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Journal articles on the topic 'Equation de Lindblad'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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1

Tarasov, Vasily E. "Quantum Maps with Memory from Generalized Lindblad Equation." Entropy 23, no. 5 (April 28, 2021): 544. http://dx.doi.org/10.3390/e23050544.

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In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.

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2

Fagnola, Franco, and Carlos M. Mora. "Basic Properties of a Mean Field Laser Equation." Open Systems & Information Dynamics 26, no. 03 (September 2019): 1950015. http://dx.doi.org/10.1142/s123016121950015x.

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We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form, and we prove the uniqueness of the solution to the nonautonomous linear adjoint quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form. Moreover, we obtain rigorously the Maxwell–Bloch equations from the mean field laser equation.

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3

ISAR, A., A. SANDULESCU, H. SCUTARU, E. STEFANESCU, and W. SCHEID. "OPEN QUANTUM SYSTEMS." International Journal of Modern Physics E 03, no. 02 (June 1994): 635–714. http://dx.doi.org/10.1142/s0218301394000164.

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The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasiprobability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a timedependent linear partial differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time dependence of expectation values, Wigner function and Weyl operator, are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

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4

Pearle, Philip. "Simple derivation of the Lindblad equation." European Journal of Physics 33, no. 4 (April 27, 2012): 805–22. http://dx.doi.org/10.1088/0143-0807/33/4/805.

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5

Kostyakov, I. V., V. V. Kuratov, and N. A. Gromov. "Lie algebra contractions and the Lindblad equation." Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences 6 (2021): 36–41. http://dx.doi.org/10.19110/1994-5655-2021-6-36-41.

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The dynamics of an open quantum system leads to decoherence, which is accompanied by limiting transitions in the Lie algebra of observables and appearance of abelian subalgebras. It is possible to set an inverse problem as well – by a given Lie algebra contraction to find the dynamics of an open quantum system given by the Lindblad equation. The paper proposes examples of finding the Lindblad equation by the known contractions of algebra su(3).

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6

Karabanov, A. A. "Symmetry reductions of Lindblad equations – simple examples and applications." Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences 6 (2021): 49–52. http://dx.doi.org/10.19110/1994-5655-2021-6-49-52.

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Open quantum dynamics in the Markovian approximation is described by the Lindblad master equation. The Lindbladian dynamics is closed in the Lie algebra Λ = su(n), i.e. it has su(n) symmetry. We say that the Lindblad equation admits a symmetry reduction if it has an invariant vector subspace Λ0 ⊂Λ with the Lie algebraic structure. Symmetry reductions restrict dynamics to smaller subspaces that additionally are Lie algebras. In these notes, trivial reductions relying onthe reducibility of the Hamiltonian and Lindblad operators are described. Examples of nontrivial reductions in the infinite temperature limit and the parity preserving Majorana reductions are presented. Applicationsto open spin dynamics are discussed.

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7

FUJII, KAZUYUKI. "ALGEBRAIC STRUCTURE OF A MASTER EQUATION WITH GENERALIZED LINDBLAD FORM." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1033–40. http://dx.doi.org/10.1142/s0219887808003168.

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The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv: 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra su(1,1) were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution.

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8

Vacchini, Bassano. "General structure of quantum collisional models." International Journal of Quantum Information 12, no. 02 (March 2014): 1461011. http://dx.doi.org/10.1142/s0219749914610115.

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We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely positive maps, a completely positive trace preserving transformation and a waiting time distribution characterizing a renewal process. The relationship between this construction and a Lindblad dynamics is clarified by expressing the solution of a Lindblad master equation in terms of demixtures over different stochastic trajectories for the statistical operator weighted by suitable probabilities on the trajectory space.

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9

Binney, James. "Angle-action variables for orbits trapped at a Lindblad resonance." Monthly Notices of the Royal Astronomical Society 495, no. 1 (May 19, 2020): 886–94. http://dx.doi.org/10.1093/mnras/staa092.

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ABSTRACT The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasi-periodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.

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10

Ou, Congjie, Yuho Yokoi, and Sumiyoshi Abe. "Spin Isoenergetic Process and the Lindblad Equation." Entropy 21, no. 5 (May 17, 2019): 503. http://dx.doi.org/10.3390/e21050503.

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A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained.

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11

Chruściński, Dariusz, and Saverio Pascazio. "A Brief History of the GKLS Equation." Open Systems & Information Dynamics 24, no. 03 (September 2017): 1740001. http://dx.doi.org/10.1142/s1230161217400017.

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12

OZHIGOV, YU I., and N. B. VICTOROVA. "DESCRIPTION OF THE SIMPLEST NON-MARKOV PROCESS USING A DIFFERENTIAL EQUATION FOR THE QUANTUM STATE VECTOR." Computational Nanotechnology 10, no. 2 (June 30, 2023): 9–15. http://dx.doi.org/10.33693/2313-223x-2023-10-2-9-15.

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The Jaynes-Cummings model with one atom and a photon is considered. A photon leaks out of the cavity (optical resonator). An atom can be in an excited and ground state. Usually, the dynamics of the probability of finding a photon in a cavity is considered using the basic quantum Lindblad equation, in which the density matrix acts as an unknown function. The Lindblad equation describes a quantum Markov random process. The article attempts to replace the equation from the density matrix with an ersatz of the Lindblad equation, which is a differential equation from the state wave vector. The quantum master equation involves the use of a matrix with a dimension equal to the dimension of the state space, which increases the complexity of the calculations, since it requires a quadratically large memory. For example, for the dimension of the main space equal to a billion, the memory required to solve the basic quantum equation will be about a quintillion, which is a problem even for supercomputers. Whereas a billion-long column fits easily into the memory of a personal computer and can be easily processed on a personal laptop. The ersatz of the quantum master equation, which we are constructing, cannot accurately describe the dynamics of the density matrix and therefore cannot serve as an exact replacement for the quantum master equation. Our ersatz will describe a special process of exchange with the environment.

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13

Dubois, Jonathan, Ulf Saalmann, and Jan M. Rost. "Semi-classical Lindblad master equation for spin dynamics." Journal of Physics A: Mathematical and Theoretical 54, no. 23 (May 7, 2021): 235201. http://dx.doi.org/10.1088/1751-8121/abf79b.

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14

Lange, Stefan, and Carsten Timm. "Random-matrix theory for the Lindblad master equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 2 (February 2021): 023101. http://dx.doi.org/10.1063/5.0033486.

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15

Manzano, Daniel. "A short introduction to the Lindblad master equation." AIP Advances 10, no. 2 (February 1, 2020): 025106. http://dx.doi.org/10.1063/1.5115323.

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16

Hod, Oded, César A. Rodríguez-Rosario, Tamar Zelovich, and Thomas Frauenheim. "Driven Liouville von Neumann Equation in Lindblad Form." Journal of Physical Chemistry A 120, no. 19 (February 16, 2016): 3278–85. http://dx.doi.org/10.1021/acs.jpca.5b12212.

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17

Chetrite, R., and K. Mallick. "Quantum Fluctuation Relations for the Lindblad Master Equation." Journal of Statistical Physics 148, no. 3 (August 2012): 480–501. http://dx.doi.org/10.1007/s10955-012-0557-z.

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18

Bogoliubov, Nikolai M., and Andrei V. Rybin. "The Irreversible Quantum Dynamics of the Three-Level su(1, 1) Bosonic Model." Symmetry 14, no. 12 (December 1, 2022): 2542. http://dx.doi.org/10.3390/sym14122542.

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We study the quantum dynamics of the opened three-level su(1, 1) bosonic model. The effective non-Hermitian Hamiltonians describing the system of the Lindblad equation in the short time limit are constructed. The obtained non-Hermitian Hamiltonians are exactly solvable by the Algebraic Bethe Ansatz. This approach allows representing biorthogonal and nonorthogonal bases of the system. We analyze the biorthogonal expectation values of a number of particles in the zero mode and represent it in the determinantal form. The time-dependent density matrix satisfying the Lindblad master equation is found in terms of the nonorthogonal basis.

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19

Ozorio de Almeida, A. M., and O. Brodier. "Nonlinear semiclassical dynamics of open systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1935 (January 28, 2011): 260–77. http://dx.doi.org/10.1098/rsta.2010.0261.

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A semiclassical approximation for an evolving density operator, driven by a ‘closed’ Hamiltonian and ‘open’ Markovian Lindblad operators, is reviewed. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian is a quadratic function and the Lindblad operators are linear functions of positions and momenta. The semiclassical formulae are interpreted within a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra ‘open’ term in the double Hamiltonian is generated by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by the definition of a propagator, here developed in both representations. Generalized asymptotic equilibrium solutions are thus presented for the first time.

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20

Bravyi, Sergey, and Robert Konig. "Classical simulation of dissipative fermionic linear optics." Quantum Information and Computation 12, no. 11&12 (November 2012): 925–43. http://dx.doi.org/10.26421/qic12.11-12-2.

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Fermionic linear optics is a limited form of quantum computation which is known to be efficiently simulable on a classical computer. We revisit and extend this result by enlarging the set of available computational gates: in addition to unitaries and measurements, we allow dissipative evolution governed by a Markovian master equation with linear Lindblad operators. We show that this more general form of fermionic computation is also simulable efficiently by classical means. Given a system of $N$~fermionic modes, our algorithm simulates any such gate in time $O(N^3)$ while a single-mode measurement is simulated in time $O(N^2)$. The steady state of the Lindblad equation can be computed in time $O(N^3)$.

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21

Kirchanov, V. S. "The Lindblad equation for a quantum dissipative harmonic oscillator." ВЕСТНИК ПЕРМСКОГО УНИВЕРСИТЕТА. ФИЗИКА, no. 2 (2018): 5–12. http://dx.doi.org/10.17072/1994-3598-2018-2-05-12.

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22

Andrianov, A. A., M. V. Ioffe, and O. O. Novikov. "Supersymmetrization of the Franke–Gorini–Kossakowski–Lindblad–Sudarshan equation." Journal of Physics A: Mathematical and Theoretical 52, no. 42 (September 23, 2019): 425301. http://dx.doi.org/10.1088/1751-8121/ab4338.

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23

Chebotarev, A. M., J. C. Garcia, and R. B. Quezada. "On the lindblad equation with unbounded time-dependent coefficients." Mathematical Notes 61, no. 1 (January 1997): 105–17. http://dx.doi.org/10.1007/bf02355012.

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24

Chebotarev, Alexander M. "Quantum Stochastic Differential Equation is Unitarily Equivalent to a Symmetric Boundary Value Problem in Fock Space." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (April 1998): 175–99. http://dx.doi.org/10.1142/s0219025798000120.

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We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of the Schrödinger equations in Fock space: the strong resolvent limit is unitarily equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitarily equivalent to the symmetric (or Stratonovich) form of QSDE. We also prove that QSDE is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps in phase and amplitude of components of Fock vectors belonging to the range of the resolvent. The corresponding Markov evolution equation (the Lindblad or Markov master equation) is derived from the boundary value problem for the Schrödinger equation.

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25

Barthel, Thomas, and Yikang Zhang. "Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (November 1, 2022): 113101. http://dx.doi.org/10.1088/1742-5468/ac8e5c.

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Abstract The dynamics of Markovian open quantum systems are described by Lindblad master equations. For fermionic and bosonic systems that are quasi-free, i.e. with Hamiltonians that are quadratic in the ladder operators and Lindblad operators that are linear in the ladder operators, we derive the equation of motion for the covariance matrix. This determines the evolution of Gaussian initial states and the steady states, which are also Gaussian. Using ladder super-operators (a.k.a. third quantization), we show how the Liouvillian can be transformed to a many-body Jordan normal form which also reveals the full many-body spectrum. Extending previous work by Prosen and Seligman, we treat fermionic and bosonic systems on equal footing with Majorana operators, shorten and complete some derivations, also address the odd-parity sector for fermions, give a criterion for the existence of bosonic steady states, cover non-diagonalizable Liouvillians also for bosons, and include quadratic systems. In extension of the quasi-free open systems, quadratic open systems comprise additional Hermitian Lindblad operators that are quadratic in the ladder operators. While Gaussian states may then evolve into non-Gaussian states, the Liouvillian can still be transformed to a useful block-triangular form, and the equations of motion for k-point Green’s functions form a closed hierarchy. Based on this formalism, results on criticality and dissipative phase transitions in such models are discussed in a companion paper.

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26

Meyerov, Iosif, Evgeny Kozinov, Alexey Liniov, Valentin Volokitin, Igor Yusipov, Mikhail Ivanchenko, and Sergey Denisov. "Transforming Lindblad Equations into Systems of Real-Valued Linear Equations: Performance Optimization and Parallelization of an Algorithm." Entropy 22, no. 10 (October 6, 2020): 1133. http://dx.doi.org/10.3390/e22101133.

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With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper, we address master equations of the Lindblad form, which are a popular theoretical tools in quantum optics, cavity quantum electrodynamics, and optomechanics. By using the generalized Gell–Mann matrices as a basis, any Lindblad equation can be transformed into a system of ordinary differential equations with real coefficients. Recently, we presented an implementation of the transformation with the computational complexity, scaling as O(N5logN) for dense Lindbaldians and O(N3logN) for sparse ones. However, infeasible memory costs remains a serious obstacle on the way to large models. Here, we present a parallel cluster-based implementation of the algorithm and demonstrate that it allows us to integrate a sparse Lindbladian model of the dimension N=2000 and a dense random Lindbladian model of the dimension N=200 by using 25 nodes with 64 GB RAM per node.

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27

Vander Griend, Peter. "Bottomonium observables in an open quantum system using the quantum trajectories method." EPJ Web of Conferences 258 (2022): 05005. http://dx.doi.org/10.1051/epjconf/202225805005.

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We solve the Lindblad equation describing the Brownian motion of a Coulombic heavy quark-antiquark pair in a strongly coupled quark gluon plasma using the Monte Carlo wave function method. The Lindblad equation has been derived in the framework of pNRQCD and fully accounts for the quantum and non-Abelian nature of the system. The hydrodynamics of the plasma is realistically implemented through a 3+1D dissipative hydrodynamics code. We compute the bottomonium nuclear modification factor and elliptic flow and compare with the most recent LHC data. The computation does not rely on any free parameter, as it depends on two transport coefficients that have been evaluated independently in lattice QCD. Our final results, which include late-time feed down of excited states, agree well with the available data from LHC 5.02 TeV PbPb collisions.

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28

Teixeira, W. S., F. L. Semião, J. Tuorila, and M. Möttönen. "Assessment of weak-coupling approximations on a driven two-level system under dissipation." New Journal of Physics 24, no. 1 (December 31, 2021): 013005. http://dx.doi.org/10.1088/1367-2630/ac43ee.

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Abstract The standard weak-coupling approximations associated to open quantum systems have been extensively used in the description of a two-level quantum system, qubit, subjected to relatively weak dissipation compared with the qubit frequency. However, recent progress in the experimental implementations of controlled quantum systems with increased levels of on-demand engineered dissipation has motivated precision studies in parameter regimes that question the validity of the approximations, especially in the presence of time-dependent drive fields. In this paper, we address the precision of weak-coupling approximations by studying a driven qubit through the numerically exact and non-perturbative method known as the stochastic Liouville–von Neumann equation with dissipation. By considering weak drive fields and a cold Ohmic environment with a high cutoff frequency, we use the Markovian Lindblad master equation as a point of comparison for the SLED method and study the influence of the bath-induced energy shift on the qubit dynamics. We also propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit. In addition, we study signatures of the well-known Mollow triplet and observe its meltdown owing to dissipation in an experimentally feasible parameter regime of circuit electrodynamics. Besides shedding light on the practical limitations of the Lindblad equation, we expect our results to inspire future experimental research on engineered open quantum systems, the accurate modeling of which may benefit from non-perturbative methods.

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29

BERETTA, GIAN PAOLO. "WELL-BEHAVED NONLINEAR EVOLUTION EQUATION FOR STEEPEST-ENTROPY-ASCENT DISSIPATIVE QUANTUM DYNAMICS." International Journal of Quantum Information 05, no. 01n02 (February 2007): 249–55. http://dx.doi.org/10.1142/s0219749907002700.

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In this paper, we outline the main features of the nonlinear quantum evolution equation proposed by the present author. Such an equation may be used as a model of reduced subsystem dynamics to complement various historical and contemporary efforts to extend linear Markovian theories of dissipative phenomena and relaxation based on master equations, Lindblad and Langevin equations, to the nonlinear and far nonequilibrium domain. It may also be used as the fundamental dynamical principle in theories that attempt to unite mechanics and thermodynamics, such as the Hatsopoulos–Gyftopoulos unified theory which motivated the original development of this well-behaved general nonlinear equation for the evolution of the density operator capable of generating irreversible deterministic relaxation to thermodynamic equilibrium from any far nonequilibrium state even for an isolated system.

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Kimura, Gen, Shigeru Ajisaka, and Kyouhei Watanabe. "Universal Constraints on Relaxation Times for d-Level GKLS Master Equations." Open Systems & Information Dynamics 24, no. 04 (December 2017): 1740009. http://dx.doi.org/10.1142/s1230161217400091.

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In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are measurable in experiments, our constraints provide a direct experimental test for the validity of the GKLS master equations, and hence for the conditions of the complete positivity and Markovianity.

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31

El Anouz, K., A. El Allati, and F. Saif. "Study different quantum teleportation amounts by solving Lindblad master equation." Physica Scripta 97, no. 3 (February 9, 2022): 035102. http://dx.doi.org/10.1088/1402-4896/ac5084.

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Abstract A realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending the excited atom through two serial cavities which contain the radiation field. Thus, the Lindblad master equations which describe the evolution of the reduced density matrix regarding the radiation field generated from the excited atom inside the cavities are solved in Markovian and non-Markovian regimes. Thereby, the rate of entanglement inherent in the total field-field system is evaluated using various witnesses by calculating analytically the concurrence and quantum discord, where we illustrate quantitatively the advantage of using an initial EPR and NOON states in the presence of radiation field losses. As an application, a scheme of quantum teleportation using two partial entangled channels is investigated. Finally, a comparative study between fidelity and the different levels of entanglement of the teleported state in the two regimes is also given.

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32

Ba Omar, Hisham, Miguel Ángel Escobedo, Ajaharul Islam, Michael Strickland, Sabin Thapa, Peter Vander Griend, and Johannes Heinrich Weber. "QTRAJ 1.0: A Lindblad equation solver for heavy-quarkonium dynamics." Computer Physics Communications 273 (April 2022): 108266. http://dx.doi.org/10.1016/j.cpc.2021.108266.

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33

Davidsson, Eric, and Markus Kowalewski. "Simulating photodissociation reactions in bad cavities with the Lindblad equation." Journal of Chemical Physics 153, no. 23 (December 21, 2020): 234304. http://dx.doi.org/10.1063/5.0033773.

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34

Kosov, Daniel S., Tomaž Prosen, and Bojan Žunkovič. "Lindblad master equation approach to superconductivity in open quantum systems." Journal of Physics A: Mathematical and Theoretical 44, no. 46 (October 21, 2011): 462001. http://dx.doi.org/10.1088/1751-8113/44/46/462001.

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35

Bengs, Christian. "Markovian exchange phenomena in magnetic resonance and the Lindblad equation." Journal of Magnetic Resonance 322 (January 2021): 106868. http://dx.doi.org/10.1016/j.jmr.2020.106868.

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36

Bondarev, Boris V. "Lindblad Equation for Harmonic Oscillator: Uncertainty Relation Depending on Temperature." Applied Mathematics 08, no. 11 (2017): 1529–38. http://dx.doi.org/10.4236/am.2017.811111.

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37

Strunz, Walter T. "Finite Temperature Dynamics of the Total State in an Open System Model." Open Systems & Information Dynamics 12, no. 01 (March 2005): 65–80. http://dx.doi.org/10.1007/s11080-005-0487-1.

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We determine the dynamics of the total state of a system and environment for an open system model, at finite temperature. Based on a partial Husimi representation, our framework describes the full dynamics very efficiently through equations in the Hilbert space of the open system only. We briefly review the zero-temperature case and present the corresponding new finite temperature theory, within the usual Born-Markov approximation. As we will show, from a reduced point of view, our approach amounts to the derivation of a stochastic Schrödinger equation description of the dynamics. We show how the reduced density operator evolves according to the expected (finite temperature) master equation of Lindblad form.

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38

Villegas-Martínez, B. M., F. Soto-Eguibar, and H. M. Moya-Cessa. "Application of Perturbation Theory to a Master Equation." Advances in Mathematical Physics 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/9265039.

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We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating theQ-function, the average number of photons, and the distance between density matrices.

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39

Oliveira, Mário J. de. "Classical stochastic approach to quantum mechanics and quantum thermodynamics." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 3 (March 22, 2024): 033207. http://dx.doi.org/10.1088/1742-5468/ad3198.

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Abstract We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated with a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector, which turns out to be of the Lindblad type. When the noise changes only the phase of φ j , the Schrödinger and the quantum Liouville equations are obtained. The component ψ j of the wave vector obeying the Schrödinger equation is related to the stochastic wave vector by | ψ j | 2 = ⟨ | ϕ j | 2 ⟩ .

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40

ISAR, A., A. SANDULESCU, and W. SCHEID. "PHASE SPACE REPRESENTATION FOR OPEN QUANTUM SYSTEMS WITHIN THE LINDBLAD THEORY." International Journal of Modern Physics B 10, no. 22 (October 10, 1996): 2767–79. http://dx.doi.org/10.1142/s0217979296001240.

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The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this function is given by a sum of three parts: the classical one, the quantum corrections and the contribution due to the opening of the system. In the particular case of a harmonic oscillator, quantum corrections do not exist.

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41

Bogoliubov, Nikolai M., and Andrei V. Rybin. "The Generalized Tavis—Cummings Model with Cavity Damping." Symmetry 13, no. 11 (November 8, 2021): 2124. http://dx.doi.org/10.3390/sym13112124.

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In this Communication, we consider a generalised Tavis–Cummings model when the damping process is taken into account. We show that the quantum dynamics governed by a non-Hermitian Hamiltonian is exactly solvable using the Quantum Inverse Scattering Method, and the Algebraic Bethe Ansatz. The leakage of photons is described by a Lindblad-type master equation. The non-Hermitian Hamiltonian is diagonalised by state vectors, which are elementary symmetric functions parametrised by the solutions of the Bethe equations. The time evolution of the photon annihilation operator is defined via a corresponding determinant representation.

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42

Strickland, Michael. "Bottomonium suppression and flow in heavy-ion collisions." EPJ Web of Conferences 259 (2022): 04001. http://dx.doi.org/10.1051/epjconf/202225904001.

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The strong suppression of bottomonia production in ultra-relativistic heavy-ion collisions is a smoking gun for the creation of a deconfined quarkgluon plasma (QGP). In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the QGP through the use of pNRQCD and an open quantum systems approach. This approach allows one to evolve the heavyquarkonium reduced density matrix, taking into account non-unitary effective Hamiltonian evolution of the wave-function and quantum jumps between different angular momentum and color states. In the case of a strong coupled QGP in which Ebind ≪ T, mD ≪ 1=a0, the corresponding evolution equation is Markovian and can therefore be mapped to a Lindblad evolution equation. To solve the resulting Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm and couple the non-abelian quantum evolution to a realistic 3+1D viscous hydrodynamical background. Using a large number of Monte-Carlo sampled bottomonium trajectories, we make predictions for bottomonium RAA and elliptic flow as a function of centrality and transverse momentum and compare to data collected by the ALICE, ATLAS, and CMS collaborations.

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43

Groszkowski, Peter, Alireza Seif, Jens Koch, and A. A. Clerk. "Simple master equations for describing driven systems subject to classical non-Markovian noise." Quantum 7 (April 6, 2023): 972. http://dx.doi.org/10.22331/q-2023-04-06-972.

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Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. We present a systematic method based on generalized cumulant expansions for deriving a time-local master equation for such systems. This master equation has an intuitive form that directly parallels a standard Lindblad equation, but contains several surprising features: the combination of driving and non-Markovianity results in effective time-dependent dephasing rates that can be negative, and the noise can generate Hamiltonian renormalizations even though it is classical. We analyze in detail the highly relevant case of a Rabi-driven qubit subject to various kinds of non-Markovian noise including 1/f fluctuations, finding an excellent agreement between our master equation and numerically-exact simulations over relevant timescales. The approach outlined here is more accurate than commonly employed phenomenological master equations which ignore the interplay between driving and noise.

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44

Antão, T. V. C., and N. M. R. Peres. "Two-level systems coupled to Graphene plasmons: A Lindblad equation approach." International Journal of Modern Physics B 35, no. 20 (August 10, 2021): 2130007. http://dx.doi.org/10.1142/s0217979221300073.

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In this paper, we review the theory of open quantum systems and macroscopic quantum electrodynamics, providing a self-contained account of many aspects of these two theories. The former is presented in the context of a qubit coupled to a electromagnetic thermal bath, the latter is presented in the context of a quantization scheme for surface-plasmon polaritons (SPPs) in graphene based on Langevin noise currents. This includes a calculation of the dyadic Green’s function (in the electrostatic limit) for a Graphene sheet between two semi-infinite linear dielectric media, and its subsequent application to the construction of SPP creation and annihilation operators. We then bring the two fields together and discuss the entanglement of two qubits in the vicinity of a graphene sheet which supports SPPs. The two qubits communicate with each other via the emission and absorption of SPPs. We find that a Schrödinger cat state involving the two qubits can be partially protected from decoherence by taking advantage of the dissipative dynamics in graphene. A comparison is also drawn between the dynamics at zero temperature, obtained via Schrödinger’s equation, and at finite temperature, obtained using the Lindblad equation.

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45

Asano, Masanari, Masanori Ohya, Yoshiharu Tanaka, Andrei Khrennikov, and Irina Basieva. "On Application of Gorini-Kossakowski-Sudarshan-Lindblad Equation in Cognitive Psychology." Open Systems & Information Dynamics 18, no. 01 (March 2011): 55–69. http://dx.doi.org/10.1142/s1230161211000042.

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We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology — the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1, 2], Croson [3], Hofstader [4, 5] demonstrated that in general real players do not use "rational strategy" provided by classical game theory; this psychological phenomenon was called the disjunction effect. We elaborate a model of quantum-like decision making which can explain this effect ("irrationality" of plays). Our model is based on quantum information theory. The main result of this paper is the derivation of Gorini-Kossakowski-Sudarshan-Lindblad equation whose equilibrium solution gives the quantum state used for decision making. It is the first application of this equation in cognitive psychology.

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46

Prosen, Tomaž. "Spectral theorem for the Lindblad equation for quadratic open fermionic systems." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 07 (July 23, 2010): P07020. http://dx.doi.org/10.1088/1742-5468/2010/07/p07020.

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47

Selstø, Sølve. "Non-Hermitian quantum mechanics in the context of the Lindblad equation." Journal of Physics: Conference Series 388, no. 15 (November 5, 2012): 152016. http://dx.doi.org/10.1088/1742-6596/388/15/152016.

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Cao, Yu, and Jianfeng Lu. "Lindblad equation and its semiclassical limit of the Anderson-Holstein model." Journal of Mathematical Physics 58, no. 12 (December 2017): 122105. http://dx.doi.org/10.1063/1.4993431.

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49

Isar, A., A. Sandulescu, and W. Scheid. "Lindblad master equation for the damped harmonic oscillator with deformed dissipation." Physica A: Statistical Mechanics and its Applications 322 (May 2003): 233–46. http://dx.doi.org/10.1016/s0378-4371(02)01828-9.

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50

Barchielli, A., and C. Pellegrini. "Jump-diffusion unravelling of a non-Markovian generalized Lindblad master equation." Journal of Mathematical Physics 51, no. 11 (November 2010): 112104. http://dx.doi.org/10.1063/1.3514539.

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