Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

Tupkary, Devashish; Dhar, Abhishek; Kulkarni, Manas; Purkayastha, Archak

doi:10.1103/physreva.105.032208

Cited by 53 publications

(27 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fleming et al 223 (see also Ref. 224 ) show that the above ambiguity in the steady state is a consequence of the perturbative approach used to construct the master equation: solving a 2n order perturbative master equation will yield the diagonal elements of the steady state accurate only to order 2n − 2 (while the off-diagonal elements are determined to order 2n). So resolving the second order indeterminacy requires expanding the master equation to fourth order, and then using degenerate perturbation theory to find the needed corrections, thus fixing W in the above.…”

Section: Weak Coupling: Bloch-redfield Master Equation (Brme)mentioning

confidence: 99%

Open quantum system dynamics and the mean force Gibbs state

Trushechkin,

Merkli,

Cresser

et al. 2021

Preprint

View full text Add to dashboard Cite

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at decreasing system sizes, i.e. for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? And if not, how may the steady state depend on the interaction details? Here we provide an overview of recent progress on answering these questions. We expand on the state-of-the-art along two general avenues: First we take the static point-of-view which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and non-equilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point-of-view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm which proves return to equilibrium, i.e. convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics, and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics and quantum optics, and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology, to magnetism and nanoscale heat management.

show abstract

Section: Weak Coupling: Bloch-redfield Master Equation (Brme)mentioning

confidence: 99%

Open quantum system dynamics and the mean force Gibbs state

Trushechkin,

Merkli,

Cresser

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…where recall that C k,k is defined in Eq. (34). The total particle number is given by summing over all lattice sites,…”

Section: B Methods 2: Redfield Quantum Master Equation Approachmentioning

confidence: 99%

Filling an empty lattice by local injection of quantum particles

Trivedi¹,

Agarwalla²,

Dhar³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

“…This strategy provides computational simplicity and speedup leading to its extensive use for studying spin and fermionic chains [9,11,15,17,19,23,24,31]. Such local Lindblad approximation of the coupling of the system to a quantum environment generically results in violation of local conservation laws near the edges [32]. Here we assume here that energy transport properties in the bulk of the chain are unaffected by this.…”

Section: Modelmentioning

confidence: 99%

Energy transport in Z3 chiral clock model

Nishad,

Sreejith

2021

Preprint

View full text Add to dashboard Cite

We characterize the energy transport in a one dimensional Z 3 chiral clock model. The model generalizes the Z 2 symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter θ, in addition to f and J which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, this cannot be transformed to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of size up to 48. We present the estimated NESS current and its scaling exponent γ with respect to system size as a function of θ at different f /J. The estimated γ(f /J, θ) point to a ballistic energy transport along a line of integrable points f = J cos 3θ in the parameter space; all other points deviate from ballistic transport, and indicate super-diffusive or diffusive behavior within the range of system sizes accessible.

show abstract

Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

Cited by 53 publications

References 64 publications

Open quantum system dynamics and the mean force Gibbs state

Open quantum system dynamics and the mean force Gibbs state

Filling an empty lattice by local injection of quantum particles

Energy transport in Z3 chiral clock model

Contact Info

Product

Resources

About