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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : Tree growth parameter in the Eden model on face-centered hypercubic lattices
Место публикации : Theor. Math. Phys. - 2005. - Vol. 144, Is. 3. - P.1361-1371. - ISSN 0040-5779, DOI 10.1007/s11232-005-0165-z
Примечания : Cited References: 19
Предметные рубрики: BRANCHED POLYMERS
HIGH-TEMPERATURES
EXPANSION
CLUSTERS
SYSTEMS
TIME
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : The coordinate of a singular point of the time correlation functions for a heteronuclear spin system of a crystal
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 2005. - Vol. 100, Is. 4. - P775-783. - ISSN 1063-7761, DOI 10.1134/1.1926438
Примечания : Cited References: 24
Предметные рубрики: FLUCTUATION SPECTRUM
CROSS-RELAXATION
NMR ABSORPTION
SHAPE
WINGS
LINE
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E.
Заглавие : Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures
Место публикации : Theor. Math. Phys.: PLENUM PUBL CORP, 2000. - Vol. 123, Is. 1. - P511-523. - ISSN 0040-5779, DOI 10.1007/BF02551058
Примечания : Cited References: 21
Предметные 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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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., Shauro V. P.
Заглавие : On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I=1
Разночтения заглавия :авие SCOPUS: On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin i = 1
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 113, Is. 2. - P181-191. - ISSN 1063-7761, DOI 10.1134/S1063776111060094
Примечания : Cited References: 48. - This work was supported by the Russian Foundation for Basic Research (project no. 09-07-00138) and the Dynasty Foundation.
Предметные рубрики: QUANTUM COMPUTATION
MAGNETIC-RESONANCE
ALGORITHMS
ELEMENTS
PULSES
DESIGN
QUDITS
GATES
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : On the radius of convergence of series in powers of time for spin correlation functions of the Heisenberg magnet at high temperature
Место публикации : Theor. Math. Phys.: PLENUM PUBL CORP, 1997. - Vol. 112, Is. 3. - P1182-1191. - ISSN 0040-5779, DOI 10.1007/BF02583049
Примечания : Cited References: 22
Предметные 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Kucherov M. M.
Заглавие : On the effect of an inhomogeneous magnetic field on high-frequency asymptotic behaviors of correlation functions of spin lattices
Место публикации : JETP Letters. - 2018. - Vol. 107, Is. 9. - P.553-557. - ISSN 0021-3640, DOI 10.1134/S002136401809014X. - ISSN 1090-6487(eISSN)
Примечания : Cited References: 39
Предметные 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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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 журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : On the coordinate of a singular point of time correlation functions for the system of nuclear magnetic moments of a crystal
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 2003. - Vol. 97, Is. 1. - P78-84. - ISSN 1063-7761, DOI 10.1134/1.1600799
Примечания : Cited References: 22
Предметные рубрики: DIPOLAR FLUCTUATION SPECTRUM
FREE-INDUCTION DECAY
CROSS-RELAXATION
DOUBLE-RESONANCE
SPIN SYSTEMS
NMR-SPECTRA
LINE SHAPE
IRREVERSIBILITY
ABSORPTION
CAF2
Ключевые слова (''Своб.индексиров.''): 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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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : On the coordinate of a singular point of the time correlation function for a spin system on a simple hypercubic lattice at high temperatures
Место публикации : Theor. Math. Phys. - 2002. - Vol. 131, Is. 3. - P.862-872. - ISSN 0040-5779, DOI 10.1023/A:1015935809388
Примечания : Cited References: 19
Предметные рубрики: NUCLEAR-DOUBLE-RESONANCE
HEISENBERG MAGNET
DEPENDENCE
MODEL
Ключевые слова (''Своб.индексиров.''): 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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