Topic
Correlation function (quantum field theory)
About: Correlation function (quantum field theory) is a research topic. Over the lifetime, 1533 publications have been published within this topic receiving 27106 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, the authors studied the limit behavior as N→∞ and showed that the norming constants tend to infinity more rapidly than the usual norming sequence when the correlation function r(n) tends slowly to 0, and generalized the results to the case when the parameter set is multi-dimensional.
Abstract: Let a stationary Gaussian sequence X
n
, n=... −1,0,1, ... and a real function H(x) be given. We define the sequences
$$Y_n^N = \frac{1}{{A_N }} \cdot \sum\limits_{j = \left( {n - 1} \right)N}^{nN - 1} {H\left( {X_j } \right)}$$
,n=... −1,0,1...; N=1,2, ... where A
N
are appropriate norming constants. We are interested in the limit behaviour as N→∞. The case when the correlation function r(n)=EX
0
X
n
tends slowly to 0 is investigated. In this situation the norming constants A>
N
tend to infinity more rapidly than the usual norming sequence A>
N
=√N. Also the limit may be a non-Gaussian process. The results are generalized to the case when the parameter-set is multi-dimensional.
716 citations
TL;DR: In this article, the relationship between quantum chaos and pseudorandomness was studied by developing probes of unitary design, and it was shown that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential.
Abstract: We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
519 citations
Journal Article•
TL;DR: To what extent an average-response computer can be utilized for computing a cross-correlation function is shown, and two methods are described, both with respect to the results and to the accuracy obtainable.
Abstract: This paper shows to what extent an average-response computer can be utilized for computing a cross-correlation function. This type of computer needs synchronization pulses, and the simplest methods of computation are those in which these pulses are directly derived from one of the signals (triggered correlation). The first method is to generate a synchronization pulse whenever the signal crosses a pre-set threshold in any direction. In this case, the computer output function is shown to be proportional to the true correlation function, for Gaussian signals. In a second method, synchronization pulses are produced when the signal crosses the threshold in a specified (e.g., positive) direction. Then the computer output is found to be contaminated by a systematic error, which, in turn, depends on the derivative of the correlation function. These two methods are described in detail, both with respect to the results and to the accuracy obtainable. Several other, less important, methods are only briefly described.
499 citations
TL;DR: As a continuation of Part I, the spectral correlation function is presented for a variety of types of digitally modulated signals, including digital pulse-amplitude, pulse-width, and pulse-position modulation, and various types of phase- shift keying and frequency-shift keying.
Abstract: As a continuation of Part I, the spectral correlation function is presented for a variety of types of digitally modulated signals. These include digital pulse-amplitude, pulse-width, and pulse-position modulation, and various types of phase-shift keying and frequency-shift keying. The magnitudes of the spectral correlation functions are graphed as the heights of surfaces above a bifrequency plane, and these graphs are used as visual aids for comparison and contrast of the spectral correlation properties of different modulation types.
437 citations
TL;DR: It is shown that resonance fluorescence, i.e., the resonant emission of a coherently driven two-level system, can be realized with a semiconductor quantum dot and second-order correlation measurements further confirm nonclassical light emission.
Abstract: We show that resonance fluorescence, i.e., the resonant emission of a coherently driven two-level system, can be realized with a semiconductor quantum dot. The dot is embedded in a planar optical microcavity and excited in a waveguide mode so as to discriminate its emission from residual laser scattering. The transition from the weak to the strong excitation regime is characterized by the emergence of oscillations in the first-order correlation function of the fluorescence, $g(\ensuremath{\tau})$, as measured by interferometry. The measurements correspond to a Mollow triplet with a Rabi splitting of up to $13.3\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$. Second-order correlation measurements further confirm nonclassical light emission.
426 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 44 |
| 2024 | 84 |
| 2023 | 158 |
| 2022 | 1,096 |
| 2021 | 58 |
| 2020 | 47 |