Explicit examples of probability distributions for the energy density in two-dimensional conformal field theory

Anthony, Matthew C.; Fewster, Christopher J.

doi:10.1103/physrevd.101.025010

Cited by 3 publications

(3 citation statements)

References 15 publications

(56 reference statements)

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“…The latter method can be applied to the cases of the vacuum and certain other special states, including thermal equilibrium states and also highest weight states [4]. Each method rests on the solution to certain subsidiary problems and closed form results are only available in particular cases [1, 4,16], though the method of [4] is also amenable to numerical treatment.…”

Section: Exact Results In 2-dimensional Conformal Field Theorymentioning

confidence: 99%

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Probability distributions for space and time averaged quantum stress tensors

Fewster

Ford

2020

Phys. Rev. D

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We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement process for a stress tensor component, such as the energy density of a quantized field in its vacuum state. Although spatial averaging reduces the probability of large vacuum fluctuations compared to time averaging alone, we find that the probability distribution decreases more slowly than exponentially as the magnitude of the measured energy density increases. This implies that vacuum fluctuations can sometimes dominate over thermal fluctuations and potentially have observable effects. I. INTRODUCTIONAlthough the vacuum state of a quantum field theory is an eigenstate of the Hamiltonian, the integral of the energy density over all space, it is not an eigenstate of the local energy density or of other components of the stress tensor.This implies the existence of vacuum fluctuations of the energy density and other quadratic operators. For these fluctuations to be finite, and hence physically meaningful, these operators must be averaged over a finite spacetime region. We can view the averaging process as representing the outcome of a measurement of the operator. The energy density at a single spacetime point is not measurable, and hence not meaningful. However, the spacetime average is meaningful, and will have finite fluctuations described by a probability distribution.The study of the probability distributions for quantum stress tensors was begun in Ref.[1] for conformal field theory (CFT) in two spacetime dimensions, and continued in Refs.[2] and [3] for quantum fields in flat four dimensional spacetime. Further results on CFT appear in [4]. Let x denote a dimensionless measure of the averaged stress tensor component T . If τ is a measure of the size of the sampling region, then in units where = c = 1, we may take x = τ d T , where d is the dimension of the spacetime. Let P (x) denote a probability distribution so that P (x) dx is the probability in a measurement of finding an outcome in the interval [x, x + dx]. There are two key features of P (x) for a quadratic operator, such as the energy density, which have emerged in the papers just cited: 1) There is a negative lower bound on the region where P (x) = 0 if T ≥ 0 at the classical level, and 2) P (x) can fall more slowly than exponentially, leading to an enhanced probability for large positive fluctuations relative to thermal fluctuations.By contrast, the probability distribution for the spacetime average of a linear operator, such as the electric field, is a Gaussian function.If T is a non-negative quantity in classical physics, such as the energy density, its quantization typically admits quantum states for which its expectation value is below the vacuum value. In particular, if the vacuum expectation value vanishes there exist states for which its expectation value is negative, T < 0, so regions where the mean energy d...

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Section: Exact Results In 2-dimensional Conformal Field Theorymentioning

confidence: 99%

“…For any unitary positive energy CFT, the probability distribution of T L (F L ) in the vacuum state is known in closed form [1] (see [4,16] for some other closed form expressions) and is given by the shifted Gamma distribution…”

Section: Exact Results In 2-dimensional Conformal Field Theorymentioning

confidence: 99%

Probability distributions for space and time averaged quantum stress tensors

Fewster

Ford

2020

Phys. Rev. D

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“…Physically, we may interpret this averaging as encoding the details of experimental measurements, though the correspondence between the two remains under investigation. In two-dimensional conformal field theory with a Gaussian temporal sampling function, the probability P (x) of measuring a fluctuation of magnitude x is a shifted Gamma distribution [12][13][14] bounded below by the optimal quantum inequality bound [15]. In four dimensions, the situation is qualitatively similar, and studies have been conducted for time averaging [16,17] and spacetime averaging [18].…”

Section: Introductionmentioning

confidence: 99%

Space and time averaged quantum stress tensor fluctuations

Ford

Schiappacasse

2021

Phys. Rev. D

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Observing physical effects of large quantum stress tensor fluctuations requires knowledge of the interaction between the probe and the particles of the underlying quantum fields. The quantum stress tensor operators must first be averaged in time alone or space and time to confer meaningful results, the details of which may correspond to the physical measurement process. We build on prior results to characterize the particle frequencies associated with quantum fluctuations of different magnitudes. For the square of time derivatives of the massless scalar field in a spherical cavity, we find that these frequencies are bounded above in a power law behavior. Our findings provide a way identify the largest quantum fluctuation that may be probed in experiments relying on frequency-dependent interactions.

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Frequency spectra analysis of space- and time-averaged quantum stress tensor fluctuations

Ford²,

Schiappacasse³

2023

Phys. Rev. D

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Explicit examples of probability distributions for the energy density in two-dimensional conformal field theory

Cited by 3 publications

References 15 publications

Probability distributions for space and time averaged quantum stress tensors

Probability distributions for space and time averaged quantum stress tensors

Space and time averaged quantum stress tensor fluctuations

Frequency spectra analysis of space- and time-averaged quantum stress tensor fluctuations

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