Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions

2005 ◽  
Vol 122 (6) ◽  
pp. 064102 ◽  
Author(s):  
Xin Chen ◽  
Yinghua Wu ◽  
Victor S. Batista
Keyword(s):  
Fourier Transform ◽  
Correlation Functions ◽  
Matching Pursuit ◽  
Split Operator ◽  
Thermal Correlation

Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

2005 ◽  
Vol 122 (11) ◽  
pp. 114114 ◽  
Author(s):  
Yinghua Wu ◽  
Michael F. Herman ◽  
Victor S. Batista
Keyword(s):  
Fourier Transform ◽  
Quantum Dynamics ◽  
Matching Pursuit ◽  
Split Operator

scholarly journals Dispersion formulas in QFTs, CFTs and holography

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
David Meltzer
Keyword(s):  
Fourier Transform ◽  
Correlation Functions ◽  
Momentum Space ◽  
Conformal Blocks ◽  
Dispersion Formula ◽  
Space Dispersion

Abstract We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

scholarly journals Thermal correlation functions of twisted quantum fields

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Prasad Basu ◽  
Rahul Srivastava ◽  
Sachindeo Vaidya
Keyword(s):  
Correlation Functions ◽  
Quantum Fields ◽  
Thermal Correlation

Higher order exponential split operator method for solving time-dependent Schrödinger equations

1992 ◽  
Vol 70 (2) ◽  
pp. 555-559 ◽  
Author(s):  
André D. Bandrauk ◽  
Hai Shen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operator Method ◽  
Computation Time ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exponential Form ◽  
Operator Solution ◽  
Split Operator

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

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