Numerical evaluation and robustness of the quantum mean-force Gibbs state

Chiu, Yiu-Fung; Strathearn, Aidan; Keeling, Jonathan

doi:10.1103/physreva.106.012204

Cited by 17 publications

(3 citation statements)

References 48 publications

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“…MPO算法推广到多个浴的情况 [59] . Ye和Chan [60] 在2021年研究了更复杂浴下的影响泛函的张量网络构造方法. Chiu等 [61] 在2022年将TEMPO算法应用到虚时演化的情况 .…”

Section: 放系统中关联函数的方法该方法给出的关联函数是非马尔可夫的因此超越了通常使用的量子回归unclassified

Time-evolving matrix product operator method and its applications in open quantum system

Chen¹

2023

Acta Phys. Sin.

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Quantum open systems play an important role in the development of quantum sciences, therefore the study of corresponding numerical method is of great significance. For calculation of quantum open systems, the quasi-adiabatic propagator path integral, which was invented in 1990s, is one of the few numerically exact methods. However, its computational complexity scales exponentially with system size and correlation length, and due to this disadvantage its application is limited in practical calculation. In recent years, the study and application of tensor network has made rapid progress. Representing the path integral by tensor network makes scaling of the computational complexity polynomially, which greatly improve the computational efficiency. Such a new method is called time-evolving matrix product operators. At the very beginning, the reduced density matrix is represented as a matrix product state. Then the time evolution of the system can be achieved by iteratively applying matrix product operators on the matrix product state. The iterative process is amenable to the standard matrix product states compression algorithm, which keeps the computational cost at polynomial scales. The time-evolving matrix product operators is an efficient, numerically exact and fully non-Markovian method, which has a broad application prospect in the study of quantum open systems. For instance, it is already used in the study of the thermalization, heat statistic, heat transfer and optimal control of the quantum open systems, and conversely it can be also used to investigate the effect of the system on the environment. In addition, the TEMPO method is naturally connected to the process tensor which can be used to calculate the correlation function of the system efficiently. This article gives a review of this method and its applications.

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Section: 放系统中关联函数的方法该方法给出的关联函数是非马尔可夫的因此超越了通常使用的量子回归unclassified

Time-evolving matrix product operator method and its applications in open quantum system

Chen¹

2023

Acta Phys. Sin.

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“…Specifically, when considering a system strongly coupled to an environment, its thermal state is described by a "Hamiltonian of mean force" that accounts for the environmental interaction. In those cases where this effective Hamiltonian is known [10,[58][59][60][61], the correction to the bare Hamiltonian is also quadratic rather than linear. It is tempting to speculate that these two phenomena may be related to each other.…”

Section: Discussionmentioning

confidence: 99%

The wave operator representation of quantum and classical dynamics

McCaul¹,

Zhdanov²,

Bondar³

2023

Preprint

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The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator representation of quantum dynamics, and explore its connection to standard methods of quantum dynamics, such as the Wigner phase space function. This method takes as its central object the square root of the density matrix, and consequently enjoys several unusual advantages over standard representations. By combining this with purification techniques imported from quantum information, we are able to obtain a number of results. Not only is this formalism able to provide a natural bridge between phase and Hilbert space representations of both quantum and classical dynamics, we also find the wave operator representation leads to novel semiclassical approximations of both real and imaginary time dynamics, as well as a transparent correspondence to the classical limit. This is demonstrated via the example of quadratic and quartic Hamiltonians, while the potential extensions of the wave operator and its application to quantum-classical hybrids is discussed. We argue that the wave operator provides a new perspective that links previously unrelated representations, and is a natural candidate model for scenarios (such as hybrids) in which positivity cannot be otherwise guaranteed.

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“…Here, the thermal equilibrium state is described by the mean force (Gibbs) state, which has been studied comprehensively in the classical and quantum regime for one-dimensional and isotropic three-dimensional interactions with the environment [11][12][13][14][15]. Recently, it has been shown that for the one-dimensional θ -angled spin-boson model, the quantum mean force state becomes precisely the classical mean force state in the large-spin limit [16].…”

Section: Introductionmentioning

confidence: 99%