Stochastic process behind nonlinear thermodynamic quantum master equation. II. Simulation

Flakowski, Jérôme; Schweizer, Marco; Öttinger, Hans Christian

doi:10.1103/physreva.86.032102

Cited by 13 publications

(16 citation statements)

References 36 publications

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“…Unravelings, in which the evolution of density matrices is obtained from suitably constructed stochastic processes in Hilbert space, are a fundamental tool for studying the solutions of linear [1] and nonlinear [28,29] quantum master equations. The linear zerotemperature quantum master equation (12) is easy to simulate.…”

Section: Summary and Discussionmentioning

confidence: 99%

Zero-temperature limit of thermodynamic quantum master equations

Öttinger

2018

Phys. Rev. A

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We investigate the zero-temperature limit of thermodynamic quantum master equations that govern the time evolution of density matrices for dissipative quantum systems. The quantum master equations for T = 0 and for T > 0 possess completely different structures: (i) the equation for T = 0 is linear in the deviation from the ground-state density matrix, whereas the equation for T > 0, in general, is seriously nonlinear, and (ii) the Gibbs state is obtained as the steady-state solution of the nonlinear equation for T > 0, whereas the ground state cannot be found from the equation for T = 0. Nevertheless, the equation for T = 0 can reproduce the behavior for T 0 remarkably well. We discuss some implications of that observation for dissipative quantum field theory.

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Section: Summary and Discussionmentioning

confidence: 99%

Zero-temperature limit of thermodynamic quantum master equations

Öttinger

2018

Phys. Rev. A

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“…For J μ , Lorentz transformation behavior is achieved by construction of the spinors, which are chosen to be trivial for particles at rest and then need to have a suitable momentum dependence for moving particles. The correct relativistic transformation behavior is hence hidden in the collision amplitudes (19) and (20).…”

Section: B Lorentz Invariancementioning

confidence: 99%

Kinetic theory and stochastic simulation of field quanta

Öttinger

2014

Phys. Rev. D

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We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual transverse photons. For our explicitly time-dependent approach, we introduce proper time-correlation functions. We then develop a stochastic simulation technique for solving the resulting kinetic equation. To illustrate the validity and potential of the proposed ideas, we show how a very simple simulation of the dynamics of field quanta can be used to obtain the leading-order contribution to the anomalous magnetic moment of the electron.PHYSICAL REVIEW D 90, 085005 (2014) 1550-7998=2014=90 (8)=085005(16) 085005-1

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“…Such a scheme is complementary to those based on the solutions of master equations. 4,[9][10][11][12][13] However, it does not require to approximate in any form the memory effects of the bath since its degrees of freedom are described explicitly, in the spirit of molecular dynamics simulations. 31,32 From this point of view, the approach presented here provides a non-Markovian route to the simulation of quantum effects in classical spin baths.…”

Section: H(s) = H Sb (S) +ĥ(S)mentioning

confidence: 99%

“…[6][7][8] Full quantum theories of both system and environment are difficult to simulate and usually one resorts to approach based on master equations. 4,[9][10][11][12][13] However, there are many situations where the environment's coordinates can be considered to follow the laws of classical mechanics. When such coordinates are canonically conjugate momenta and positions, one approach to treat these situations is provided by the quantum-classical Liouville equation.…”

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confidence: 99%

Communication: Quantum dynamics in classical spin baths

Sergi

2013

The Journal of Chemical Physics

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A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.

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Stochastic process behind nonlinear thermodynamic quantum master equation. II. Simulation

Cited by 13 publications

References 36 publications

Zero-temperature limit of thermodynamic quantum master equations

Zero-temperature limit of thermodynamic quantum master equations

Kinetic theory and stochastic simulation of field quanta

Communication: Quantum dynamics in classical spin baths

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