Dynamics of Characteristic and One-Point Correlation Functions of Multi-Mode Bosonic Systems: Exactly Solvable Model

Kiselev, Alexei D.; Ali, Ranim; Rybin, A. V.

doi:10.3390/sym13122309

Cited by 1 publication

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References 40 publications

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“…In the remaining part of this section, our task is to provide general analytical expressions for these dynamical characteristics. More specifically, in Section 2.1 , we, following our previous studies [ 43 , 55 ], present an exactly solvable model of Lindblad dynamics and its solution in the form suitable for our purposes. Then, in Section 2.2 , we apply the results to deduce general relations for Gaussian states.…”

Section: General Approachmentioning

confidence: 99%

“…By using the method of characteristics to solve the initial value problem for the dynamical Equation ( 24 ) with the initial condition

we can derive the following expression for the normally ordered characteristic function [ 43 , 55 ]:

where

is the identity

matrix. In Appendix B , this result is used to deduce the expression for the kernel of the Green’s function that determines time dependence of the Glauber–Sudarshan P function.…”

Section: General Approachmentioning

confidence: 99%

“…In Section 2.1 , our starting point is the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation (the general form of quantum kinetic equations which preserves the complete positivity of the dynamics [ 52 , 53 , 54 ]) for the multi-mode bosonic system interacting with the thermal bath and we, following Refs. [ 43 , 55 ], present its exact solution derived by solving the dynamical equation for the normally ordered characteristic function. In Section 2.2 , we deduce general formulas that characterize the temporal evolution of Gaussian states using the generalized two-point fidelity, the evolution speed and the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

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Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

Kiselev

Ali

Rybin

2022

Entropy

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We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert–Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

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Section: General Approachmentioning

confidence: 99%

“…By using the method of characteristics to solve the initial value problem for the dynamical Equation ( 24 ) with the initial condition

we can derive the following expression for the normally ordered characteristic function [ 43 , 55 ]:

where

is the identity

matrix. In Appendix B , this result is used to deduce the expression for the kernel of the Green’s function that determines time dependence of the Glauber–Sudarshan P function.…”

Section: General Approachmentioning

confidence: 99%