scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

scholarly journals PATH INTEGRATION IN RELATIVISTIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (09) ◽  
pp. 1629-1635 ◽  
Author(s):  
IAN H. REDMOUNT ◽  
WAI-MO SUEN
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Wkb Approximation ◽  
Relativistic Quantum Mechanics ◽  
Path Integral Formulation ◽  
Quantum Theories ◽  
Short Time

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

Generalized turbulence space-correlation and wave-number spectrum-function pairs

1968 ◽  
Vol 46 (19) ◽  
pp. 2133-2153 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Correlation Function ◽  
Exponential Decay ◽  
Power Law ◽  
Computer Calculation ◽  
Wave Number ◽  
Large Wave ◽  
Space Correlation ◽  
Power Law Decay ◽  
Wave Numbers ◽  
Spectrum Function

A new generalized pair of space-correlation and wave-number spectrum functions, which has properties indicated by fluid dynamics and by intuition, is proposed. In contrast with previously used combinations, both are analytic functions and smooth and cover the complete range of their arguments. For example, the spectrum form can apply to all wave numbers rather than to any limited portion, such as the inertial range. Whenever convolution is necessary, it becomes a routine computer calculation. Furthermore, the correlation function has a zero first derivative and a negative second derivative at the origin, giving both an integral scale and a microscale for the turbulence. The spectrum function can have an inertial region with some power-law decay for intermediate wave numbers and has an exponential decay for very large wave numbers. There are three adjustable parameters, determined by experiment, namely, the spectral power-law decay index, the turnover point where this power law starts, and the turnover point where the power dependence changes to an exponential decay. A library of such spectrum functions is not required, since the single proposed function, with its adjustable parameters, can be made to fit most data. One can also allow any even power of wave number for the spectral dependence in the limit of zero wave number. Simple anisotropic functional forms can readily be incorporated. It is indicated that two inertial falloffs with different power laws can be provided and the resultant correlation function is derivable by convolution. The results are applied to simplified versions of plasma electron density fluctuations and to velocity fluctuations of the background fluid. Various scales of turbulence and the related pressure-correlation function are derived. Expressions of correlation functions of amplitude and phase over parallel-line-of-sight propagation paths are also deduced.The proposed pair of functions should only be considered as a generalized model of Tatarski's form, which allows easy conversion from the correlation to the spectrum function and vice versa. Perhaps even more realistic forms can be invented.

scholarly journals Power-law decay of the spatial correlation function in exciton-polariton condensates

2012 ◽  
Vol 109 (17) ◽  
pp. 6467-6472 ◽  
Author(s):  
G. Roumpos ◽  
M. Lohse ◽  
W. H. Nitsche ◽  
J. Keeling ◽  
M. H. Szymanska ◽  
...  
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Power Law ◽  
Spatial Correlation Function ◽  
Power Law Decay

scholarly journals Spin and Dynamics in Relativistic Quantum Theories

2014 ◽  
Vol 56 (6-9) ◽  
pp. 395-399 ◽  
Author(s):  
W. N. Polyzou ◽  
W. Glöckle ◽  
H. Witała
Keyword(s):  
Relativistic Quantum ◽  
Quantum Theories

TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID

2012 ◽  
Vol 26 (29) ◽  
pp. 1250146 ◽  
Author(s):  
BHASKAR SEN GUPTA ◽  
SHANKAR P. DAS
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Hard Sphere ◽  
Numerical Solutions ◽  
Packing Fraction ◽  
Equilibrium Density ◽  
Density Correlation ◽  
Density Correlation Function ◽  
Basic Model ◽  
The One

The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

On the closed-form output correlation function of power-law devices

1966 ◽  
Vol 54 (11) ◽  
pp. 1625-1626 ◽  
Author(s):  
M. Fukada ◽  
S. Rauch
Keyword(s):  
Correlation Function ◽  
Closed Form ◽  
Power Law

Charmonia production in W → (cc̄)Ds(∗) decays

2021 ◽  
Vol 36 (09) ◽  
pp. 2150058
Author(s):  
A. V. Luchinsky ◽  
A. K. Likhoded
Keyword(s):  
Quantum Chromodynamics ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Branching Fractions ◽  
Color Singlet ◽  
Leading Order ◽  
Paper Production ◽  
Quantum Numbers ◽  
Numerical Predictions ◽  
State Formula

In this paper, production of charmonium state [Formula: see text] in exclusive [Formula: see text] decays is analyzed in the framework of both leading order Non-relativistic Quantum Chromodynamics (NRQCD) and light-cone (LC) expansion models. Analytical and numerical predictions for the branching fractions of these decays in both the approaches are given. The typical value of the branching fractions is [Formula: see text][Formula: see text][Formula: see text] and it turns out that the LC results are significantly larger than NRQCD ones (approximately two or four times increase depending on the quantum numbers of the final particles), so the effect of internal quark motion should be taken into account. Some rough estimates of color-octet contributions are presented and it is shown that these contributions could be comparable with color-singlet results.

scholarly journals When an oscillating center in an open system undergoes power law decay

2018 ◽  
Vol 57 (3) ◽  
pp. 750-768 ◽  
Author(s):  
Sandip Saha ◽  
Gautam Gangopadhyay
Keyword(s):  
Power Law ◽  
Open System ◽  
Power Law Decay
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