11 research outputs found
Amoebas of complex hypersurfaces in statistical thermodynamics
The amoeba of a complex hypersurface is its image under a logarithmic
projection. A number of properties of algebraic hypersurface amoebas are
carried over to the case of transcendental hypersurfaces. We demonstrate the
potential that amoebas can bring into statistical physics by considering the
problem of energy distribution in a quantum thermodynamic ensemble. The
spectrum of the ensemble is assumed to be
multidimensional; this leads us to the notions of a multidimensional
temperature and a vector of differential thermodynamic forms. Strictly
speaking, in the paper we develop the multidimensional Darwin and Fowler method
and give the description of the domain of admissible average values of energy
for which the thermodynamic limit exists.Comment: 18 pages, 5 figure
Anisotropy of the magnetoresistance hysteresis in the granular superconductor Y-Ba-Cu-O at different magnetic-field and transport-current orientations
Dissipation in granular high-temperature superconductors (HTSs) during the passage of macroscopic transport current j is mainly determined by carrier tunneling through intergrain boundaries (Josephson junctions). In the presence of external magnetic field H, it is necessary to take into account the significant magnetic flux compression, which can lead to the situation when the effective field Beff in the intergrain boundaries exceeds the external field by an order of magnitude. This is observed as a wide hysteresis of the field dependence of magnetoresistance R(H). In this study, we investigate the R(H) hysteresis evolution in granular 1β2-3 HTSs in different jβH orientations. The magnetic flux compression significantly affects the magnetoresistance and its hysteresis for both perpendicular (H β₯ j) and parallel (H Η j) orientations. The obtained experimental data on the R(H) hysteresis at the arbitrary angles ΞΈβ=ββ H, j are explained using the approach developed for describing the magnetoresistance hysteresis in granular HTSs with regard to the magnetic flux compression and the model representations proposed by Daghero et al. [Phys. Rev. B 66(13), 11478 (2002)]. A concept of the effective field in the intergrain medium explains the well-known anisotropy of the magnetotransport properties of granular HTSs
Anisotropy of the magnetoresistive properties of granular high-temperature superconductors resulting from magnetic flux compression in the intergrain medium
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°.Π‘ ΡΠ΅Π»ΡΡ Π²ΡΡΡΠ½Π΅Π½ΠΈΡ ΠΏΡΠΈΡΠΈΠ½Ρ ΠΈΠ·Π²Π΅ΡΡΠ½ΠΎΠΉ Π°Π½ΠΈΠ·ΠΎΡΡΠΎΠΏΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ΅ ΠΏΠΎΠ»Π΅ (H) β
ΡΡΠ°Π½ΡΠΏΠΎΡΡΠ½ΡΠΉ ΡΠΎΠΊ (j) ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΡΡ
ΡΠ²ΠΎΠΉΡΡΠ² Π³ΡΠ°Π½ΡΠ»ΡΡΠ½ΡΡ
Π²ΡΡΠΎΠΊΠΎΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΡΡ
ΡΠ²Π΅ΡΡ
ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠΎΠ² (ΠΠ’Π‘Π) ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠ΅ Π³ΠΈΡΡΠ΅ΡΠ΅Π·ΠΈΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ
ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΡ R(H) ΠΎΠ±ΡΠ°Π·ΡΠ° ΠΠ’Π‘Π ΠΈΡΡΡΠΈΠ΅Π²ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΏΡΠΈ ΠΏΠ΅ΡΠΏΠ΅Π½Π΄ΠΈΠΊΡΠ»ΡΡΠ½ΠΎΠΉ (H β₯ j) ΠΈ
ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΠΎΠΉ (H || j) ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²
ΠΌΠ΅ΠΆΠ³ΡΠ°Π½ΡΠ»ΡΠ½ΡΡ
Π³ΡΠ°Π½ΠΈΡΠ°Ρ
(ΡΠ΅ΡΠ΅Π· ΠΊΠΎΡΠΎΡΡΠ΅ ΡΡΠ½Π½Π΅Π»ΠΈΡΡΡΡ Π½ΠΎΡΠΈΡΠ΅Π»ΠΈ ΡΠ²Π΅ΡΡ
ΠΏΡΠΎΠ²ΠΎΠ΄ΡΡΠ΅Π³ΠΎ ΡΠΎΠΊΠ°)
ΠΏΡΠΎΠ²Π΅Π΄ΡΠ½ Π°Π½Π°Π»ΠΈΠ· Π³ΠΈΡΡΠ΅ΡΠ΅Π·ΠΈΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ R(H). ΠΠ΅Π»ΠΈΡΠΈΠ½Π° ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°, Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΠ΅Π³ΠΎ
ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ ΡΡΠ΅ΠΏΠ΅Π½Ρ ΡΠΆΠ°ΡΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΠ° Π² ΠΌΠ΅ΠΆΠ³ΡΠ°Π½ΡΠ»ΡΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅, Π΄Π»Ρ
ΠΏΠ΅ΡΠΏΠ΅Π½Π΄ΠΈΠΊΡΠ»ΡΡΠ½ΠΎΠΉ ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ ΠΎΠΊΠ°Π·Π°Π»Π°ΡΡ ΠΏΡΠΈΠΌΠ΅ΡΠ½ΠΎ Π² Π΄Π²Π° ΡΠ°Π·Π° Π±ΠΎΠ»ΡΡΠ΅, ΡΠ΅ΠΌ Π΄Π»Ρ
ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΠΎΠΉ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ Ρ
ΠΎΡΠΎΡΠΎ ΠΎΠ±ΡΡΡΠ½ΡΠ΅Ρ Π½Π°Π±Π»ΡΠ΄Π°Π΅ΠΌΡΡ ΠΌΠ½ΠΎΠ³ΠΈΠΌΠΈ Π°Π²ΡΠΎΡΠ°ΠΌΠΈ Π°Π½ΠΈΠ·ΠΎΡΡΠΎΠΏΠΈΡ
ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΡΡ
ΡΠ²ΠΎΠΉΡΡΠ² Π³ΡΠ°Π½ΡΠ»ΡΡΠ½ΡΡ
ΠΠ’Π‘Π (Π²ΠΊΠ»ΡΡΠ°Ρ ΠΈ Π΄Π°Π½Π½ΡΠ΅ ΠΏΠΎ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΡΠΌ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΠΌ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΡ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π°)
Anisotropy of the magnetoresistive properties of granular high-temperature superconductors resulting from magnetic flux compression in the intergrain medium
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°.Π‘ ΡΠ΅Π»ΡΡ Π²ΡΡΡΠ½Π΅Π½ΠΈΡ ΠΏΡΠΈΡΠΈΠ½Ρ ΠΈΠ·Π²Π΅ΡΡΠ½ΠΎΠΉ Π°Π½ΠΈΠ·ΠΎΡΡΠΎΠΏΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ΅ ΠΏΠΎΠ»Π΅ (H) β
ΡΡΠ°Π½ΡΠΏΠΎΡΡΠ½ΡΠΉ ΡΠΎΠΊ (j) ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΡΡ
ΡΠ²ΠΎΠΉΡΡΠ² Π³ΡΠ°Π½ΡΠ»ΡΡΠ½ΡΡ
Π²ΡΡΠΎΠΊΠΎΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΡΡ
ΡΠ²Π΅ΡΡ
ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠΎΠ² (ΠΠ’Π‘Π) ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠ΅ Π³ΠΈΡΡΠ΅ΡΠ΅Π·ΠΈΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ
ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΡ R(H) ΠΎΠ±ΡΠ°Π·ΡΠ° ΠΠ’Π‘Π ΠΈΡΡΡΠΈΠ΅Π²ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΏΡΠΈ ΠΏΠ΅ΡΠΏΠ΅Π½Π΄ΠΈΠΊΡΠ»ΡΡΠ½ΠΎΠΉ (H β₯ j) ΠΈ
ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΠΎΠΉ (H || j) ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²
ΠΌΠ΅ΠΆΠ³ΡΠ°Π½ΡΠ»ΡΠ½ΡΡ
Π³ΡΠ°Π½ΠΈΡΠ°Ρ
(ΡΠ΅ΡΠ΅Π· ΠΊΠΎΡΠΎΡΡΠ΅ ΡΡΠ½Π½Π΅Π»ΠΈΡΡΡΡ Π½ΠΎΡΠΈΡΠ΅Π»ΠΈ ΡΠ²Π΅ΡΡ
ΠΏΡΠΎΠ²ΠΎΠ΄ΡΡΠ΅Π³ΠΎ ΡΠΎΠΊΠ°)
ΠΏΡΠΎΠ²Π΅Π΄ΡΠ½ Π°Π½Π°Π»ΠΈΠ· Π³ΠΈΡΡΠ΅ΡΠ΅Π·ΠΈΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ R(H). ΠΠ΅Π»ΠΈΡΠΈΠ½Π° ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°, Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΠ΅Π³ΠΎ
ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ ΡΡΠ΅ΠΏΠ΅Π½Ρ ΡΠΆΠ°ΡΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΡΠΎΠΊΠ° Π² ΠΌΠ΅ΠΆΠ³ΡΠ°Π½ΡΠ»ΡΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅, Π΄Π»Ρ
ΠΏΠ΅ΡΠΏΠ΅Π½Π΄ΠΈΠΊΡΠ»ΡΡΠ½ΠΎΠΉ ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ ΠΎΠΊΠ°Π·Π°Π»Π°ΡΡ ΠΏΡΠΈΠΌΠ΅ΡΠ½ΠΎ Π² Π΄Π²Π° ΡΠ°Π·Π° Π±ΠΎΠ»ΡΡΠ΅, ΡΠ΅ΠΌ Π΄Π»Ρ
ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΠΎΠΉ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ Ρ
ΠΎΡΠΎΡΠΎ ΠΎΠ±ΡΡΡΠ½ΡΠ΅Ρ Π½Π°Π±Π»ΡΠ΄Π°Π΅ΠΌΡΡ ΠΌΠ½ΠΎΠ³ΠΈΠΌΠΈ Π°Π²ΡΠΎΡΠ°ΠΌΠΈ Π°Π½ΠΈΠ·ΠΎΡΡΠΎΠΏΠΈΡ
ΠΌΠ°Π³Π½ΠΈΡΠΎΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΡΡ
ΡΠ²ΠΎΠΉΡΡΠ² Π³ΡΠ°Π½ΡΠ»ΡΡΠ½ΡΡ
ΠΠ’Π‘Π (Π²ΠΊΠ»ΡΡΠ°Ρ ΠΈ Π΄Π°Π½Π½ΡΠ΅ ΠΏΠΎ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΡΠΌ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΠΌ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΡ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ΅Π·ΠΈΡΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π°)
Anisotropy of the magnetoresistance hysteresis in the granular superconductor Y-Ba-Cu-O at different magnetic-field and transport-current orientations
Dissipation in granular high-temperature superconductors (HTSs) during the passage of macroscopic transport current j is mainly determined by carrier tunneling through intergrain boundaries (Josephson junctions). In the presence of external magnetic field H, it is necessary to take into account the significant magnetic flux compression, which can lead to the situation when the effective field Beff in the intergrain boundaries exceeds the external field by an order of magnitude. This is observed as a wide hysteresis of the field dependence of magnetoresistance R(H). In this study, we investigate the R(H) hysteresis evolution in granular 1β2-3 HTSs in different jβH orientations. The magnetic flux compression significantly affects the magnetoresistance and its hysteresis for both perpendicular (H β₯ j) and parallel (H Η j) orientations. The obtained experimental data on the R(H) hysteresis at the arbitrary angles ΞΈβ=ββ H, j are explained using the approach developed for describing the magnetoresistance hysteresis in granular HTSs with regard to the magnetic flux compression and the model representations proposed by Daghero et al. [Phys. Rev. B 66(13), 11478 (2002)]. A concept of the effective field in the intergrain medium explains the well-known anisotropy of the magnetotransport properties of granular HTSs