Exact solutions for spin-1/2 systems using dynamical manipulation techniques

A model of an arbitrary spin coupled to a bath of spins $\frac{1}{2}$ in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales $1/(A\sqrt{N})$ , where $A$ is the coupling constant and $N$ is the number of spins in the bath.A model of an arbitrary spin coupled to a bath of spins $\frac{1}{2}$ in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales $1/(A\sqrt{N})$, where $A$ is the coupling constant and $N$ is the number of spins in the bath.

arXiv:1401.7572Physical Review AJan 13, 201414 citations

Static and dynamic properties of a one-dimensional spin-1/2 system

Aviva Shooman, Léa Ferreira dos Santos

Bulletin of the American Physical SocietyMar 4, 20190 citations

Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques

Heinz‐Peter Breuer, Daniel Klaus Burgarth, Francesco Petruccione

The reduced dynamics of a central spin coupled to a bath of $N$ spin- $\frac{1}{2}$ particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.The reduced dynamics of a central spin coupled to a bath of $N$ spin-$\frac{1}{2}$ particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.

arXiv:quant-ph/0401051Physical Review BJul 30, 2004256 citations

Manipulation and dynamics of quantum spin systems

Kristel F. L. Michielsen

Jan 1, 20170 citations

Precision control of charge coherence in parallel double dot systems through spin-orbit interaction

Jinshuang Jin, Matisse Wei-Yuan Tu, Nien-En Wang +1 more

In terms of the exact quantum master equation solution for open electronic systems, the coherent dynamics of two charge states described by two parallel quantum dots with one fully polarized electron on either dot is investigated in the presence of spin-orbit interaction. We demonstrate that the double dot system can stay in a dynamically decoherence free space. The coherence between two double dot charge states can be precisely manipulated through a spin-orbit coupling. The effects of the temperature, the finite bandwidth of lead, and the energy deviations during the coherence manipulation are also explored.In terms of the exact quantum master equation solution for open electronic systems, the coherent dynamics of two charge states described by two parallel quantum dots with one fully polarized electron on either dot is investigated in the presence of spin-orbit interaction. We demonstrate that the double dot system can stay in a dynamically decoherence free space. The coherence between two double dot charge states can be precisely manipulated through a spin-orbit coupling. The effects of the temperature, the finite bandwidth of lead, and the energy deviations during the coherence manipulation are also explored.

arXiv:1103.5099The Journal of Chemical PhysicsAug 13, 20134 citations

Exact results for the dynamics of one-dimensional spin-systems

U. Brandt, K. Jacoby

The European Physical Journal BJun 1, 197692 citations

A model of an arbitrary spin coupled to a bath of spins

\frac{1}{2}

in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales

1/(A\sqrt{N})

, where

A

is the coupling constant and

N

is the number of spins in the bath.

The reduced dynamics of a central spin coupled to a bath of

N

spin-

\frac{1}{2}

particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.