1,478 research outputs found
Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization
The symlectic quantum tomography for the general linear quantization is
introduced. Using the approach based upon the Wigner function techniques the
evolution equation of quantum tomograms is derived for a parametric driven
oscillator.Comment: 11 page
Π‘ΠΈΠ½ΡΠ΅Π· ΡΠ° N-Π°Π»ΠΊΡΠ»ΡΠ²Π°Π½Π½Ρ Π΄ΡΠ΅ΡΠΈΠ» 4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΡΠ²
It has been shown that the ternary condensation of oxaloacetic ester (diethyl 2-oxosuccinate), aromatic aldehydesΒ and 3-amino-1,2,4-triazole or 5-aminotetrazole in dimethylformamide results in formation of the corresponding diethyl 7-aryl-4,7-dihydroazolo[1,5-a]pyrimidin-5,6-dicarboxylates. By 1H NMR spectroscopy (according to the data of the chemical shifts of C(2)H-protons for the corresponding N(4)H- and N(4)-methylderivatives ofΒ 7-phenyl-4,7-dihydro[1,2,4]triazolo[1,5-a]pyrimidin-5,6-dicarboxylate) it has been found that alkylation of 4,7-dihydro[1,2,4]azolo[1,5-a]pyrimidin-5,6-dicarboxylates in the acetonitrileβsaturated water alkali system leads selectively to formation of N(4)-alkyl derivatives. Both the starting compounds obtained and their N(4)-methylsubstitutedΒ analogues together with relative diethyl 4-aryl-3,4-dihydropyrimidin-2(1H)-on-5,6-dicarboxylates, 6-unsubstitutedΒ 4-aryl-3,4-dihydropyrimidin-2(1H)-on-5-dicarboxylates and the derivatives of 6-COR-7-aryl-4,7-dihydro[1,2,4] triazolo[1,5-a]pyrimidines are the promising objects for studying benzyl C(7)-functionalization of 4,7-dihydroazoloΒ 1,5-a]pyrimidines, as well as of reactions associated with the presence of double C=C-bonds activated by twoΒ electron withdrawing groups. Obtaining of the key N(4)H- and N(4)Me-derivatives of 7-phenyl-4,7-dihydro[1,2,4]Β triazolo- and tetrazolo[1,5-a]pyrimidin-5,6-dicarboxylates also opens the way to the research of biological propertiesΒ of the compounds of this class. It is noteworthy that being a three-component one the reaction studied, without any doubts, are appropriate for the synthesis of the derivatives of 7-aryl-4,7-dihydro[1,2,4]triazolo- andΒ tetrazolo[1,5-a]pyrimidines containing two electron withdrawing substituents in positions 5 and 6.ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΠ΅Ρ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½Π°Ρ ΠΊΠΎΠ½Π΄Π΅Π½ΡΠ°ΡΠΈΡ ΡΠ°Π²Π΅Π»Π΅Π²ΠΎΡΠΊΡΡΡΠ½ΠΎΠ³ΠΎ ΡΡΠΈΡΠ° (Π΄ΠΈΡΡΠΈΠ» 2-ΠΎΠΊΡΠΎΡΡΠΊΡΠΈΠ½Π°ΡΠ°),Β Π°ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π»ΡΠ΄Π΅Π³ΠΈΠ΄ΠΎΠ² ΠΈ 3-Π°ΠΌΠΈΠ½ΠΎ-1,2,4-ΡΡΠΈΠ°Π·ΠΎΠ»Π° ΠΈΠ»ΠΈ 5-Π°ΠΌΠΈΠ½ΠΎΡΠ΅ΡΡΠ°Π·ΠΎΠ»Π° Π² Π΄ΠΈΠΌΠ΅ΡΠΈΠ»ΡΠΎΡΠΌΠ°ΠΌΠΈΠ΄Π΅ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΡ
Π΄ΠΈΡΡΠΈΠ» 7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠΎΠ². Π‘ ΠΏΠΎΠΌΠΎΡΡΡ 1Π Π―ΠΠ -ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΠΈΠΈ (ΠΏΠΎ Π΄Π°Π½Π½ΡΠΌ Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΄Π²ΠΈΠ³ΠΎΠ² ΡΠΈΠ³Π½Π°Π»ΠΎΠ² ΠΏΡΠΎΡΠΎΠ½ΠΎΠ² Π‘(2)HΒ Π΄Π»Ρ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΡ
N(4)H- ΠΈ N(4)ΠΠ΅-ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
Π΄ΠΈΡΡΠΈΠ» 7-ΡΠ΅Π½ΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ[1,5-a]Β ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠ°) ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π°Π»ΠΊΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ 7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠΎΠ² Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ Π°ΡΠ΅ΡΠΎΠ½ΠΈΡΡΠΈΠ»-Π½Π°ΡΡΡΠ΅Π½Π½Π°Ρ Π²ΠΎΠ΄Π½Π°Ρ ΡΠ΅Π»ΠΎΡΡ ΡΠ΅Π»Π΅ΠΊΡΠΈΠ²Π½ΠΎ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ N(4)-Π°Π»ΠΊΠΈΠ»ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
. ΠΠ°ΠΊ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ, ΡΠ°ΠΊ ΠΈ ΠΈΡ
N(4)-ΠΌΠ΅ΡΠΈΠ»Π·Π°ΠΌΠ΅ΡΠ΅Π½Π½ΡΠ΅ Π°Π½Π°Π»ΠΎΠ³ΠΈ Π½Π°ΡΡΠ΄Ρ Ρ ΡΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΠΌΠΈ Π΄ΠΈΡΡΠΈΠ» 4-Π°ΡΠΈΠ»-3,4-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-2(1Π)-ΠΎΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠ°ΠΌΠΈ, 6-Π½Π΅Π·Π°ΠΌΠ΅ΡΠ΅Π½Π½ΡΠΌΠΈ ΡΡΠΈΠ» 4-Π°ΡΠΈΠ»-3,4-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-2(1Π)-ΠΎΠ½-5-ΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠ°ΠΌΠΈ ΠΈΒ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΠΌΠΈ 6-COR-7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½ΠΎΠ² ΡΠ²Π»ΡΡΡΡΡ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌΠΈ ΠΎΠ±ΡΠ΅ΠΊΡΠ°ΠΌΠΈ Π΄Π»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ Π±Π΅Π½Π·ΠΈΠ»ΡΠ½ΠΎΠΉ Π‘(7)-ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ 4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½ΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ΅Π°ΠΊΡΠΈΠΉ, ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
Ρ Π½Π°Π»ΠΈΡΠΈΠ΅ΠΌ Π΄Π²ΠΎΠΉΠ½ΠΎΠΉ C=C-ΡΠ²ΡΠ·ΠΈ, Π°ΠΊΡΠΈΠ²ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ Π΄Π²ΡΠΌΡ Π°ΠΊΡΠ΅ΠΏΡΠΎΡΠ½ΡΠΌΠΈ Π³ΡΡΠΏΠΏΠ°ΠΌΠΈ. ΠΠΎΠ»ΡΡΠ΅Π½ΠΈΠ΅ ΠΊΠ»ΡΡΠ΅Π²ΡΡ
N(4)H- ΠΈ N(4)ΠΠ΅-ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
7-ΡΠ΅Π½ΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ- ΠΈ ΡΠ΅ΡΡΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠΎΠ² ΡΠ°ΠΊΠΆΠ΅ ΠΎΡΠΊΡΡΠ²Π°Π΅Ρ ΠΏΡΡΡ ΠΊ Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡΠΌΒ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΡΡΠΎΠ³ΠΎ ΠΊΠ»Π°ΡΡΠ°. ΠΠ°ΠΌΠ΅ΡΠΈΠΌ, ΡΡΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Π½Π°Ρ ΡΠ΅Π°ΠΊΡΠΈΡ, ΡΠ²Π»ΡΡΡΡ ΡΡΠ΅Ρ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΠΎΠΉ, Π±Π΅Π·ΡΡΠ»ΠΎΠ²Π½ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΈΡ Π΄Π»Ρ ΡΠΈΠ½ΡΠ΅Π·Π° ΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΎΡΠ½ΡΡ
Π±ΠΈΠ±Π»ΠΈΠΎΡΠ΅ΠΊ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΠΈΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ- ΠΈ ΡΠ΅ΡΡΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½ΠΎΠ², ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠΈΡ
Π΄Π²Π° ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ°ΠΊΡΠ΅ΠΏΡΠΎΡΠ½ΡΡ
Π·Π°ΠΌΠ΅ΡΡΠΈΡΠ΅Π»Ρ Π² ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡΡ
5 ΠΈ 6.ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ ΡΡΠΈΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½Π° ΠΊΠΎΠ½Π΄Π΅Π½ΡΠ°ΡΡΡ ΡΠ°Π²Π»Π΅Π²ΠΎΠΎΡΡΠΎΠ²ΠΎΠ³ΠΎ Π΅ΡΡΠ΅ΡΡ (Π΄ΡΠ΅ΡΠΈΠ» 2-ΠΎΠΊΡΠΎΡΡΠΊΡΠΈΠ½Π°ΡΡ), Π°ΡΠΎΠΌΠ°ΡΠΈΡΠ½ΠΈΡ
Π°Π»ΡΠ΄Π΅Π³ΡΠ΄ΡΠ² ΡΠ° 3-Π°ΠΌΡΠ½ΠΎ-1,2,4-ΡΡΠΈΠ°Π·ΠΎΠ»Ρ Π°Π±ΠΎ 5-Π°ΠΌΡΠ½ΠΎΡΠ΅ΡΡΠ°Π·ΠΎΠ»Ρ Π² Π΄ΠΈΠΌΠ΅ΡΠΈΠ»ΡΠΎΡΠΌΠ°ΠΌΡΠ΄Ρ ΠΏΡΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡΒ Π΄ΠΎ ΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
Π΄ΡΠ΅ΡΠΈΠ» 4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΡΠ². ΠΠ° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡΒ 1Π Π―ΠΠ -ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΡΡ (Π·Π° Π΄Π°Π½ΠΈΠΌΠΈ ΠΏΡΠΎ Ρ
ΡΠΌΡΡΠ½Ρ Π·ΡΡΠ²ΠΈ ΡΠΈΠ³Π½Π°Π»ΡΠ² ΠΏΡΠΎΡΠΎΠ½ΡΠ² Π‘(2)Π Π΄Π»Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
N(4)H- ΡΠ°Β N(4)Me-ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
Π΄ΡΠ΅ΡΠΈΠ» 7-ΡΠ΅Π½ΡΠ»-4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΡΠ²) Π²ΡΡΠ°-Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΠΎ Π°Π»ΠΊΡΠ»ΡΠ²Π°Π½Π½Ρ 4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΡΠ² Ρ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΡΠ΅ΡΠΎΠ½ΡΡΡΠΈΠ»Π½Π°ΡΠΈΡΠ΅Π½ΠΈΠΉ Π²ΠΎΠ΄Π½ΠΈΠΉ Π»ΡΠ³ ΡΠ΅Π»Π΅ΠΊΡΠΈΠ²Π½ΠΎ ΠΏΡΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡ Π΄ΠΎ ΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ N(4)-Π°Π»ΠΊΡΠ»ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
. Π―ΠΊ ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π²ΠΈΡ
ΡΠ΄Π½ΡΒ ΡΠΏΠΎΠ»ΡΠΊΠΈ, ΡΠ°ΠΊ Ρ ΡΡ
Π½Ρ N(4)-ΠΌΠ΅ΡΠΈΠ»Π·Π°ΠΌΡΡΠ΅Π½Ρ Π°Π½Π°Π»ΠΎΠ³ΠΈ ΠΏΠΎΡΡΠ΄ Π·Ρ ΡΠΏΠΎΡΡΠ΄Π½Π΅Π½ΠΈΠΌΠΈ Π΄ΡΠ΅ΡΠΈΠ» 4-Π°ΡΠΈΠ»-3,4-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-2(1Π)-ΠΎΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠ°ΠΌΠΈ, 6-Π½Π΅Π·Π°ΠΌΡΡΠ΅Π½ΠΈΠΌΠΈ Π΅ΡΠΈΠ» 4-Π°ΡΠΈΠ»-3,4-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-2(1Π)-ΠΎΠ½-5-ΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΠ°ΠΌΠΈ ΡΠ° ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΠΌΠΈ 6-COR-7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½ΡΠ² Ρ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΠΈΠΌΠΈ ΠΎΠ±βΡΠΊΡΠ°ΠΌΠΈ Π΄Π»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ Π±Π΅Π½Π·ΠΈΠ»ΡΠ½ΠΎΡ Π‘(7)-ΡΡΠ½ΠΊΡΡΠΎΠ½Π°Π»ΡΠ·Π°ΡΡΡ 4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½ΡΠ², Π° ΡΠ°ΠΊΠΎΠΆ ΡΠ΅Π°ΠΊΡΡΠΉ,Β ΠΏΠΎΠ²βΡΠ·Π°Π½ΠΈΡ
Π· Π½Π°ΡΠ²Π½ΡΡΡΡ ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΎΠ³ΠΎ C=C-Π·Π²βΡΠ·ΠΊΡ, Π°ΠΊΡΠΈΠ²ΠΎΠ²Π°Π½ΠΎΠ³ΠΎ Π΄Π²ΠΎΠΌΠ° Π°ΠΊΡΠ΅ΠΏΡΠΎΡΠ½ΠΈΠΌΠΈ Π³ΡΡΠΏΠ°ΠΌΠΈ. ΠΡΡΠΈΠΌΠ°Π½Π½ΡΒ ΠΊΠ»ΡΡΠΎΠ²ΠΈΡ
N(4)H- Ρ N(4)ΠΠ΅-ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
7-ΡΠ΅Π½ΡΠ»-4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ- ΡΠ° ΡΠ΅ΡΡΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-5,6-Π΄ΠΈΠΊΠ°ΡΠ±ΠΎΠΊΡΠΈΠ»Π°ΡΡΠ² ΡΠ°ΠΊΠΎΠΆ Π²ΡΠ΄ΠΊΡΠΈΠ²Π°Ρ ΡΠ»ΡΡ
Π΄ΠΎ Π±ΡΠΎΠ»ΠΎΠ³ΡΡΠ½ΠΈΡ
Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ ΡΠΏΠΎΠ»ΡΠΊ ΡΡΠΎΠ³ΠΎ ΠΊΠ»Π°ΡΡ. ΠΡΠ΄Π·Π½Π°ΡΠΈΠΌΠΎ,Β ΡΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π° ΡΠ΅Π°ΠΊΡΡΡ, Π±ΡΠ΄ΡΡΠΈ ΡΡΠΈΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΠΎΡ, Π±Π΅Π·ΡΠΌΠΎΠ²Π½ΠΎ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈΡΡ Π΄Π»Ρ ΡΠΈΠ½ΡΠ΅Π·Ρ ΡΠ° Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½ΡΒ ΠΊΠΎΠΌΠ±ΡΠ½Π°ΡΠΎΡΠ½ΠΈΡ
Π±ΡΠ±Π»ΡΠΎΡΠ΅ΠΊ ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
7-Π°ΡΠΈΠ»-4,7-Π΄ΠΈΠ³ΡΠ΄ΡΠΎ[1,2,4]ΡΡΠΈΠ°Π·ΠΎΠ»ΠΎ- ΡΠ° ΡΠ΅ΡΡΠ°Π·ΠΎΠ»ΠΎ[1,5-a]ΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½ΡΠ²,Β ΡΠΎ ΠΌΡΡΡΡΡΡ Π΄Π²Π° Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ°ΠΊΡΠ΅ΠΏΡΠΎΡΠ½Ρ Π·Π°ΠΌΡΡΠ½ΠΈΠΊΠΈ Ρ ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½Π½ΡΡ
5 ΡΠ° 6
Quantum dynamics, dissipation, and asymmetry effects in quantum dot arrays
We study the role of dissipation and structural defects on the time evolution
of quantum dot arrays with mobile charges under external driving fields. These
structures, proposed as quantum dot cellular automata, exhibit interesting
quantum dynamics which we describe in terms of equations of motion for the
density matrix. Using an open system approach, we study the role of asymmetries
and the microscopic electron-phonon interaction on the general dynamical
behavior of the charge distribution (polarization) of such systems. We find
that the system response to the driving field is improved at low temperatures
(and/or weak phonon coupling), before deteriorating as temperature and
asymmetry increase. In addition to the study of the time evolution of
polarization, we explore the linear entropy of the system in order to gain
further insights into the competition between coherent evolution and
dissipative processes.Comment: 11pages,9 figures(eps), submitted to PR
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
Defect detection in nano-scale transistors based on radio-frequency reflectometry
Radio-frequency reflectometry in silicon single-electron transistors (SETs)
is presented. At low temperatures (<4 K), in addition to the expected Coulomb
blockade features associated with charging of the SET dot, quasi-periodic
oscillations are observed that persist in the fully depleted regime where the
SET dot is completely empty. A model, confirmed by simulations, indicates that
these oscillations originate from charging of an unintended floating gate
located in the heavily doped polycrystalline silicon gate stack. The technique
used in this experiment can be applied for detailed spectroscopy of various
charge defects in nanoscale SETs and field effect transistorsComment: 3 pages, 3 figure
Numerical studies of variable-range hopping in one-dimensional systems
Hopping transport in a one-dimensional system is studied numerically. A fast
algorithm is devised to find the lowest-resistance path at arbitrary electric
field. Probability distribution functions of individual resistances on the path
and the net resistance are calculated and fitted to compact analytic formulas.
Qualitative differences between statistics of resistance fluctuations in Ohmic
and non-Ohmic regimes are elucidated. The results are compared with prior
theoretical and experimental work on the subject.Comment: 12 pages, 12 figures. Published versio
Concentration and power dependences of level population of 2.8-mu m laser transition in YLF : Er crystals under CW laser diode pumping
An influence of interionic cross relaxation processes (upconversion, selfquenching) on concentration and power dependences of the inverse population of ^4I_(11/2) and ^4I_(13/2) laser levels in YLF:Er crystals under CW laser-diode pumping were studied both theoretically and experimentally. Computer simulations were carried out taking into account not only pair interaction but also the multi-ion interaction in the whole system. Optimal Er concentration for 3 - Β΅m CW lasing was estimated as 10 - 15%
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