Field Theory of Many-Body Lindbladian Dynamics

Thompson, Foster; Kamenev, Alex

doi:10.48550/arxiv.2301.02953

Cited by 2 publications

(5 citation statements)

References 96 publications

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“…We note that L has a block structure. The zero matrix in the upper-left corner derives from the trace preservation of the Lindblad equation [2,8]. This block would connect the 'c'operators to each other.…”

Section: Superoperator Formalism and Non-hermitian Hamiltonianmentioning

confidence: 99%

“…while z = 0. For ϵ = ∆ the Liouvillian matrix L is not diagonalizable and therefore the Jordan decomposition is needed [8]. The symplectic transition matrix…”

Section: Pt -'Symmetry' In Coupled Harmonic Oscillatorsmentioning

confidence: 99%

“…Starting from the stationary state, new ladder operators generate 'excited states' with a simple exponential time-evolution. Recently, the connection of this approach to a covariance matrix approach of Gaussian states [7] and the Keldysh path-integral formulation of open systems has been highlighted [8,9]. The identification of eigenmodes with a simple exponential time-evolution allows one to separate fast from slow degrees of freedom efficiently.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we outline a method to 'third quantize' a quadratic bosonic Liouvillian using a symplectic transformation. This method draws inspiration from the classical mechanics of the saddle-point dynamic of the bosonic Keldysh action [8]. The main difference to [2] is that we diagonalize the Liouvillian in a single step.…”

Section: Introductionmentioning

confidence: 99%

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Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Kim,

Hassler

2023

J. Phys. A: Math. Theor.

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Open quantum systems that interact with a Markovian environment can be described by a Lindblad master equation. The generator of time-translation is given by a Liouvillian superoperator L acting on the density matrix of the system. As the Fock space for a single bosonic mode is already infinite-dimensional, the diagonalization of the Liouvillian has to be done on the creation- and annihilation-superoperators, a process called `third quantization'. We propose a method to solve the Liouvillian for quadratic systems using a single symplectic transformation. We show that the non-Hermitian effective Hamiltonian of the system, next to incorporating the dynamics of the system, is a tool to analyze its symmetries. As an example, we use the effective Hamiltonian to formulate a PT-`symmetry' of an open system. We describe how the inclusion of source terms allows us to obtain the cumulant generating function for observablessuch as the photon current.

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Section: Superoperator Formalism and Non-hermitian Hamiltonianmentioning

confidence: 99%

“…while z = 0. For ϵ = ∆ the Liouvillian matrix L is not diagonalizable and therefore the Jordan decomposition is needed [8]. The symplectic transition matrix…”

Section: Pt -'Symmetry' In Coupled Harmonic Oscillatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Kim,

Hassler

2023

J. Phys. A: Math. Theor.

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“…Recently the driven-dissipative dynamics of open quantum many-body systems has become an arena of active research [1][2][3][4][5]. Such open quantum systems have nonthermal stationary states with nontrivial non-equilibrium transient dynamics.…”

Section: Introductionmentioning

confidence: 99%

Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation

Nosov¹,

Shapiro²,

Goldstein³

et al. 2023

Preprint

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The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate lengthand time-scales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length-and time-scales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.

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Field Theory of Many-Body Lindbladian Dynamics

Cited by 2 publications

References 96 publications

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation

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