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Zobov, V. E.
Tree growth parameter in the Eden model on face-centered hypercubic lattices / V. E. Zobov, M. A. Popov // Theor. Math. Phys. - 2005. - Vol. 144, Is. 3. - P. 1361-1371, DOI 10.1007/s11232-005-0165-z. - Cited References: 19 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
BRANCHED POLYMERS
   HIGH-TEMPERATURES
   EXPANSION
   CLUSTERS
   SYSTEMS
   TIME
Кл.слова (ненормированные):
Eden model -- number of lattice trees -- Monte Carlo method -- growth parameter -- singular points of generating function -- large-dimension expansion -- face-centered hypercubic lattice -- Eden model -- Face-centered hypercubic lattice -- Growth parameter -- Large-dimension expansion -- Monte Carlo method -- Number of lattice trees -- Singular points of generating function
Аннотация: In the Eden model, we investigate how the tree growth parameter depends on the space dimension d for face-centered hypercubic lattices. We find the first three terms of the 1/d-expansion for this parameter directly from the generating function without calculating the number of trees because the growth parameter is the reciprocal coordinate of the singular point of the tree generating function. The same growth parameter was calculated by computer experiment where the ratios between the numbers of trees without intersections and trees without restrictions in the dimensions 3, 4, 6, 8, and 10 were estimated by the Monte Carlo method on face-centered cubic lattices. The results of the two methods agree well. Comparing with the previously performed computer experiment for simple hypercubic lattices, we observe that the values of the singular exponents for the tree generating functions are close for two different types of lattices.

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Держатели документа:
RAS, Siberian Branch, Kirenskii Inst Phys, Novosibirsk, Russia
Krasnoyarsk State Univ, Krasnoyarsk, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Branch, RAS, Russian Federation
Krasnoyarsk State University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
The coordinate of a singular point of the time correlation functions for a heteronuclear spin system of a crystal / V. E. Zobov, M. A. Popov // J. Exp. Theor. Phys. - 2005. - Vol. 100, Is. 4. - P. 775-783, DOI 10.1134/1.1926438. - Cited References: 24 . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
FLUCTUATION SPECTRUM
   CROSS-RELAXATION
   NMR ABSORPTION
   SHAPE
   WINGS
   LINE
Кл.слова (ненормированные):
Correlation methods -- Crystal lattices -- Crystallography -- Functions -- Integral equations -- Lithium compounds -- Nuclear magnetic resonance -- Quantum theory -- Random processes -- Autocorrelation functions (ACF) -- Dipole-dipole interactions (DDI) -- Heteronuclear spin systems -- Self-consistent fluctuating field (SCFF) -- Crystals
Аннотация: The singularities of the time autocorrelation functions (ACFs) for a heteronuclear spin system of a crystal are investigated. Exact expressions are obtained for ten moments of the spectra of ACFs in the approximation of a self-consistent fluctuating field (SCFF) with arbitrary axial symmetry. These expressions are applied to determine the coordinate of the lowest singular point of these functions on the imaginary-time axis for a spin system with a dipole-dipole interaction (DDI). The leading corrections to this coordinate due to the correlation of local fields in real crystals are calculated. These corrections are determined by lattice sums with triangles of four bonds and pairs of four bonds. Numerical values of the coordinate are obtained for a LiF crystal in a magnetic field directed along three crystallographic axes. An increase in the coordinate of the singular point, which follows from the theory and leads to a faster falloff of the wings of the ACF spectra, qualitatively agrees with experiment. © 2005 Pleiades Publishing, Inc.

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Держатели документа:
Russian Acad Sci, Siberian Div, Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Krasnoyarsk State Univ, Krasnoyarsk 660041, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Krasnoyarsk State University, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures / V. E. Zobov // Theor. Math. Phys. - 2000. - Vol. 123, Is. 1. - P. 511-523, DOI 10.1007/BF02551058. - Cited References: 21 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
BRANCHED POLYMERS
   HEISENBERG MAGNET
   EXPANSION
   MODELS
Аннотация: Time-dependent autocorrelation functions are investigated for the Heisenberg model with spins 1/2 on d-dimensional simple cubic lattices of large dimensions d at infinite temperature. The autocorrelation function on the imaginary time axis is interpreted as the generating function of bond trees constructed with double bonds. These trees provide the leading terms with respect to lid for the time-expansion coefficients of the autocorrelation function. The correction terms from branch intersections to the generating function in the Bethe approximation are derived for these trees. A procedure is suggested for finding the correction to the coordinate of the singular point of the generating function (i.e., to the reciprocal of the branch growth-rate parameter) from the above correction terms without calculating the number of trees. The leading correction terms of order 1/sigma(2) (where sigma = 2d - 1) are found for the coordinates of the singular points of the autocorrelation function in question and for the generating function of the trees constructed with single bonds in the Eden model.

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Держатели документа:
RAS, LV Kirensky Phys Inst, Siberian Div, Krasnoyarsk, Russia
ИФ СО РАН

Доп.точки доступа:
Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids / V. E. Zobov, A. A. Lundin // J. Exp. Theor. Phys. - 2006. - Vol. 103, Is. 6. - P. 904-916, DOI 10.1134/S1063776106120089. - Cited References: 39 . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
NUCLEAR-MAGNETIC-RESONANCE
   LINE-SHAPE
   SPIN SYSTEMS
   DYNAMICS
   SPECTRA
   COHERENCES
   STATE
   BEHAVIOR
   CRYSTAL
   MODEL
Кл.слова (ненормированные):
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 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 is obtained. The value of 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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Держатели документа:
Russian Acad Sci, Siberian Div, Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Russian Acad Sci, Semenov Inst Chem Phys, Moscow 117977, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 117977, Russian Federation

Доп.точки доступа:
Lundin, A. A.; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I=1 / V. E. Zobov, V. P. Shauro // J. Exp. Theor. Phys. - 2011. - Vol. 113, Is. 2. - P. 181-191, DOI 10.1134/S1063776111060094. - Cited References: 48. - This work was supported by the Russian Foundation for Basic Research (project no. 09-07-00138) and the Dynasty Foundation. . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
QUANTUM COMPUTATION
   MAGNETIC-RESONANCE
   ALGORITHMS
   ELEMENTS
   PULSES
   DESIGN
   QUDITS
   GATES
Кл.слова (ненормированные):
Logical operators -- Nuclear spins -- Numerical optimizations -- Optimality -- Physical parameters -- Quadrupole nuclei -- Qutrits -- Radio frequencies -- RF pulse -- Three level systems -- Time dependence -- Time-optimal -- Computer control systems -- Computer simulation -- Fourier transforms -- Optimization -- Quantum computers -- Resonance -- Nuclear quadrupole resonance
Аннотация: Elementary logical operators (selective rotation, Fourier transform, controllable phase shift, and SUM gate) are considered for a quantum computer based on three-level systems (qutrits) represented by nuclear spins I = 1 under nuclear magnetic resonance conditions. The computer simulation of the realization of these operators by means of simple and composite selective radiofrequency (RF) pulses and optimized RF pulses is performed. The time dependence of the amplitude of last pulses is found by numerical optimization at different durations. Two variants are proposed for realization of a two-qutrit SUM gate by using one-qutrit or two-qutrit optimized RF pulses. The calculated time dependences of realization errors were used to study the time optimality of different methods for obtaining gates, proposed earlier and in this paper. The advantages and disadvantages of each of the methods are evaluated for different values of physical parameters.

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Держатели документа:
[Zobov, V. E.
Shauro, V. P.] Russian Acad Sci, Siberian Branch, LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
ИФ СО РАН
L.V. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation

Доп.точки доступа:
Shauro, V. P.; Шауро, Виталий Павлович; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
On the radius of convergence of series in powers of time for spin correlation functions of the Heisenberg magnet at high temperature / V. E. Zobov, M. A. Popov // Theor. Math. Phys. - 1997. - Vol. 112, Is. 3. - P. 1182-1191, DOI 10.1007/BF02583049. - Cited References: 22 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
AUTO-CORRELATION FUNCTION
   INFINITE-TEMPERATURE
   PARAMAGNET
   DYNAMICS
   MODEL
Аннотация: The convergence of series in powers of time for spin autocorrelation functions of the Heisenberg magnet are investigated at infinite temperatures on lattices of different dimensions d. The calculation data available at the present time for the coefficients of these series are used to estimate the corresponding radii of convergence, whose growth with decreasing d is revealed and explained in a self-consistent approximation. To this end, a simplified nonlinear equation corresponding to this approximation is suggested and solved for the autocorrelation function of a system with an arbitrary number Z of nearest neighbors. The coefficients of the expansion in powers of time for the solution are represented in the form of trees on the Bethe lattice with the coordination number Z. A computer simulation method is applied to calculate the expansion coefficients for trees embedded in square, triangular, and simple cubic lattices under the condition that the intersection of tree branches is forbidden. It is found that the excluded volume effect that manifests itself in a decrease in these coefficients and in an increase in the coordinate and exponent of the singularity of the autocorrelation function on the imaginary time axis is intensified with decreasing lattice dimensions.

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Держатели документа:
Russian Acad Sci, LV Kirensky Phys Inst, Siberian Div, Krasnoyarsk, Russia
Krasnoyarsk State Univ, Krasnoyarsk, Russia
ИФ СО РАН

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
}
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    Zobov, V. E.
    On the effect of an inhomogeneous magnetic field on high-frequency asymptotic behaviors of correlation functions of spin lattices / V. E. Zobov, M. M. Kucherov // JETP Letters. - 2018. - Vol. 107, Is. 9. - P. 553-557, DOI 10.1134/S002136401809014X. - Cited References: 39 . - ISSN 0021-3640. - ISSN 1090-6487
Рубрики:
HEISENBERG PARAMAGNET
   SYSTEMS
   TIME
   RELAXATION
   DYNAMICS
   SPECTRA
Аннотация: Singular points of spin autocorrelation functions on the imaginary time axis, which determine the arguments of exponential high-frequency asymptotic behaviors, have been analyzed. It has been shown that randomly distributed inhomogeneous magnetic fields expand the wings of spectra of autocorrelation functions and, thereby, intensify the heating of a system subjected to variable magnetic fields, which are used to create effective Hamiltonians or at the saturation of inhomogeneously broadened EPR lines.

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Публикация на русском языке Зобов, Владимир Евгеньевич. О влиянии неоднородного магнитного поля на высокочастотные асимптотики корреляционных функций спиновых решеток [Текст] / В. Е. Зобов, М. М. Кучеров // Письма в Журн. эксперим. и теор. физ. - 2018. - Т. 107 Вып. 9-10. - С. 578-582

Держатели документа:
Russian Acad Sci, Siberian Branch, Fed Res Ctr KSC, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Space & Informat Technol, Krasnoyarsk 660074, Russia.

Доп.точки доступа:
Kucherov, M. M.; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
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 / V. E. Zobov, A. A. Lundin // JETP Letters. - 2017. - Vol. 105, Is. 8. - P. 514-518, DOI 10.1134/S0021364017080148. - Cited References: 27 . - ISSN 0021-3640
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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Публикация на русском языке Зобов, Владимир Евгеньевич. О влиянии неоднородного магнитного поля и многочастичной локализации на рост со временем второго момента многоквантового ЯМР [Текст] / В. Е. Зобов, А. А. Лундин // Письма в Журн. эксперим. и теор. физ. : Наука, 2017. - Т. 105 Вып. 7-8. - С. 499-503

Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russian Federation
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russian Federation

Доп.точки доступа:
Lundin, A. A.; Зобов, Владимир Евгеньевич
}
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Zobov, V. E.
On the coordinate of a singular point of time correlation functions for the system of nuclear magnetic moments of a crystal / V. E. Zobov, M. A. Popov // J. Exp. Theor. Phys. - 2003. - Vol. 97, Is. 1. - P. 78-84, DOI 10.1134/1.1600799. - Cited References: 22 . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
DIPOLAR FLUCTUATION SPECTRUM
   FREE-INDUCTION DECAY
   CROSS-RELAXATION
   DOUBLE-RESONANCE
   SPIN SYSTEMS
   NMR-SPECTRA
   LINE SHAPE
   IRREVERSIBILITY
   ABSORPTION
   CAF2
Кл.слова (ненормированные):
Absorption spectroscopy -- Barium compounds -- Crystallography -- Lattice constants -- Magnetic fields -- Nuclear magnetic resonance -- Absorption spectrum -- Dipole-dipole interaction -- Magnetic field directions -- Nuclear magnetic moments -- Magnetic moments
Аннотация: The hypothesis concerning the existence of singular points on the imaginary time axis for a correlation function of a system with the dipole-dipole interaction of nuclear spins of a crystal is verified. Within the framework of the self-consistent fluctuating field theory taking into account the principal corrections related to the correlation of local fields, a result for this coordinate is obtained in terms of the ratios of lattice sums. Experimental values of this coordinate are calculated from the wings of the nuclear magnetic resonance absorption spectrum of a BaF2 crystal for the magnetic field directions along the three crystallographic axes. Good agreement of the theoretical and experimental results justifies this hypothesis. (C) 2003 MAIK "Nauka / Interperiodica".

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Держатели документа:
Russian Acad Sci, Siberian Div, LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
Krasnoyarsk State Univ, Krasnoyarsk 660041, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Krasnoyarsk State University, Krasnoyarsk, 660041, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
}
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10.

Zobov, V. E.
On the coordinate of a singular point of the time correlation function for a spin system on a simple hypercubic lattice at high temperatures / V. E. Zobov, M. A. Popov // Theor. Math. Phys. - 2002. - Vol. 131, Is. 3. - P. 862-872, DOI 10.1023/A:1015935809388. - Cited References: 19 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
NUCLEAR-DOUBLE-RESONANCE
   HEISENBERG MAGNET
   DEPENDENCE
   MODEL
Кл.слова (ненормированные):
spin dynamics -- correlation functions -- power series in time -- frequency moments -- singular points -- generated functions -- lattice trees -- multidimensional expansion -- Correlation functions -- Frequency moments -- Generated functions -- Lattice trees -- Multidimensional expansion -- Power series in time -- Singular points -- Spin dynamics
Аннотация: Using the d(-1) expansion method (d is the space dimension), we estimate the coordinate of the time-dependent autocorrelation function singular point on the imaginary time axis for the spin 1/2 Heisenberg model on a simple hypercubic lattice at high temperatures. We represent the coefficients of the time expansion (the spectral moments) for the autocorrelation function as the sums of the weighted lattice figures in which the trees constructed from the double bonds give the leading contributions with respect to d(-1) and the same trees with the built-in squares from six bonds or diagrams with the fourfold bonds give the contribution of the next-to-leading order. We find the corrections to the coordinate of the autocorrelation function singular point that are due to the latter contributions.

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Держатели документа:
RAS, Siberian Branch, LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
Krasnoyarsk State Univ, Krasnoyarsk, Russia
ИФ СО РАН
Kirensky Institute of Physics, Siberian Branch, RAS, Krasnoyarsk, Russian Federation
Kirensky State University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
}
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