Definition
Okumaya devam et...
← Previous revision | Revision as of 06:01, 6 May 2024 |
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| |journal=AIP Advances | volume=10 | page=025106 | year=2020|issue=2|arxiv=1906.04478|bibcode=2020AIPA...10b5106M|s2cid=184487806}}</ref>) | |journal=AIP Advances | volume=10 | page=025106 | year=2020|issue=2|arxiv=1906.04478|bibcode=2020AIPA...10b5106M|s2cid=184487806}}</ref>) |
| <math>\dot\rho=-{i\over\hbar}[H,\rho]+\sum_{i}^{} \gamma_i\left(L_i\rho L_i^\dagger -\frac{1}{2} \left\{L_i^\dagger L_i, \rho\right\} \right)</math> | :<math>\dot\rho=-{i\over\hbar}[H,\rho]+\sum_{i}^{} \gamma_i\left(L_i\rho L_i^\dagger -\frac{1}{2} \left\{L_i^\dagger L_i, \rho\right\} \right)</math> |
| where <math>\{a, b\} = ab + ba </math> is the [[anticommutator]], <math>H</math> is the system Hamiltonian, describing the unitary aspects of the dynamics, and <math>L_i</math> are a set of '''jump operators''' describing the dissipative part of the dynamics. The shape of the jump operators describes how the environment acts on the system, and must ultimately be determined from microscopic models of the system-environment dynamics. Finally, <math>\gamma_i \geq 0</math> are a set of non-negative coefficients called damping rates. If all <math>\gamma_i = 0</math> one recovers the von Neumann equation <math>\dot\rho=-(i/\hbar)[H,\rho]</math> describing unitary dynamics, which is the quantum analog of the classical [[Liouville's theorem (Hamiltonian)|Liouville equation]]. | where <math>\{a, b\} = ab + ba </math> is the [[anticommutator]], <math>H</math> is the system Hamiltonian, describing the unitary aspects of the dynamics, and <math>L_i</math> are a set of '''jump operators''' describing the dissipative part of the dynamics. The shape of the jump operators describes how the environment acts on the system, and must ultimately be determined from microscopic models of the system-environment dynamics. Finally, <math>\gamma_i \geq 0</math> are a set of non-negative coefficients called damping rates. If all <math>\gamma_i = 0</math> one recovers the von Neumann equation <math>\dot\rho=-(i/\hbar)[H,\rho]</math> describing unitary dynamics, which is the quantum analog of the classical [[Liouville's theorem (Hamiltonian)|Liouville equation]]. |
Okumaya devam et...