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 11 publications

(1 citation statement)

References 48 publications

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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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Section: Discussionmentioning

confidence: 99%

The wave operator representation of quantum and classical dynamics

McCaul¹,

Zhdanov²,

Bondar³

2023

Preprint

View full text Add to dashboard Cite

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Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

Chen

Cheng

2022

J. Chem. Phys.

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We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system + bath) is held in canonical thermal equilibrium by weak coupling with a “super-bath”. Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long range interaction systems.

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Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit

Трушечкин

2022

Phys. Rev. A

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

Cited by 11 publications

References 48 publications

The wave operator representation of quantum and classical dynamics

The wave operator representation of quantum and classical dynamics

Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit

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