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A fast time domain ...
A fast time domain solver for the equilibrium Dyson equation
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- Kaye, Jason (författare)
- Center for Computational Mathematics, Flatiron Institute, New York NY, USA; Center for Computational Quantum Physics, Flatiron Institute, New York NY, USA
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Strand, Hugo U. R., 1983- (författare)
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(creator_code:org_t)
- Springer, 2023
- 2023
- Engelska.
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Ingår i: Advances in Computational Mathematics. - : Springer. - 1019-7168 .- 1572-9044. ; 49:4
- Relaterad länk:
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https://doi.org/10.1...
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visa fler...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
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- We consider the numerical solution of the real-time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph and the Sachdev-Ye-Kitaev model.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Nonlinear Volterra integral equations
- Fast algorithms
- Equilibrium Dyson equation
- Many-body Green's function methods
- 81-10
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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