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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Зобов, Владимир Евгеньевич, Лундин, Андрей Арнольдович
Заглавие : О втором моменте многоквантового спектра ЯМР твердого тела
Место публикации : Химическая физика. - Москва: Федеральное государственное унитарное предприятие Академический научно-издательский, производственно-полиграфический и книгораспространительский центр Наука, 2008. - Т. 27, № 9. - С. 18-25. - ISSN 0207-401X
ГРНТИ : 31.15
Аннотация: Новые экспериментальные данные о зависимости роста числа коррелированных спинов от времени в условиях наблюдения многоквантового ЯМР в твердом теле обработаны на основе развитой нами ранее микроскопической теории для описания роста второго момента спектра многоквантового ЯМР. Показано, что, как и следует из теории, рост экспоненциален в зависимости от времени для кристаллов с совершенно различными структурами. Полученные результаты обсуждаются на основе полуфеноменологических моделей.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2006. - Vol. 103, Is. 6. - P904-916. - ISSN 1063-7761, DOI 10.1134/S1063776106120089
Примечания : Cited References: 39
Предметные рубрики: NUCLEAR-MAGNETIC-RESONANCE
LINE-SHAPE
SPIN SYSTEMS
DYNAMICS
SPECTRA
COHERENCES
STATE
BEHAVIOR
CRYSTAL
MODEL
Ключевые слова (''Своб.индексиров.''): correlation methods--mathematical models--nuclear magnetic resonance spectroscopy--spectrum analysis--time series analysis--four-spin time correlation--multispin correlations--second moment--time power series--quantum theory
Аннотация: The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment n(2)(t) of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of n(2)(t) is obtained. The value of n(2)(t) is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Reversible and Irreversible propagation of quantum information and its manifestation in multiple-quantum NMR spectra in solids
Коллективы : Ministry of Science and Higher Education of the Russian Federation [0082-2019-0001, AAAA-A19-119012890064-7]
Место публикации : J. Exp. Theor. Phys. - 2020. - Vol. 131, Is. 2. - P.273-279. - ISSN 1063-7761, DOI 10.1134/S1063776120060096. - ISSN 1090-6509(eISSN)
Примечания : Cited References: 33. - This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the State Task 0082-2019-0001 (State Registration Number AAAA-A19-119012890064-7)
Предметные рубрики: DYNAMICS
LOCALIZATION
SIMULATIONS
COHERENCES
Аннотация: On the basis of the earlier developed statistical theory of the growth of the effective size of correlated clusters (the number of correlated spins), an expression for the shape of the multiple-quantum (MQ) NMR spectrum is obtained that takes into account the loss of coherence in a spin system due, for example, to the controlled intervention of the experimenter. It is shown that the scrambling and decoherence processes in the MQ spectrum of the multiparticle system of a solid are not separated, unlike the corresponding spectra of some large isolated molecules [27] in a solution. The relations obtained allow one to extract the necessary information about the above processes (scrambling and decoherence) from the dependence of the MQ spectra on experimental parameters.
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Quantum and classical correlations in the solid-state NMR free induction decay
Место публикации : International Conference Magnetic Resonance: Fundamental Research and Pioneering Applications: Book of abstracts. - 2014. - Ст.P 77. - P.160
Примечания : Cited References: 16
Аннотация: The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S 1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Quantum and classical correlations in the solid-state NMR free induction decay
Место публикации : Appl. Magn. Reson.: Springer, 2014. - Vol. 45, Is. 11. - P.1169-1177. - ISSN 0937-9347, DOI 10.1007/s00723-014-0562-2. - ISSN 1613-7507
Примечания : Cited References: 16
Предметные рубрики: LATTICE
SPINS
Аннотация: The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S 1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : On the Second Moment of the Multiquantum NMR Spectrum of a Solid
Место публикации : Russ. J. Phys. Chem. B: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2008. - Vol. 2, Is. 5. - P676-683. - ISSN 1990-7931, DOI 10.1134/S1990793108050035
Примечания : Cited References: 39
Предметные рубрики: MULTIPLE-QUANTUM NMR
DEPENDENT BEHAVIOR
MAGNETIC-MOMENTS
SPIN CLUSTERS
LINE-SHAPE
DYNAMICS
COHERENCES
SYSTEMS
CRYSTAL
GROWTH
Аннотация: New experimental data on the time dependence of an increase in the number of correlated spins under the conditions of the observation of the multiquantum NMR spectrum of a solid are processed on the basis of a microscopic theory for describing the growth of the second moment of multiquantum NMR developed by us earlier. As follows from the theory, the growth is an exponential function of time for crystals with quite diverse structures. The results are discussed on the basis of semiphenomenological models.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : On the effect of an inhomogeneous magnetic field and many-body localization on the increase in the second moment of multiple-quantum NMR with time
Место публикации : JETP Letters. - 2017. - Vol. 105, Is. 8. - P.514-518. - ISSN 00213640 (ISSN), DOI 10.1134/S0021364017080148
Примечания : Cited References: 27
Аннотация: A change in the time dependence of the second moment of the distribution of intensities of coherences with various orders in the spectrum of multiple-quantum NMR in a solid at the inclusion of an inhomogeneous magnetic field in the effective interaction is studied. Both the secular dipole–dipole and nonspecular twoquantum interactions are considered as nucleus–nucleus interactions, which correspond to traditional experimental realizations. It is shown that, with an increase in the magnitude of the inhomogeneous field, an exponential increase in the second moment of multiple-quantum NMR with time changes to a power-law increase. The results obtained in this work indicate that this second moment, which determines the average number of dynamically correlated spins, can be used as a convenient characteristic for studying a transition to a many-body localized state. © 2017, Pleiades Publishing, Inc.
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : On the decoherence in large NMR quantum registers
Коллективы : "Micro- and nanoelectronics – 2023", International Conference
Место публикации : Proceedings of the International Conference "Micro- and Nanoelectronics – 2023": Book of abstracts. - 2023. - Ст.q2-06. - P.83
Примечания : Cited References: 7
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : On the control of the spread of quantum information in multiple quantum NMR spectroscopy of solids
Коллективы : "Micro- and Nano-Electronics", International Conference, "Микро- и наноэлектроника", международная конференция, Квантовая информатика, симпозиум, Российская академия наук, Физико-технологический институт имени К.А. Валиева РАН
Разночтения заглавия :Загл. обл.: IС "Micro- and Nanoelectronics" (ICMNE-2021) with the extended session “Quantum Informatics” (QI-2021)
Место публикации : Proceedings of the International Conference "Micro- and Nanoelectronics – 2021". ICMNE – 2021: book of abstracts : Oct. 4-8, 2021, Moscow - Zvenigorod, Russia. - 2021. - Ст.q3-02. - P.149
Примечания : Cited References: 5
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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Multiple-quantum NMR spectroscopy and quantum information spreading control in the spin systems of solids
Место публикации : J. Exp. Theor. Phys. - 2022. - Vol. 135, Is. 5. - P.752-761. - ISSN 10637761 (ISSN), DOI 10.1134/S1063776122110139. - ISSN 10906509 (eISSN)
Примечания : Cited References: 49. - This work was supported within the State assignment of the Ministry of Science and Higher Education of the Russian Federation (registration number 1021051201992-1)
Аннотация: Multiple-quantum (MQ) solid-state NMR spectroscopy allows the growth of multiple-spin correlations and, thus, the spreading of quantum information in the object under study to be observed. Recently, in [11] it was proposed to control this process through a controlled perturbation added to the effective Hamiltonian that causes degradation of correlated spin clusters with a rate determined by the number of spins K in a cluster. However, this perturbation can also lead to degradation whose rate is determined by the coherence order M. In this paper, to investigate the influence of a small added perturbation, we used an expansion into orthogonal operators that allowed the cluster size distribution to be taken into account. In our calculations we realized a simple model with known amplitudes of the expansion into a complete set of orthogonal operators in the absence of a perturbation. We performed numerical calculations of the “preparation time” dependences of the MQ spectra, their second moments, and the coherence orders at which the MQ spectra decrease by a factor of e as well as the average correlated spin cluster sizes K¯. The coherence-order-dependent contribution to the degradation is shown to change the shape of the MQ spectrum. In particular, as the preparation time increases, the MQ spectrum can be stabilized, while the growth of K¯ is retained. Due to the change in the shape of the MQ spectrum, the relations of its characteristics to the number K¯ change compared to those for the Gaussian function (traditionally used to process the experiments). These changes should be taken into account when studying the spreading of quantum information through MQ spectroscopy.
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11.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Multiple-quantum NMR spectral intensity profiles under decoherence effects
Коллективы : "Modern Development of Magnetic Resonance", International conference
Место публикации : Modern Development of Magnetic Resonance: abstracts int. conf./ ed. Salikhov K. M. - Kazan, 2022. - P.19
Примечания : Библиогр.: 4
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12.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Modeling multiparticle coherences in solid-state nuclear spin systems using infinite-range interaction
Место публикации : Theor. Math. Phys. - 2004. - Vol. 141, Is. 3. - P.1737-1749. - ISSN 0040-5779, DOI 10.1023/B:TAMP.0000049765.41265.dd
Примечания : Cited References: 24
Предметные рубрики: MULTIPLE-QUANTUM DYNAMICS
NMR-SPECTRA
TEMPERATURE DYNAMICS
SHAPE
VAN
Ключевые слова (''Своб.индексиров.''): multipulse method--dipole-dipole interaction--multispin coherence--time correlation function--rotating reference frame--dipole-dipole interaction--multipulse method--multispin coherence--rotating reference frame--time correlation function
Аннотация: Using the exactly solvable model known in statistical physics as the infinite-range interaction model (the van der Waals model), we obtain expressions for the hierarchy of multispin multiquantum time correlation functions for a solid-state paramagnetic nuclear spin system with magnetic dipole-dipole interaction between nuclei. These functions are observed experimentally using contemporary multiquantum NMR spectroscopy methods. We write the complete set of orthogonal multispin operators explicitly and find the time dependence for amplitudes of multiparticle time correlation functions. The proposed model describes the behavior of multiparticle correlation functions well, at least for not very large numbers n of expansion harmonics. The theoretical results agree well with the experimental data obtained for hexamethylbenzol.
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13.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Effect of intramolecular interaction on time growth of second moment of multiple quantum NMR in solids
Место публикации : INTERNATIONAL CONFERENCE ON RESONANCES IN CONDENSED MATTER: ALTSHULER100. Ser. Journal of Physics Conference Series: IOP PUBLISHING LTD, 2011. - Vol. 324: International Conference on Resonances in Condensed Matter (JUN 21-25, 2011, Kazan, RUSSIA). - Ст.12010. - ISBN 1742-6588, DOI 10.1088/1742-6596/324/1/012010
Примечания : Cited References: 12
Предметные рубрики: COHERENCES
DYNAMICS
Ключевые слова (''Своб.индексиров.''): dipole dipole interactions--double-quantum--intramolecular interactions--multiple quantum nmr--nuclear spin system--quantum spectrum--rate increase--second moments--solids containing methyl groups--time dependence--functional groups--quantum optics--solids--spin dynamics--hamiltonians
Аннотация: The time dependence of the NMR multiple quantum spectrum in solids containing methyl groups is investigated. We studied both of types of the nuclear spin systems: namely linking by secular part of the mutual dipole-dipole interaction and linking by effective double quantum Hamiltonian. It is revealed for the first type of systems the rate with the time of the growing up of the second moment when intramolecular interaction is present becomes less in compare with situation when a strong intramolecular interaction is absent. On the contrary for the second type of Hamiltonian the above rate increases.
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14.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Effect of degradation processes caused by a small perturbation on the growth of the average cluster size of correlated spins in multiple quantum NMR spectroscopy of solids
Место публикации : Appl. Magn. Reson. - 2021. - Vol. 52. Is. 7. - P.879–892. - ISSN 09379347 (ISSN), DOI 10.1007/s00723-021-01342-1
Примечания : Cited References: 33. - The study is funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of the State assignment, State registration number AAAA-A19-119012890064-7
Аннотация: Multiple quantum (MQ) NMR spectroscopy of solids allows one to observe the growth and decay of multispin correlations. As a rule, the average size of the cluster of correlated spins is extracted from the width of the MQ spectrum. In the present article, the size distribution of such clusters is explored. To obtain the above distribution, the solutions for the amplitudes of the decomposition over complete sets of orthogonal operators for the two different models were used. By means of these models, we have taken into account the dependence of cluster degradation (the degradation of a cluster means, e.g., destruction of correlations in cluster or loss of particles in it) through two positions. The first one defines by the cluster size while the second one depends on the MQ coherence order of the cluster. It is shown that in dependence of the relation the rates of these degradation processes, the width of the MQ spectrum carries different information. If the first process is faster that the second one, then the width of the MQ spectrum is still determined by the average cluster size. When the velocity ratio becomes inverse, the width of the MQ spectrum takes on a smaller value, which is a consequence of the faster degradation of the MQ spectrum components with large orders of coherence.
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15.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Dependence of the relaxation rate of coherent states on the number of correlated spins and the order of coherence
Колич.характеристики :6 с
Место публикации : JETP Lett. - 2023. - Vol. 117, Is. 12. - P.932-937. - ISSN 00213640 (ISSN), DOI 10.1134/S0021364023601525. - ISSN 10906487 (eISSN)
Примечания : Cited References: 29. - This work was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment no. 122040500060-4)
Аннотация: The relaxation of the components of the multiple-quantum NMR spectrum of a solid under the effect of the dipole–dipole interactions during the evolution period is considered. It is taken into account that clusters of dynamically correlated spins of different sizes are formed in the preparatory period, and their degradation depends on their size and coherence order. To calculate the size distribution function of clusters and their degradation function, a physical model including relaxation processes is developed. Using this model, an analytical result for a multiple-quantum spectrum is obtained. Agreement is obtained between the theoretical and experimental dependences of the coherence degradation rates in adamantane scaled by the square root of the average cluster size. The parameters of the above functions are found from the comparison of these dependences.
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16.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Decay of multispin multiquantum coherent states in the NMR of a solid
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 112, Is. 3. - P451-459. - ISSN 1063-7761, DOI 10.1134/S1063776111020129
Примечания : Cited References: 24
Предметные рубрики: SYSTEMS
SPECTRA
Ключевые слова (''Своб.индексиров.''): adiabatic approximations--andersons--coherent state--dynamic phenomena--experimental data--local fields--model-based--radiospectroscopy--relaxation functions--spin precession--theoretical result--two-component--coherent light
Аннотация: A model based on the Anderson adiabatic approximation, which is widely used for describing various aspects of dynamic phenomena in conventional radiospectroscopy, is proposed for describing the decay of multispin multiquantum coherent states in a solid. The coherent state relaxation function is represented by the product of two functions corresponding to spin precession in a two-component local field with a correlated and an uncorrelated component. Theoretical results of this study explain the experimental data reported in a number of publications and are in good agreement with these data.
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17.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Decay of Multispin Multiple-Quantum Coherent States in the NMR of a Solid and the Stabilization of Their Intensity Profile with Time
Разночтения заглавия :авие SCOPUS: Decay of multispin multiple-quantum coherent states in the NMR of a solid and the stabilization of their intensity profile with time
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 113, Is. 6. - P1006-1014. - ISSN 1063-7761, DOI 10.1134/S1063776111140111
Примечания : Cited References: 27
Ключевые слова (''Своб.индексиров.''): cluster sizes--coherent state--decay rate--effective size--experimental data--intensity profiles--coherent light--decay (organic)--stabilization
Аннотация: Variations, experimentally observed in [14], in the intensity profiles of multiple-quantum (MQ) coherences in the presence of two special types of perturbations are explained on the basis of the theory, earlier developed by the authors, of the growth of the effective size of correlated clusters (the number of correlated spins) and the relaxation of MQ coherent states [23]. The intensity and the character of perturbation were controlled by the experimenters. It is shown that the observed stabilization of profiles with time is not associated with the stabilization of the cluster size. Quite the contrary, a cluster of correlated spins monotonically grows, while the observed variations in the intensity profile and its stabilization with time are attributed to the dependence of the decay rate of an MQ coherence on its order (its position in the MQ spectrum). The results of the theory are in good agreement with the experimental data.
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18.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Lundin A. A., Zobov V. E.
Заглавие : The stabilization of width of multiple-quantum NMR spectrum induced by decoherence
Коллективы : "Spin physics, spin chemistry, and spin technology", Internnational conference, Физико-технический институт им. А.Ф. Иоффе РАН, Казанский физико-технический институт им. Е. К. Завойского Казанского научного центра РАН, "Инно-мир", центр межрегионального инновационного развития
Место публикации : Int. conf. "Spin physics, spin chem., and spin technol.". - 2015. - P.112
Примечания : Библиогр.: 4 назв.
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19.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Lundin A. A., Zobov V. E.
Заглавие : Solid-state NMR free induction decay, simulated by the system of classical magnetic moments and quantum correlations
Коллективы : [AAAA-A19-119012890064-7]
Место публикации : Russ. J. Phys. Chem. B. - 2021. - Vol. 15, Is. 5. - P.839-847. - ISSN 1990-7931, DOI 10.1134/S1990793121050079. - ISSN 1990-7923(eISSN)
Примечания : Cited References: 34. - This study was carried out as part of state assignment 0082-2019-0001 (registration number AAAA-A19-119012890064-7)
Предметные рубрики: HIGH-TEMPERATURE DYNAMICS
HEISENBERG-MODEL
SPIN SIMULATIONS
SHAPE
Аннотация: In the past decade, nuclear magnetic resonance (NMR) has been actively used to study the basic principles of quantum computers. It is assumed that quantum correlations play a significant role in their performance. They exist at both low and high temperatures. At the same time, the time correlation functions of nuclear spin systems of solids determine the observed signals in traditional NMR implementations. The separation of such signals into quantum and classical components has not previously been carried out and will be performed in this study for the most important of the correlational functions observed in magnetic resonance: the free induction decay (FID).
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20.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Lundin A. A., Zobov V. E.
Заглавие : Order dependence of the profile of the intensities of multiple-quantum coherences
Место публикации : J. Exp. Theor. Phys.: MAIK Nauka-Interperiodica / Springer, 2015. - Vol. 120, Is. 5. - P.762-771. - ISSN 1063, DOI 10.1134/S1063776115040093. - ISSN 10906509(eISSN)
Примечания : Cited References:62
Предметные рубрики: PARAMAGNETIC SPIN SYSTEMS
FREE-INDUCTION DECAY
NMR-SPECTRA
AUTOCORRELATION FUNCTIONS
FLUCTUATION SPECTRUM
TEMPERATURE DYNAMICS
LINE-SHAPE
SOLIDS
IRREVERSIBILITY
BEHAVIOR
Аннотация: A modification of the widespread phenomenological model theory of multiple-quantum (MQ) nuclear magnetic resonance spectra of a single cluster of correlated spins has been developed. In contrast to the mentioned theory, the size distribution of such clusters has been consistently taken into account. To obtain the distribution, solutions for the amplitudes of the expansion in the complete set of orthogonal operators are used. Expressions specifying the dependence of the profile of the intensities of MQ coherences on their number n (order) have been obtained. The total form of the dependence has been evaluated by means of the numerical implementation of the resulting expressions. The asymptotic expressions for large n values (wings of the spectrum) have been obtained analytically by the saddle-point method. It has been shown that the dependence under study has a Gaussian central part and exponential wings. The results obtained are in agreement with the previous calculations for some model systems and existing experimental data.
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