Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Cresser, J. D.; Anders, Janet

doi:10.1103/physrevlett.127.250601

Cited by 53 publications

(101 citation statements)

References 69 publications

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“…As noted elsewhere [5,20], the steady state of the polaron theory is equivalent to the projected ensemble of Ref. [8], and so matches the HMF Gibbs state in the limit as systemreservoir coupling goes to infinity.…”

Section: Introductionmentioning

confidence: 59%

“…In this section we compare the time evolution of a quantum system strongly coupled to an environment, as predicted by TEMPO [16,18], against various thermodynamic ensembles. We do this using a simple generalized spin-boson model, as also studied by Cresser and Anders [8]. Our system Hamiltonian takes the form H S = (ω q /2)σ z , in terms of system Pauli operators σ x,y,z , while the reservoir Hamiltonian and coupling is as in Eq.…”

Section: Dynamics Of the Generalized Qubit-boson Modelmentioning

confidence: 99%

“…We choose ω q = k B T = 1, ω c = 10 in all our results, and vary α, θ. [8] have shown that at large coupling ρ HMF = ρ proj . For intermediate coupling however these differ.…”

Section: Dynamics Of the Generalized Qubit-boson Modelmentioning

confidence: 99%

“…This concept is very useful when considering the thermodynamics of small quantum systems strongly coupled to their environment [5][6][7]. Recent work [5,8] has provided analytic expressions for the form of the HMF Gibbs state in the limits of weak and strong system-reservoir coupling.…”

Section: Introductionmentioning

confidence: 99%

“…In the strong-coupling limit, while general arguments of ergodicity should make the HMF Gibbs state robust, the litera-ture is less clear. In particular, recent predictions [14,15] for the steady state of a strong-coupling master equation differ from the strong-coupling form of the HMF Gibbs state [8]. To help address this question, Cresser and Anders [8] have shown that at strong coupling, in cases where the system-reservoir coupling is proportional to a single system operator X, the Hamiltonian of Mean Force takes the projected form H HMF = n |n n|H S |n n|, where |n are the eigenstates of X.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical evaluation and robustness of the quantum mean force Gibbs state

Chiu,

Strathearn,

Keeling

2021

Preprint

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We introduce a numerical method to determine the Hamiltonian of Mean Force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the Time Evolving Matrix Product Operator (TEMPO) algorithm to imaginary time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.

show abstract

Section: Introductionmentioning

confidence: 59%

Section: Dynamics Of the Generalized Qubit-boson Modelmentioning

confidence: 99%

“…We choose ω q = k B T = 1, ω c = 10 in all our results, and vary α, θ. [8] have shown that at large coupling ρ HMF = ρ proj . For intermediate coupling however these differ.…”

Section: Dynamics Of the Generalized Qubit-boson Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical evaluation and robustness of the quantum mean force Gibbs state

Chiu,

Strathearn,

Keeling

2021

Preprint

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Dynamics of a strongly coupled quantum heat engine—Computing bath observables from the hierarchy of pure states

Boettcher,

Hartmann,

Beyer

et al. 2024

The Journal of Chemical Physics

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We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both in its initial transient phase and, also later, in its periodic steady state. A quantum Otto engine with a qubit as an inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths sensitively depends on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of bath interactions. We visualize these various work contributions using the analog of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit.

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Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach

Brenes,

Min,

Anto-Sztrikacs

et al. 2024

The Journal of Chemical Physics

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Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system–bath configurations without resorting to a perturbative description of the system–bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system–bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

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Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Cited by 53 publications

References 69 publications

Numerical evaluation and robustness of the quantum mean force Gibbs state

Numerical evaluation and robustness of the quantum mean force Gibbs state

Dynamics of a strongly coupled quantum heat engine—Computing bath observables from the hierarchy of pure states

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach

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