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Статті в журналах з теми "Non Markovian evolution"

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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

CHRUŚCIŃSKI, DARIUSZ, and ANDRZEJ KOSSAKOWSKI. "MARKOVIAN VERSUS NON-MARKOVIAN EVOLUTION: GEOMETRIC PERSPECTIVE." International Journal of Geometric Methods in Modern Physics 09, no. 02 (March 2012): 1260019. http://dx.doi.org/10.1142/s0219887812600195.

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Анотація:

We analyze two criteria of (non)Markovianity: one based on the mathematical concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We illustrate these concepts from the geometric perspective using simple examples of qubit dynamics.

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2

Chruściński, D., and A. Kossakowski. "From Markovian semigroup to non-Markovian quantum evolution." EPL (Europhysics Letters) 97, no. 2 (January 1, 2012): 20005. http://dx.doi.org/10.1209/0295-5075/97/20005.

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3

Chruściński, Dariusz. "Characterizing non-Markovian quantum evolution." Physica Scripta T153 (March 1, 2013): 014009. http://dx.doi.org/10.1088/0031-8949/2013/t153/014009.

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4

Costanza, G. "Non-Markovian stochastic evolution equations." Physica A: Statistical Mechanics and its Applications 402 (May 2014): 224–35. http://dx.doi.org/10.1016/j.physa.2014.01.038.

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5

Kumar, N. Pradeep, Subhashish Banerjee, R. Srikanth, Vinayak Jagadish, and Francesco Petruccione. "Non-Markovian Evolution: a Quantum Walk Perspective." Open Systems & Information Dynamics 25, no. 03 (September 2018): 1850014. http://dx.doi.org/10.1142/s1230161218500142.

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Анотація:

Quantum non-Markovianity of a quantum noisy channel is typically identified with information backflow or, more generally, with departure of the intermediate map from complete positivity. But here, we also indicate certain non-Markovian channels that cannot be witnessed by the CP-divisibility criterion. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.

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6

Corn, Brittany, Jun Jing, and Ting Yu. "Non-Markovian quantum trajectroy unravellings of entanglement." Quantum Information and Computation 16, no. 5&6 (April 2016): 483–97. http://dx.doi.org/10.26421/qic16.5-6-5.

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Анотація:

The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.

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7

Kosiol, Carolin, and Nick Goldman. "Markovian and Non-Markovian Protein Sequence Evolution: Aggregated Markov Process Models." Journal of Molecular Biology 411, no. 4 (August 2011): 910–23. http://dx.doi.org/10.1016/j.jmb.2011.06.005.

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8

Yannouleas, C. "The time evolution in extended RPA: Markovian versus non-markovian aspects." Physics Letters B 157, no. 2-3 (July 1985): 129–33. http://dx.doi.org/10.1016/0370-2693(85)91531-x.

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9

Teretenkov, A. E. "Exact Non-Markovian Evolution with Several Reservoirs." Physics of Particles and Nuclei 51, no. 4 (July 2020): 479–84. http://dx.doi.org/10.1134/s1063779620040711.

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10

Yu, Ting, and J. H. Eberly. "Entanglement evolution in a non-Markovian environment." Optics Communications 283, no. 5 (March 2010): 676–80. http://dx.doi.org/10.1016/j.optcom.2009.10.042.

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11

Olla, Piero, and Luca Pignagnoli. "Local evolution equations for non-Markovian processes." Physics Letters A 350, no. 1-2 (January 2006): 51–55. http://dx.doi.org/10.1016/j.physleta.2005.10.007.

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12

Awasthi, Natasha, Joshi Dheeraj Kumar, and Surbhi Sachdev. "Variation of quantum speed limit under Markovian and non-Markovian noisy environment." Laser Physics Letters 19, no. 3 (January 28, 2022): 035201. http://dx.doi.org/10.1088/1612-202x/ac4be5.

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Анотація:

Abstract The time required for a given quantum system to evolve is known as the quantum speed limit (QSL), which can be used to characterize the speed of evolution of a quantum system. We study QSL time for Markovian and non-Markovian dynamics. Investigating the effect of QSL under non-unitary evolution is of fundamental interest. In this work, we derive QSL time for maximally entangled state and apply its results under various noise channels. We discuss measure of QSL, how correlations affect the rate of QSL. Further, we carried an investigation on connection between non-Markovianity and QSL. We show that the non Markovian evolution can speed up quantum evolution, therefore lead to smaller QSL time. We have established the connections between correlated channels, information loss and non-Markovianity. This theory may suggest some further connections to retrieve back information from surrounding and preserves decoherence.

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13

Semina, I., V. Semin, F. Petruccione, and A. Barchielli. "Stochastic Schrödinger Equations for Markovian and non-Markovian Cases." Open Systems & Information Dynamics 21, no. 01n02 (March 12, 2014): 1440008. http://dx.doi.org/10.1142/s1230161214400083.

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Анотація:

Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples — the damped harmonic oscillator and a two-level atom with homodyne photodetection. We then consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.

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14

Krein, G., G. Menezes, and N. F. Svaiter. "Markovian versus non-Markovian stochastic quantization of a complex-action model." International Journal of Modern Physics A 29, no. 06 (March 4, 2014): 1450030. http://dx.doi.org/10.1142/s0217751x14500304.

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Анотація:

We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to Maxwell–Chern–Simons electrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution towards equilibrium of complex-action problems. This feature of non-Markovian stochastic quantization might be beneficial in large-scale numerical simulations of complex action field theories on a lattice.

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15

Lorenzo, Salvatore, Francesco Ciccarello, G. Massimo Palma, and Bassano Vacchini. "Quantum Non-Markovian Piecewise Dynamics from Collision Models." Open Systems & Information Dynamics 24, no. 04 (December 2017): 1740011. http://dx.doi.org/10.1142/s123016121740011x.

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Анотація:

Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [1]. These dynamics have been defined in terms of a waiting-time distribution between quantum jumps, along with quantum maps describing the effect of jumps and the system evolution between them. Here, we present a quantum collision model with memory, whose reduced dynamics in the continuous-time limit reproduces the above class of non-Markovian piecewise dynamics, thus providing an explicit microscopic realization.

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16

Han, Feng. "Entanglement Evolution and Transfer in Non-Markovian Reservoirs." International Journal of Theoretical Physics 49, no. 2 (December 5, 2009): 395–401. http://dx.doi.org/10.1007/s10773-009-0215-7.

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17

HUANG, X. L., L. C. WANG, and X. X. YI. "ENTANGLEMENT EVOLUTION OF A PAIR OF TWO-LEVEL SYSTEMS IN NON-MARKOVIAN ENVIRONMENT." International Journal of Quantum Information 07, no. 01 (February 2009): 385–93. http://dx.doi.org/10.1142/s0219749909004931.

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Анотація:

The entanglement evolution of a pair of two-level systems is studied in this paper. The two systems without mutual interaction are independently coupled to different two-band non-Markovian environments. By comparing our results to others in the literature, we find that taking one of the Bell states as the initial state, certain non-Markovian effect protects the entanglement in short time scale, while on long time scale it leads to the entanglement sudden death (ESD), which never occurs for this initial state in the Markovian case. Finally, by analyzing the parameters in our model, a relation between disentanglement and decoherence is established and discussed.

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18

Mortezapour, Ali, Mahdi Ahmadi Borji, DaeKil Park, and Rosario Lo Franco. "Non-Markovianity and Coherence of a Moving Qubit inside a Leaky Cavity." Open Systems & Information Dynamics 24, no. 03 (September 2017): 1740006. http://dx.doi.org/10.1142/s1230161217400066.

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Анотація:

Non-Markovian features of a system evolution, stemming from memory effects, may be utilized to transfer, storage, and revive basic quantum properties of the system states. It is well known that an atom qubit undergoes non-Markovian dynamics in high quality cavities. Here we consider the qubit-cavity interaction in the case when the qubit is in motion inside a leaky cavity. We show that, owing to the inhibition of the decay rate, the coherence of the travelling qubit remains closer to its initial value as time goes by compared to that of a qubit at rest. We also demonstrate that quantum coherence is preserved more efficiently for larger qubit velocities. This is true independently of the evolution being Markovian or non-Markovian, albeit the latter condition is more effective at a given value of velocity. We however find that the degree of non-Markovianity is eventually weakened as the qubit velocity increases, despite a better coherence maintenance.

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19

Kossakowski, Andrzej, and Rolando Rebolledo. "On non-Markovian Time Evolution in Open Quantum Systems." Open Systems & Information Dynamics 14, no. 03 (September 2007): 265–74. http://dx.doi.org/10.1007/s11080-007-9051-5.

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Анотація:

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

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20

Chruściński, Dariusz. "On Time-Local Generators of Quantum Evolution." Open Systems & Information Dynamics 21, no. 01n02 (March 12, 2014): 1440004. http://dx.doi.org/10.1142/s1230161214400046.

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Анотація:

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

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21

Xiong, Heng-Na, Yi Li, Yixiao Huang, and Zichun Le. "Multi-qubit non-Markovian dynamics in photonic crystal with infinite cavity-array structure." Quantum Information and Computation 18, no. 3&4 (March 2018): 265–82. http://dx.doi.org/10.26421/qic18.3-4-6.

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Анотація:

We study the exact non-Markovian dynamics of a multi-qubit system coupled to a photonic-crystal waveguide with infinite cavity-array structure. A general solution of the evolution state of the system is solved for a general initial state in the single-excitation subspace. With this solution, we find that the non-Markovian effect of the environment on the system could be enhanced not only by increasing the system-environment coupling strength but also by adding the qubit number in the system. The explicit non-Markovian dynamics are discussed under two initial states to see the non-Markovian effect on entanglement preservation and entanglement generation. We find that the non-Markovian effect tends to preserve the system in its initial state.

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22

Kossakowski, Andrzej, and Rolando Rebolledo. "On Completely Positive Non-Markovian Evolution of a d-Level System." Open Systems & Information Dynamics 15, no. 02 (June 2008): 135–41. http://dx.doi.org/10.1142/s1230161208000122.

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23

Martin, Tchoffo, Tsamouo Tsokeng Arthur, Fouokeng Georges Collince, and Lukong Cornelius Fai. "Time evolution of quantum correlations in superconducting flux-qubits under classical noises." International Journal of Quantum Information 15, no. 02 (March 2017): 1750015. http://dx.doi.org/10.1142/s0219749917500150.

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Анотація:

We analyze the dynamics of both entanglement and quantum discord (QD) in a system of two non-interacting flux-qubits initially prepared in a Bell's state and subjected to either static or random telegraph noises (RTNs). Both independent and common sources of system-environment coupling are considered either in the Markovian or non-Markovian regime and the results are compared to those of ordinary qubits. Under suitable conditions, both entanglement and QD are more robust in flux-qubit systems than classical ones. In the Markovian regime where the decay is monotonic, they are both stronger in different environment coupling than in common coupling, while the opposite is found in the non-Markovian regime where the dynamics is stressed by sudden death and revival phenomena, more robust in qubits than in flux-qubits under dynamical RTN. Weakness of revival amplitudes is interpreted as a noise spectrum-related induced interaction affecting quantum features of the system, while energy level non-degeneracy (at zero-splitting) of flux-qubits induces a phase factor that set conditions under which entangled states can be experimentally witnessed in flux-qubit systems. Note that the energy levels non-degeneracy has no particular effect on other entanglement measures apart from entanglement witnesses.

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24

MAZZOLA, LAURA, JYRKI PIILO, and SABRINA MANISCALCO. "FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS." International Journal of Quantum Information 09, no. 03 (April 2011): 981–91. http://dx.doi.org/10.1142/s021974991100754x.

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Анотація:

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

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25

Liu, Xin, Wei Wu, and Changkui Hu. "Dynamic of the Gaussian quantum discord and effect of non-Markovian degree." Canadian Journal of Physics 93, no. 4 (April 2015): 481–85. http://dx.doi.org/10.1139/cjp-2014-0258.

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Анотація:

We study the dynamic of the Gaussian quantum discord in a continuous-variable system subject to a common non-Markovian environment with zero-temperature. By considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that Gaussian discord has a very different dynamic characteristic in a non-Markovian evolution versus a Markov process, and can be created by the memory effect, which features non-Markovianity. We also study the relationship between Gaussian discord and the non-Markovian degree of the environment. The results may offer us an effective experimental method to get more quantum correlations.

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26

Zheng Li-Ming, Liu Song-Hao, and Wang Fa-Qiang. "Geometric phase evolution of atom under non-Markovian environment." Acta Physica Sinica 58, no. 4 (2009): 2430. http://dx.doi.org/10.7498/aps.58.2430.

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27

Megier, Nina, Andrea Smirne, and Bassano Vacchini. "Evolution Equations for Quantum Semi-Markov Dynamics." Entropy 22, no. 7 (July 21, 2020): 796. http://dx.doi.org/10.3390/e22070796.

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Анотація:

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.

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28

RODRÍGUEZ-ROSARIO, CÉSAR A., and E. C. G. SUDARSHAN. "NON-MARKOVIAN OPEN QUANTUM SYSTEMS: SYSTEM–ENVIRONMENT CORRELATIONS IN DYNAMICAL MAPS." International Journal of Quantum Information 09, no. 07n08 (October 2011): 1617–34. http://dx.doi.org/10.1142/s0219749911008325.

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Анотація:

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

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29

Jadach, S., and M. Skrzypek. "Solving constrained Markovian evolution in QCD with the help of the non-Markovian Monte Carlo." Computer Physics Communications 175, no. 8 (October 2006): 511–27. http://dx.doi.org/10.1016/j.cpc.2006.06.004.

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30

Khalil, Tarek, and Jean Richert. "Evolution of Open Quantum Systems: Time Scales, Stochastic and Continuous Processes." Quanta 10, no. 1 (November 21, 2021): 42–54. http://dx.doi.org/10.12743/quanta.v10i1.157.

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Анотація:

The study of the physical properties of open quantum systems is at the heart of many investigations, which aim to describe their dynamical evolution on theoretical ground and through physical realizations. Here, we develop a presentation of different aspects, which characterize these systems and confront different physical situations that can be realized leading to systems, which experience Markovian, non-Markovian, divisible or non-divisible interactions with the environments to which they are dynamically coupled. We aim to show how different approaches describe the evolution of quantum systems subject to different types of interactions with their environments.Quanta 2021; 10: 42–54.

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31

Costanza, G. "A theorem allowing the derivation of deterministic evolution equations from stochastic evolution equations. III The Markovian–non-Markovian mix." Physica A: Statistical Mechanics and its Applications 391, no. 6 (March 2012): 2167–81. http://dx.doi.org/10.1016/j.physa.2011.11.055.

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32

Chruściński, Dariusz, Andrzej Kossakowski, Paolo Aniello, Giuseppe Marmo, and Franco Ventriglia. "A Class of Commutative Dynamics of Open Quantum Systems." Open Systems & Information Dynamics 17, no. 03 (September 2010): 255–77. http://dx.doi.org/10.1142/s1230161210000163.

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Анотація:

We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via the spectral analysis of the corresponding time-dependent generators. We consider both Markovian and non-Markovian cases.

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33

CHRUŚCIŃSKI, DARIUSZ, and ANDRZEJ KOSSAKOWSKI. "LOCAL APPROACH TO THE NON-MARKOVIAN EVOLUTION OF QUANTUM SYSTEMS." International Journal of Quantum Information 09, supp01 (January 2011): 129–38. http://dx.doi.org/10.1142/s0219749911007149.

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Анотація:

We analyze a local approach to the non-Markovian evolution of open quantum systems. It turns out that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. The price one pays for the local approach is that the corresponding generator might be highly singular and it keeps the memory about the starting point "t0". This is the very essence of non-Markovianity. We illustrate a local approach by simple examples.

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34

Roux, Filippus S. "Non-Markovian evolution of photonic quantum states in atmospheric turbulence." Journal of Optics 18, no. 5 (March 15, 2016): 055203. http://dx.doi.org/10.1088/2040-8978/18/5/055203.

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35

Lepov, V., and A. Loginov. "Non-Markovian evolution approach to structural modeling of material fracture." World Journal of Engineering 9, no. 3 (June 2012): 207–12. http://dx.doi.org/10.1260/1708-5284.9.3.207.

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36

Chruściński, Dariusz, and Paweł Należyty. "Non-Markovian Quantum Evolution: Time-Local Generators and Memory Kernels." Reports on Mathematical Physics 77, no. 3 (June 2016): 399–414. http://dx.doi.org/10.1016/s0034-4877(16)30036-2.

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37

Zeng, Ye-Xiong, Tesfay Gebremariam, Ming-Song Ding, and Chong Li. "The Influence of Non-Markovian Characters on Quantum Adiabatic Evolution." Annalen der Physik 531, no. 1 (November 14, 2018): 1800234. http://dx.doi.org/10.1002/andp.201800234.

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38

Styliaris, Georgios, and Paolo Zanardi. "Symmetries and monotones in Markovian quantum dynamics." Quantum 4 (April 30, 2020): 261. http://dx.doi.org/10.22331/q-2020-04-30-261.

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Анотація:

What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of scalar functions over quantum states that are monotonic under the time evolution. The aforementioned monotones can be utilized to identify states that are non-reachable from an initial state by the time evolution and include all constraints imposed by conserved quantities, providing a generalization of Noether's theorem for this class of dynamics. As a special case, the generator itself can be considered a symmetry, resulting in non-trivial constraints over the time evolution, even if all conserved quantities trivialize. The construction utilizes tools from quantum information-geometry, mainly the theory of monotone Riemannian metrics. We analyze the prototypical cases of dephasing and Davies generators.

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39

Barchielli, Alberto, and Matteo Gregoratti. "Quantum measurements in continuous time, non-Markovian evolutions and feedback." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5364–85. http://dx.doi.org/10.1098/rsta.2011.0515.

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Анотація:

In this article, we reconsider a version of quantum trajectory theory based on the stochastic Schrödinger equation with stochastic coefficients, which was mathematically introduced in the 1990s, and we develop it in order to describe the non-Markovian evolution of a quantum system continuously measured and controlled, thanks to a measurement-based feedback. Indeed, realistic descriptions of a feedback loop have to include delay and thus need a non-Markovian theory. The theory allows us to put together non-Markovian evolutions and measurements in continuous time, in agreement with the modern axiomatic formulation of quantum mechanics. To illustrate the possibilities of such a theory, we apply it to a two-level atom stimulated by a laser. We introduce closed loop control too, via the stimulating laser, with the aim of enhancing the ‘squeezing’ of the emitted light, or other typical quantum properties. Note that here we change the point of view with respect to the usual applications of control theory. In our model, the ‘system’ is the two-level atom, but we do not want to control its state, to bring the atom to a final target state. Our aim is to control the ‘Mandel Q -parameter’ and the spectrum of the emitted light; in particular, the spectrum is not a property at a single time, but involves a long interval of times (a Fourier transform of the autocorrelation function of the observed output is needed).

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40

Chen, Yusui, J. Q. You, and Ting Yu. "Non-Markovian quantum interference in multilevel quantum systems: exact master equation approach." Quantum Information and Computation 18, no. 15&16 (December 2018): 1261–71. http://dx.doi.org/10.26421/qic18.15-16-1.

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We study the non-Markovian dynamics of multilevel quantum systems coupled with a bosonic dissipative environment. Based on the known exact quantum-state diffusion (QSD) equations, we propose a systematic approach to derive exact time-convolutionless master equations for multilevel quantum systems. Through a combination of analytical and numerical approaches, we extract the non-Markovian dynamics of quantum interference in different time scales. Also, we demonstrate the evolution of quantum interference in a four-level system controlled by an external electromagnetic field. Our findings are extended to few-body quantum networks, with a universal formalism established.

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41

Lizama, Carlos, and Rolando Rebolledo. "On a Class of Non-Markovian Langevin Equations." Open Systems & Information Dynamics 20, no. 04 (November 25, 2013): 1350016. http://dx.doi.org/10.1142/s1230161213500169.

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This paper proposes a generalized Langevin's equation for a small classical mechanical system embedded in a reservoir. The interaction of the main system with the reservoir is given by a Gaussian transform as introduced in our previous paper [8]. Thus, a first result proves the existence of a strong solution to this equation in the space where the Gaussian transform (or non-Markovian noise) is defined. The interpretation of the noise is obtained by considering a finite number n of oscillating particles with discrete frequencies in the reservoir. The action of this discrete reservoir on the small system is described by a memory kernel and a sequence of zero-mean Gaussian processes. So, an integro-differential equation for the evolution of a generic particle in the main system arises for each n. This equation has a unique solution Xn which converges in distribution towards the solution of the initial non-Markovian Langevin's equation.

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Dannevik, William P. "Efficient solution of non-Markovian covariance evolution equations in fluid turbulence." Journal of Scientific Computing 1, no. 2 (1986): 151–82. http://dx.doi.org/10.1007/bf01061391.

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Sridharan, V., and P. R. Jayashree. "A non-Markovian evolution model of HIV population with bunching behaviour." Korean Journal of Computational & Applied Mathematics 5, no. 3 (September 1998): 695–705. http://dx.doi.org/10.1007/bf03008892.

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44

Finsterhölzl, Regina, Manuel Katzer, Andreas Knorr, and Alexander Carmele. "Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution." Entropy 22, no. 9 (September 4, 2020): 984. http://dx.doi.org/10.3390/e22090984.

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This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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Agop, Maricel, Stefan Irimiciuc, Dan Dimitriu, Cristina Marcela Rusu, Andrei Zala, Lucian Dobreci, Adrian Valentin Cotîrleț, et al. "Novel Approach for EKG Signals Analysis Based on Markovian and Non-Markovian Fractalization Type in Scale Relativity Theory." Symmetry 13, no. 3 (March 11, 2021): 456. http://dx.doi.org/10.3390/sym13030456.

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Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of SL(2R)-type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author’s proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.).

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Dąbrowska, Anita, Dariusz Chruściński, Sagnik Chakraborty, and Gniewomir Sarbicki. "Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket." New Journal of Physics 23, no. 12 (December 1, 2021): 123019. http://dx.doi.org/10.1088/1367-2630/ac3c60.

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Abstract An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

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Kershenbaum, Arik, Ann E. Bowles, Todd M. Freeberg, Dezhe Z. Jin, Adriano R. Lameira, and Kirsten Bohn. "Animal vocal sequences: not the Markov chains we thought they were." Proceedings of the Royal Society B: Biological Sciences 281, no. 1792 (October 7, 2014): 20141370. http://dx.doi.org/10.1098/rspb.2014.1370.

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Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the ‘renewal process’ (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica , Carolina chickadees Poecile carolinensis , free-tailed bats Tadarida brasiliensis , rock hyraxes Procavia capensis , pilot whales Globicephala macrorhynchus , killer whales Orcinus orca and orangutans Pongo spp . The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins.

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Plastina, F., A. Sindona, J. Goold, N. Lo Gullo, and S. Lorenzo. "Decoherence in a Fermion Environment: Non-Markovianity and Orthogonality Catastrophe." Open Systems & Information Dynamics 20, no. 03 (September 2013): 1340005. http://dx.doi.org/10.1142/s1230161213400052.

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We analyze the non-Markovian character of the dynamics of an open two-level atom interacting with a gas of ultra-cold fermions. In particular, we discuss the connection between the phenomena of orthogonality catastrophe and Fermi edge singularity occurring in such a kind of environment and the memory-keeping effects which are displayed in the time evolution of the open system.

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Tilloy, Antoine. "Time-local unraveling of non-Markovian stochastic Schrödinger equations." Quantum 1 (September 19, 2017): 29. http://dx.doi.org/10.22331/q-2017-09-19-29.

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Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.

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50

Deng, Baogen, Ju-Ju Hu, and Ying-Hua Ji. "Factorization law of entanglement evolution between three qubits in non-Markovian environments." Optik 127, no. 24 (December 2016): 11893–900. http://dx.doi.org/10.1016/j.ijleo.2016.09.049.

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