A stochastic Dyson series expansion

2006 ◽  
pp. 227-232 ◽  
Author(s):  
K. R. Parthasarathy ◽  
K. B. Sinha
Keyword(s):  
Series Expansion ◽  
Dyson Series

scholarly journals Numerical Contour Integration

2021 ◽  
Author(s):  
Erickson Tjoa
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Series Expansion ◽  
Complex Analysis ◽  
Green’S Functions ◽  
Contour Integration ◽  
Second Order ◽  
Quantum Field ◽  
Dyson Series ◽  
Wightman Functions

We present a straightforward implementation of contour integration by setting options for Integrate and NIntegrate, taking advantage of powerful results in complex analysis. As such, this article can be viewed as documentation to perform numerical contour integration with the existing built-in tools. We provide examples of how this method can be used when integrating analytically and numerically some commonly used distributions, such as Wightman functions in quantum field theory. We also provide an approximating technique when time-ordering is involved, a commonly encountered scenario in quantum field theory for computing second-order terms in Dyson series expansion and Feynman propagators. We believe our implementation will be useful for more general calculations involving advanced or retarded Green’s functions, propagators, kernels and so on.

scholarly journals Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit: Divergences and resolution

2014 ◽  
Vol 141 (19) ◽  
pp. 194101 ◽  
Author(s):  
Juzar Thingna ◽  
Hangbo Zhou ◽  
Jian-Sheng Wang
Keyword(s):  
Steady State ◽  
Series Expansion ◽  
Quantum Transport ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Dyson Series

scholarly journals Mean field dynamics of some open quantum systems

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170856
Author(s):  
Marco Merkli ◽  
Alireza Rafiyi
Keyword(s):  
Quantum System ◽  
Series Expansion ◽  
Open Quantum Systems ◽  
Mean Field ◽  
Quantum Systems ◽  
Fixed Number ◽  
Field Interaction ◽  
Dyson Series ◽  
Quantum Particles ◽  
Energy Conserving

We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of N . The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit N → ∞ , of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.

Series Expansion Methods for Strongly Interacting Lattice Models

2006 ◽  
Author(s):  
Jaan Oitmaa ◽  
Chris Hamer ◽  
Weihong Zheng
Keyword(s):  
Series Expansion ◽  
Lattice Models ◽  
Strongly Interacting

Motion Mode Decomposition Based on Discrete Fourier Series Expansion

2012 ◽  
Vol 132 (3) ◽  
pp. 366-373 ◽  
Author(s):  
Yoshiyuki Hatta ◽  
Tomoyuki Shimono
Keyword(s):  
Fourier Series ◽  
Series Expansion ◽  
Fourier Series Expansion ◽  
Discrete Fourier Series ◽  
Mode Decomposition ◽  
Motion Mode

Truncation Error for the Simpson’s 1/3 Rule Based on Taylor Series Expansion

2020 ◽  
Author(s):  
Antonio Carlos Foltran ◽  
Carlos Henrique Marchi ◽  
Luís Mauro Moura
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Truncation Error ◽  
Taylor Series Expansion ◽  
Rule Based

Some Notes on Taylors Series Expansion with ODE´S

2015 ◽  
Vol 18 (2) ◽  
pp. 149-156
Author(s):  
Shawki A.M. Abbas ◽  
Keyword(s):  
Series Expansion
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