# Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains

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## Abstract

**:**

## 1. Introduction

## 2. Dissipative Finite Bose–Hubbard Chain

## 3. Computation Scheme for Two-Point Correlation Functions

#### Quantum Regression Hierarchy

## 4. Mean-Field Approximation

#### Illustrative Results

## 5. Beyond Mean-Field Approximation

## 6. Density–Density Correlation Function

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Magnitude of the spectral weight function ${A}_{j,k}$ for an initially pure Bose–Einstein condensate with ${n}_{1}(0)=500$, ${n}_{2}(0)=50$, ${n}_{3}(0)=450$, and interaction $U{N}_{0}/J=10$; the dissipation rate is set to ${\gamma}_{2}/J=5$. (

**a**) interwell correlations $\left|{A}_{2,1}({t}^{\prime},t)\right|$; (

**b**) onsite correlations $\left|{A}_{1,1}({t}^{\prime},t)\right|$.

**Figure 2.**Magnitude of the spectral weight function ${A}_{j,k}$ for an initially pure Bose–Einstein condensate with ${n}_{1}(0)=500$, ${n}_{2}(0)=50$, ${n}_{3}(0)=450$, and interaction $U{N}_{0}/J=10$; the dissipation rate is set to zero, ${\gamma}_{2}=0$. (

**a**) interwell correlations $\left|{A}_{2,1}({t}^{\prime},t)\right|$; (

**b**) onsite correlations $\left|{A}_{1,1}({t}^{\prime},t)\right|$.

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Denis, Z.; Wimberger, S.
Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains. *Condens. Matter* **2018**, *3*, 2.
https://doi.org/10.3390/condmat3010002

**AMA Style**

Denis Z, Wimberger S.
Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains. *Condensed Matter*. 2018; 3(1):2.
https://doi.org/10.3390/condmat3010002

**Chicago/Turabian Style**

Denis, Zakari, and Sandro Wimberger.
2018. "Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains" *Condensed Matter* 3, no. 1: 2.
https://doi.org/10.3390/condmat3010002