetime (for any quantum state, not just the
standard vacuum states).Comment: 7 pages, ReV_Te
Use of mathematical derivatives (time-domain differentiation) on chromatographic data to enhance the detection and quantification of an unknown 'rider' peak
Two samples of an anticancer prodrug, AQ4N, were submitted for HPLC assay and showed an unidentified impurity that eluted as a 'rider' on the tail of the main peak. Mathematical derivatization of the chromatograms offered several advantages over conventional skimmed integration. A combination of the second derivative amplitude and simple linear regression gave a novel method for estimating the true peak area of the impurity peak. All the calculation steps were carried out using a widely available spreadsheet program. (C) 2003 Elsevier B.V. All rights reserved
Measured quantum probability distribution functions for Brownian motion
The quantum analog of the joint probability distributions describing a
classical stochastic process is introduced. A prescription is given for
constructing the quantum distribution associated with a sequence of
measurements. For the case of quantum Brownian motion this prescription is
illustrated with a number of explicit examples. In particular it is shown how
the prescription can be extended in the form of a general formula for the
Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres
Restrictions on Negative Energy Density in Flat Spacetime
In a previous paper, a bound on the negative energy density seen by an
arbitrary inertial observer was derived for the free massless, quantized scalar
field in four-dimensional Minkowski spacetime. This constraint has the form of
an uncertainty principle-type limitation on the magnitude and duration of the
negative energy density. That result was obtained after a somewhat complicated
analysis. The goal of the current paper is to present a much simpler method for
obtaining such constraints. Similar ``quantum inequality'' bounds on negative
energy density are derived for the electromagnetic field, and for the massive
scalar field in both two and four-dimensional Minkowski spacetime.Comment: 17 pages, including two figures, uses epsf, minor revisions in the
Introduction, conclusions unchange
Detection of negative energy: 4-dimensional examples
We study the response of switched particle detectors to static negative
energy densities and negative energy fluxes. It is demonstrated how the
switching leads to excitation even in the vacuum and how negative energy can
lead to a suppression of this excitation. We obtain quantum inequalities on the
detection similar to those obtained for the energy density by Ford and
co-workers and in an `operational' context by Helfer. We revisit the question
`Is there a quantum equivalence principle?' in terms of our model. Finally, we
briefly address the issue of negative energy and the second law of
thermodynamics.Comment: 10 pages, 7 figure
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