arXiv subjects

L. H. Ford

Publications and source records attributed to L. H. Ford.

At least 55 records · Page 3Linked to original sources

arXiv2012

Probability distributions for quantum stress tensors in four dimensions

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. However, we also give bounds on the cumulative distribution function that are valid for any distribution fitting these moments.We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

quant-ph↗

arXiv2012

An Analog Model for Quantum Lightcone Fluctuations in Nonlinear Optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable.

gr-qc↗

arXiv2011

A Model for Non-Cancellation of Quantum Electric Field Fluctuations

A localized charged particle oscillating near a reflecting boundary is considered as a model for non-cancellation of vacuum fluctuations. Although the mean velocity of the particle is sinusoidal, the velocity variance produced by vacuum fluctuation can either grow or decrease linearly in time, depending upon the product of the oscillation frequency and the distance to the boundary. This amounts to heating or cooling, arising from non-cancellation of electric field fluctuations, which are otherwise anticorrelated in time. Similar non-cancellations arise in quantum field effects iN time-dependent curved spacetimes. We give some estimates of the magnitude of the effect, and discuss its potential observability. We also compare the effects of vacuum fluctuations with the shot noise due to emission of a finite number of photons. We find that the two effects can be comparable in magnitude, but have distinct characteristics, and hence could be distinguished in an experiment.

quant-ph↗

arXiv2011

Quantum Stress Tensor Fluctuation Effects in Inflationary Cosmology

We review several related investigations of the effects of the quantum stress tensor of a conformal field in inflationary cosmology. Particular attention will be paid to the effects of quantum stress tensor fluctuations as a source of density and tensor perturbations in inflationary models. These effects can possibly depend upon the total expansion factor during inflation, and hence be much larger than one might otherwise expect. They have the potential to contribute a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations, and might be observable.

gr-qc↗

arXiv2011

Gravity Waves from Quantum Stress Tensor Fluctuations in Inflation

We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a non-scale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of transplanckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation.

gr-qc↗

arXiv2010

Negative Power Spectra in Quantum Field Theory

We consider the spatial power spectra associated with fluctuations of quadratic operators in field theory, such as quantum stress tensor components. We show that the power spectrum can be negative, in contrast to most fluctuation phenomena where the Wiener-Khinchine theorem requires a positive power spectrum. We show why the usual argument for positivity fails in this case, and discuss the physical interpretation of negative power spectra. Possible applications to cosmology are discussed.

quant-ph↗

arXiv2010

Quantum Modifications to Gravity Waves in de Sitter Spacetime

We treat a model in which tensor perturbations of de~Sitter spacetime, represented as a spatially flat model, are modified by the effects of the vacuum fluctuations of a massless conformally invariant field, such as the electromagnetic field. We use the semiclassical theory of gravity with the expectation value of the conformal field stress tensor as a source. We first study the stability of de~Sitter spacetime by searching for growing, spatially homogeneous modes, and conclude that it is stable within the limits of validity of the semiclassical theory. We next examine the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term which is of the same form as the original wave, but displaced in phase by -π/2, and with an amplitude which depends upon the duration of inflation. The magnitude of this effect is proportional to the change in scale factor during inflation. So long as the energy scale of inflation and the proper frequency of the mode at the beginning of inflation are well below the Planck scale, the fractional correction is small. However, modes which are transplanckian at the onset of inflation can undergo a significant correction. The increase in amplitude can potentially have observable consequences through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the duration of inflation and is greater for shorter wavelengths.

gr-qc↗

arXiv2010

Quantum Stress Tensor Fluctuations of a Conformal Field and Inflationary Cosmology

We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly scale dependent, so the absence of such effects from the observed power spectra may imply a constraint on the total duration of inflation. We discuss different views about the validity of perturbation theory at very early times during which currently observable modes are transplanckian.

gr-qc↗

arXiv2010

Probability distributions of smeared quantum stress tensors

We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted Gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for four-dimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted Gamma distribution, but that the distribution of the energy density is not.

quant-ph↗

arXiv2009

Negative Energy Densities in Quantum Field Theory

Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the quantum inequalities which limit its magnitude and duration. However, these inequalities allow the possibility that negative energy and related effects might be observable. Some recent proposals for experiments to search for sub-vacuum phenomena will be discussed. Fluctuations of the energy density around its mean value will also be considered, and some recent results on a probability distribution for the energy density in two dimensional spacetime are summarized.

quant-ph↗

arXiv2009

Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates

The use of atomic decay rates as a probe of sub-vacuum phenomena will be studied. Because electromagnetic vacuum fluctuations are essential for radiative decay of excited atomic states, decay rates can serve as a measure of the suppression of vacuum fluctuation in non-classical states, such as squeezed vacuum states. In such states the renormalized expectation value of the square of the electric field or the energy density can be periodically negative, representing suppression of vacuum fluctuations. We explore the extent to which atomic decays can be used to measure the mean squared electric field or energy density. We consider a scheme in which atoms in an excited state transit a closed cavity whose lowest mode contains photons in a non-classical state. The change in the decay probability of the atom in the cavity due to the non-classical state can, under certain circumstances, serve as a measure of the mean squared electric field or energy density in the cavity. We derive a quantum inequality bound on the decrease in this probability. We also show that the decrease in decay rate can sometimes be a measure of negative energy density or negative squared electric field. We make some estimates of the magnitude of this effect, which indicate that an experimental test might be possible.

quant-ph↗

arXiv2009

Quantum Lightcone Fluctuations in Compactified Spacetimes

We treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity. We find that the flight times of pulses can fluctuate due to modification of the graviton vacuum by the compactification. In the case of a five dimensional Kaluza-Klein theory, the mean variation in flight time can grow logarithmically with the flight distance. This effect is in principle observable, but too small to serve as a realistic probe of the existence of extra dimensions. We also examine the effect of the compactification on the widths of spectral lines, and find that there is a small line narrowing effect. This effect is also small for compactification well above the Planck scale, but might serve as a test of the existence of extra dimensions.

gr-qc↗

arXiv2009

A Fluid Analog Model for Boundary Effects in Field Theory

Quantum fluctuations in the density of a fluid with a linear phonon dispersion relation are studied. In particular, we treat the changes in these fluctuations due to non-classical states of phonons and to the presence of boundaries. These effects are analogous to similar effects in relativistic quantum field theory, and we argue that the case of the fluid is a useful analog model for effects in field theory. We further argue that the changes in the mean squared density are in principle observable by light scattering experiments.

quant-ph↗

arXiv2008

The Phononic Casimir Effect: An Analog Model

We discuss the quantization of sound waves in a fluid with a linear dispersion relation and calculate the quantum density fluctuations of the fluid in several cases. These include a fluid in its ground state. In this case, we discuss the scattering cross section of light by the density fluctuations, and find that in many situations it is small compared to the thermal fluctuations, but not negligibly small and might be observable at room temperature. We also consider a fluid in a squeezed state of phonons and fluids containing boundaries. We suggest that the latter may be a useful analog model for better understanding boundary effects in quantum field theory. In all cases involving boundaries which we consider, the mean squared density fluctuations are reduced by the presence of the boundary. This implies a reduction in the light scattering cross section, which is potentially an observable effect.

quant-ph↗

arXiv2008

Decoherence and Recoherence in Model Quantum Systems

We discuss the various manifestations of quantum decoherence in the forms of dephasing, entanglement with the environment, and revelation of "which-path" information. As a specific example, we consider an electron interference experiment. The coupling of the coherent electrons to the quantized electromagnetic field illustrates all of these versions of decoherence. This decoherence has two equivalent interpretations, in terms of photon emission or in terms of Aharonov-Bohm phase fluctuations. We consider the case when the coherent electrons are coupled to photons in a squeezed vacuum state. The time-averaged result is increased decoherence. However, if only electrons which are emitted during selected periods are counted, the decoherence can be suppressed below the level for the photon vacuum. This is the phenomenon of recoherence. This effect is closely related to the quantum violations of the weak energy condition, and is restricted by similar inequalities. We give some estimates of the magnitude of the recoherence effect and discuss prospects for observing it in an electron interferometry experiment.

quant-ph↗

arXiv2008

Quantum Density Fluctuations in Classical Liquids

We discuss the density fluctuations of a fluid due to zero point motion. These can be regarded as density fluctuations in the phonon vacuum state. We assume a linear dispersion relation with a fixed speed of sound and calculate the density correlation function. We note that this function has the same form as the correlation function for the time derivative of a relativistic massless scalar field, but with the speed of light replaced by the speed of sound. As a result, the study of density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We next calculate the differential cross section for light scattering by the zero point density fluctuations, and find a result proportional to the fifth power of the light frequency. This can be understood as the product of fourth power dependence of the usual Rayleigh cross section with the linear frequency dependence of the spectrum of zero point density fluctuations. We give some estimates of the relative magnitude of this effect compared to the scattering by thermal density fluctuations, and find that it can be of order 0.5% for water at room temperature and optical frequencies. This relative magnitude is proportional to frequency and inversely proportional to temperature. Although the scattering by zero point density fluctuation is small, it may be observable.

quant-ph↗

arXiv2008

Recoherence by Squeezed States in Electron Interferometry

Coherent electrons coupled to the quantized electromagnetic field undergo decoherence which can be viewed as due either to fluctuations of the Aharonov-Bohm phase or to photon emission. When the electromagnetic field is in a squeezed vacuum state, it is possible for this decoherence to be reduced, leading to the phenomenon of recoherence. This recoherence effect requires electrons which are emitted at selected times during the cycle of the excited mode of the electromagnetic field. We show that there are bounds on the degree of recoherence which are analogous to quantum inequality restriction on negative energy densities in quantum field theory. We make some estimates of the degree of recoherence, and show that although small, it may be observable.

quant-ph↗

arXiv2008

Brownian Motion in Robertson-Walker Space-Times from electromagnetic Vacuum Fluctuations

We consider classical particles coupled to the quantized electromagnetic field in the background of a spatially flat Robertson-Walker universe. We find that these particles typically undergo Brownian motion and acquire a non-zero mean squared velocity which depends upon the scale factor of the universe. This Brownian motion can be interpreted as due to non-cancellation of anti-correlated vacuum fluctuations in the time dependent background space-time. We consider several types of coupling to the electromagnetic field, including particles with net electric charge, a magnetic dipole moment, and electric polarizability. We also investigate several different model scale factors.

gr-qc↗