432 research outputs found
Breit-Wheeler Process in Intense Short Laser Pulses
Energy-angular distributions of electron-positron pair creation in collisions
of a laser beam and a nonlaser photon are calculated using the -matrix
formalism. The laser field is modeled as a finite pulse, similar to the
formulation introduced in our recent paper in the context of Compton scattering
[Phys. Rev. A {\bf 85}, 062102 (2012)]. The nonperturbative regime of pair
creation is considered here. The energy spectra of created particles are
compared with the corresponding spectra obtained using the modulated plane wave
approximation for the driving laser field. A very good agreement in these two
cases is observed, provided that the laser pulse is sufficiently long. For
short pulse durations, this agreement breaks down. The sensitivity of pair
production to the polarization of a driving pulse is also investigated. We show
that in the nonperturbative regime, the pair creation yields depend on the
polarization of the pulse, reaching their maximal values for the linear
polarization. Therefore, we focus on this case. Specifically, we analyze the
dependence of pair creation on the relative configuration of linear
polarizations of the laser pulse and the nonlaser photon. Lastly, we
investigate the carrier-envelope phase effect on angular distributions of
created particles, suggesting the possibility of phase control in relation to
the pair creation processes.Comment: 13 pages, 8 figure
Muon pair creation from positronium in a circularly polarized laser field
We study elementary particle reactions that result from the interaction of an
atomic system with a very intense laser wave of circular polarization. As a
specific example, we calculate the rate for the laser-driven reaction , where the electron and positron originate from a positronium
atom or, alternatively, from a nonrelativistic plasma. We distinguish
accordingly between the coherent and incoherent channels of the process. Apart
from numerical calculations, we derive by analytical means compact formulas for
the corresponding reaction rates. The rate for the coherent channel in a laser
field of circular polarization is shown to be damped because of the destructive
interference of the partial waves that constitute the positronium ground-state
wave packet. Conditions for the observation of the process via the dominant
incoherent channel in a circularly polarized field are pointed out
ΠΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ°. ΠΡΠΎΠΌ ΠΊΠ°ΠΊ Π½Π΅ΠΈΡΡΡΠΊΠ°Π΅ΠΌΡΠΉ ΠΈΡΡΠΎΡΠ½ΠΈΠΊ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈ ΡΠΈΡΡΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠΈ
The fundamentally new approach to the power problem is put forward based on the excitation of electronic quantum transitions in atom responsible for the increase in mass defect of atom. The consecutive quantum theory of hydrogen atom as a system of two particles interacting with each other β electron and proton is constructed on the basis of Diracβs model of electron. The motion of nucleus in the hydrogen atom is shown to essentially affect the physical properties of atom. The en-ergy spectrum of the atom contains two regions of bound states of electron and nucleus separated from each other by energy of the order of 2m2c2 (m2 is the mass of proton, c is the velocity of light). As a consequence, there exist such states of the atom in which the mass defect of atom reaches the value of 2m1 (m1 is the mass of electron). The existence of quantum states of atom with abnormally high mass defect and the ability of atom to make transitions from states with smaller value of mass defect to states with greater value open the prospect of creation of active thermal machines (TM) producing superfluous energy, i.e. transforming the energy of environment to active form. From the conceptual point of view, the idea of production of superfluous energy in active TM does not differ from the physical idea which is carried out in the thoroughly studied reactions of thermonuclear synthesis. In both cases, the question is the organization and maintenance in a system of interacting particles of physical processes in which the state of system changes in such a manner that the mass defect of sys-tem eventually increases in comparison with mass defect in initial state. Distinction between active TM and thermonuclear reactor consists only in the fact that physical processes of various types are used in them: in the first case β electronic processes in atoms, and in the second one β the processes going on at collision of nucleons and nuclei. The fact that both phenomena β the produc-tion of superfluous energy in active TM and the energy liberation in reaction of thermonuclear synthe-sis β are of the same physical nature and are described by the same parameter β mass defect means that production of superfluous energy is as real as thermonuclear synthesis. As the energy liberation in active TM occurs due to electronic processes in atoms instead of synthesis or splitting of atomic nu-clei, active TM will be ecologically pure energy sources. As fuel for active thermal machine, any substance can serve, the atoms of which can be in states with various values of mass defect. The re-sults of the present work do not contradict the laws of thermodynamics. The principles of action of TM described in textbooks on thermodynamics refer only to such TM which are isolated from envi-ronment (such TM can be naturally referred to as passive). The idea that it is impossible to trans-form energy of environment to active form, deeply rooted in consciousness, is the deepest and tragic delusion of the last century resulted in the orientation of economy of the planet exclusively towards passive TM. Consequences are known: research on the transformation of environment energy to active form (N.Tesla, K.E.Tsiolkovsky, P.K.Oshchepkov, etc.) have been blocked and declared as pseudo science, and the mankind appeared on the verge of ecological catastrophe by the end of the century. The real way toward resolving power problem, as is evident from the results of the paper, passes through the research directed towards the creation of active thermal machines β qualitatively new ecologically pure energy sources.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΏΡΠΈΠ½ΡΠΈΠΏΠΈΠ°Π»ΡΠ½ΠΎ Π½ΠΎΠ²ΡΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΊ ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ΅, Π² ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ Π»Π΅ΠΆΠΈΡ Π²ΠΎΠ·Π±ΡΠΆΠ΄Π΅Π½ΠΈΠ΅ Π² ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΏΠΎΠ΄ΡΠΈΡΡΠ΅ΠΌΠ΅ Π°ΡΠΎΠΌΠ° ΠΊΠ²Π°Π½ΡΠΎΠ²ΡΡ
ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄ΠΎΠ², ΠΏΡΠΈΠ²ΠΎΠ΄ΡΡΠΈΡ
ΠΊ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ Π΄Π΅ΡΠ΅ΠΊΡΠ° ΠΌΠ°ΡΡΡ Π°ΡΠΎΠΌΠ°. ΠΡΡ
ΠΎΠ΄Ρ ΠΈΠ· Π΄ΠΈΡΠ°ΠΊΠΎΠ²ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π°, ΠΏΠΎΡΡΡΠΎΠ΅Π½Π° ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½Π°Ρ ΠΊΠ²Π°Π½ΡΠΎΠ²Π°Ρ ΡΠ΅ΠΎΡΠΈΡ Π°ΡΠΎΠΌΠ° Π²ΠΎΠ΄ΠΎΡΠΎΠ΄Π° ΠΊΠ°ΠΊ ΡΠΈΡΡΠ΅ΠΌΡ Π΄Π²ΡΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΡΡΡΠΈΡ
ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΠ±ΠΎΠΉ ΡΠ°ΡΡΠΈΡ β ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π° ΠΈ ΠΏΡΠΎΡΠΎΠ½Π°. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΠ΄ΡΠ° Π² Π°ΡΠΎΠΌΠ΅ Π²ΠΎΠ΄ΠΎΡΠΎΠ΄Π° ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π²Π»ΠΈΡΠ΅Ρ Π½Π° ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ²ΠΎΠΉΡΡΠ²Π° Π°ΡΠΎΠΌΠ°. ΠΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠΏΠ΅ΠΊΡΡ Π°ΡΠΎΠΌΠ° ΡΠΎΠ΄Π΅ΡΠΆΠΈΡ Π΄Π²Π΅ ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π° ΠΈ ΡΠ΄ΡΠ°, ΡΠ°Π·Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΠ±ΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠ΅ΠΉ ΠΏΠΎΡΡΠ΄ΠΊΠ° 2m2c2 (m2 β ΠΌΠ°ΡΡΠ° ΠΏΡΠΎΡΠΎΠ½Π°, c β ΡΠΊΠΎΡΠΎΡΡΡ ΡΠ²Π΅ΡΠ°). ΠΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ ΡΡΠΎΠ³ΠΎ, ΠΈΠΌΠ΅ΡΡΡΡ ΡΠ°ΠΊΠΈΠ΅ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ Π°ΡΠΎΠΌΠ°, Π² ΠΊΠΎΡΠΎΡΡΡ
Π΄Π΅ΡΠ΅ΠΊΡ ΠΌΠ°ΡΡΡ Π°ΡΠΎΠΌΠ° Π΄ΠΎΡΡΠΈΠ³Π°Π΅Ρ Π·Π½Π°ΡΠ΅Π½ΠΈΡ 2m1 (m1 β ΠΌΠ°ΡΡΠ° ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π°). Π‘ΡΡΠ΅ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΊΠ²Π°Π½ΡΠΎΠ²ΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ Π°ΡΠΎΠΌΠ° Ρ Π°Π½ΠΎΠΌΠ°Π»ΡΠ½ΠΎ Π²ΡΡΠΎΠΊΠΈΠΌ Π΄Π΅ΡΠ΅ΠΊΡΠΎΠΌ ΠΌΠ°ΡΡΡ ΠΈ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΡ Π°ΡΠΎΠΌΠ° ΡΠΎΠ²Π΅ΡΡΠ°ΡΡ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Ρ ΠΈΠ· ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ Ρ ΠΌΠ΅Π½ΡΡΠΈΠΌ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ΠΌ Π΄Π΅ΡΠ΅ΠΊΡΠ° ΠΌΠ°ΡΡΡ Π² ΡΠΎΡΡΠΎΡΠ½ΠΈΡ Ρ Π±ΠΎΠ»ΡΡΠΈΠΌ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ΠΌ ΠΎΡΠΊΡΡΠ²Π°ΡΡ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Ρ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ Π°ΠΊΡΠΈΠ²Π½ΡΡ
ΡΠ΅ΠΏΠ»ΠΎΠ²ΡΡ
ΠΌΠ°ΡΠΈΠ½ (Π’Π), ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠΈΡ
ΠΈΠ·Π±ΡΡΠΎΡΠ½ΡΡ ΡΠ½Π΅ΡΠ³ΠΈΡ, Ρ.Π΅. ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΡΡΡΠΈΡ
ΡΠ½Π΅ΡΠ³ΠΈΡ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Ρ Π² Π°ΠΊΡΠΈΠ²Π½ΡΡ ΡΠΎΡΠΌΡ. Π‘ ΠΏΡΠΈΠ½ΡΠΈΠΏΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΈΠ΄Π΅Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π² Π°ΠΊΡΠΈΠ²Π½ΠΎΠΉ Π’Π Π½Π΅ ΠΎΡΠ»ΠΈΡΠ°Π΅ΡΡΡ ΠΎΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ΄Π΅ΠΈ, ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΠΌΠΎΠΉ Π² Ρ
ΠΎΡΠΎΡΠΎ ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π°ΠΊΡΠΈΡΡ
ΡΠ΅ΡΠΌΠΎΡΠ΄Π΅ΡΠ½ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π°. Π ΠΎΠ±ΠΎΠΈΡ
ΡΠ»ΡΡΠ°ΡΡ
ΡΠ΅ΡΡ ΠΈΠ΄Π΅Ρ ΠΎΠ± ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ ΠΏΠΎΠ΄Π΄Π΅ΡΠΆΠ°Π½ΠΈΠΈ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΡΡΡΠΈΡ
ΡΠ°ΡΡΠΈΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ², Π² ΠΊΠΎΡΠΎΡΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠ΅ ΡΠΈΡΡΠ΅ΠΌΡ ΠΈΠ·ΠΌΠ΅Π½ΡΠ΅ΡΡΡ ΡΠ°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, ΡΡΠΎ Π΄Π΅ΡΠ΅ΠΊΡ ΠΌΠ°ΡΡΡ ΡΠΈΡΡΠ΅ΠΌΡ Ρ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ΠΌ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅ΡΡΡ ΠΏΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ Π΄Π΅ΡΠ΅ΠΊΡΠΎΠΌ ΠΌΠ°ΡΡΡ Π² Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠΌ ΡΠΎΡΡΠΎΡΠ½ΠΈΠΈ. Π Π°Π·Π»ΠΈΡΠΈΠ΅ ΠΌΠ΅ΠΆΠ΄Ρ Π°ΠΊΡΠΈΠ²Π½ΠΎΠΉ Π’Π ΠΈ ΡΠ΅ΡΠΌΠΎΡΠ΄Π΅ΡΠ½ΡΠΌ ΡΠ΅Π°ΠΊΡΠΎΡΠΎΠΌ Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π»ΠΈΡΡ Π² ΡΠΎΠΌ, ΡΡΠΎ Π² Π½ΠΈΡ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠΈΠΏΠΎΠ²: Π² ΠΏΠ΅ΡΠ²ΠΎΠΌ ΡΠ»ΡΡΠ°Π΅ β ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ Π² Π°ΡΠΎΠΌΠ°Ρ
, Π° Π²ΠΎ Π²ΡΠΎΡΠΎΠΌ β ΠΏΡΠΎΡΠ΅ΡΡΡ, ΠΏΡΠΎΡΠ΅ΠΊΠ°ΡΡΠΈΠ΅ ΠΏΡΠΈ ΡΡΠΎΠ»ΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΠΈ Π½ΡΠΊΠ»ΠΎΠ½ΠΎΠ² ΠΈ ΡΠ΄Π΅Ρ. Π’ΠΎ ΠΎΠ±ΡΡΠΎΡΡΠ΅Π»ΡΡΡΠ²ΠΎ, ΡΡΠΎ ΠΎΠ±Π° ΡΠ²Π»Π΅Π½ΠΈΡ β ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΠ΅ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π² Π°ΠΊΡΠΈΠ²Π½ΠΎΠΉ Π’Π ΠΈ ΠΎΡΠ²ΠΎΠ±ΠΎΠΆΠ΄Π΅Π½ΠΈΠ΅ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π² ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠ΅ΡΠΌΠΎΡΠ΄Π΅ΡΠ½ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° β ΠΈΠΌΠ΅ΡΡ ΠΎΠ΄Π½Ρ ΠΈ ΡΡ ΠΆΠ΅ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΡΡ ΠΏΡΠΈΡΠΎΠ΄Ρ ΠΈ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΡΡ ΠΎΠ΄Π½ΠΎΠΉ ΠΈ ΡΠΎΠΉ ΠΆΠ΅ Π²Π΅Π»ΠΈΡΠΈΠ½ΠΎΠΉ β Π΄Π΅ΡΠ΅ΠΊΡΠΎΠΌ ΠΌΠ°ΡΡΡ, ΠΎΠ·Π½Π°ΡΠ°Π΅Ρ, ΡΡΠΎ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΡΡΠΎΠ»Ρ ΠΆΠ΅ ΡΠ΅Π°Π»ΡΠ½Π°, ΠΊΠ°ΠΊ ΠΈ ΡΠ΅ΡΠΌΠΎΡΠ΄Π΅ΡΠ½ΡΠΉ ΡΠΈΠ½ΡΠ΅Π·. ΠΠΎΡΠΊΠΎΠ»ΡΠΊΡ Π² Π°ΠΊΡΠΈΠ²Π½ΡΡ
Π’Π ΡΠ½Π΅ΡΠ³ΠΎΠ²ΡΠ΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π·Π° ΡΡΠ΅Ρ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π² Π°ΡΠΎΠΌΠ°Ρ
, Π° Π½Π΅ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠΈΠ½ΡΠ΅Π·Π° ΠΈΠ»ΠΈ ΡΠ°ΡΡΠ΅ΠΏΠ»Π΅Π½ΠΈΡ Π°ΡΠΎΠΌΠ½ΡΡ
ΡΠ΄Π΅Ρ, ΡΠΎ Π°ΠΊΡΠΈΠ²Π½ΡΠ΅ Π’Π Π±ΡΠ΄ΡΡ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΡΠΌΠΈ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°ΠΌΠΈ ΡΠ½Π΅ΡΠ³ΠΈΠΈ. Π’ΠΎΠΏΠ»ΠΈΠ²ΠΎΠΌ Π΄Π»Ρ Π°ΠΊΡΠΈΠ²Π½ΠΎΠΉ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΌΠ°ΡΠΈΠ½Ρ ΠΌΠΎΠΆΠ΅Ρ ΡΠ»ΡΠΆΠΈΡΡ Π»ΡΠ±ΠΎΠ΅ Π²Π΅ΡΠ΅ΡΡΠ²ΠΎ, Π°ΡΠΎΠΌΡ ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ ΠΌΠΎΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡΡ Π² ΡΠΎΡΡΠΎΡΠ½ΠΈΡΡ
Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡΠΌΠΈ Π΄Π΅ΡΠ΅ΠΊΡΠ° ΠΌΠ°ΡΡΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ Π½Π°ΡΡΠΎΡΡΠ΅ΠΉ ΡΠ°Π±ΠΎΡΡ Π½Π΅ ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠ°Ρ Π·Π°ΠΊΠΎΠ½Π°ΠΌ ΡΠ΅ΡΠΌΠΎΠ΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ. Π‘Ρ
Π΅ΠΌΠ° ΠΈ ΠΏΡΠΈΠ½ΡΠΈΠΏΡ Π΄Π΅ΠΉΡΡΠ²ΠΈΡ Π’Π, ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΠΌΡΠ΅ Π² ΡΡΠ΅Π±Π½ΠΈΠΊΠ°Ρ
ΠΏΠΎ ΡΠ΅ΡΠΌΠΎΠ΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ΅, ΠΎΡΠ½ΠΎΡΡΡΡΡ Π»ΠΈΡΡ ΠΊ ΡΠ°ΠΊΠΈΠΌ Π’Π, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΈΠ·ΠΎΠ»ΠΈΡΠΎΠ²Π°Π½Ρ ΠΎΡ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Ρ (ΡΠ°ΠΊΠΈΠ΅ Π’Π Π΅ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π½Π°Π·Π²Π°ΡΡ ΠΏΠ°ΡΡΠΈΠ²Π½ΡΠΌΠΈ). ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΎ ΠΏΡΠΈΠ½ΡΠΈΠΏΠΈΠ°Π»ΡΠ½ΠΎΠΉ Π½Π΅Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΏΡΠ΅Π²ΡΠ°ΡΠ΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Ρ Π² Π°ΠΊΡΠΈΠ²Π½ΡΡ ΡΠΎΡΠΌΡ, Π³Π»ΡΠ±ΠΎΠΊΠΎ ΡΠΊΠΎΡΠ΅Π½ΠΈΠ²ΡΠ΅Π΅ΡΡ Π² ΡΠΎΠ·Π½Π°Π½ΠΈΠΈ, ΡΠ²Π»ΡΠ΅ΡΡΡ Π³Π»ΡΠ±ΠΎΡΠ°ΠΉΡΠΈΠΌ ΠΈ ΡΡΠ°Π³ΠΈΡΠ΅ΡΠΊΠΈΠΌ Π·Π°Π±Π»ΡΠΆΠ΄Π΅Π½ΠΈΠ΅ΠΌ ΠΏΡΠΎΡΠ»ΠΎΠ³ΠΎ Π²Π΅ΠΊΠ°, ΠΏΡΠΈΠ²Π΅Π΄ΡΠΈΠΌ ΠΊ ΠΎΡΠΈΠ΅Π½ΡΠ°ΡΠΈΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΈ ΠΏΠ»Π°Π½Π΅ΡΡ ΠΈΡΠΊΠ»ΡΡΠΈΡΠ΅Π»ΡΠ½ΠΎ Π½Π° ΠΏΠ°ΡΡΠΈΠ²Π½ΡΠ΅ Π’Π. ΠΠΎΡΠ»Π΅Π΄ΡΡΠ²ΠΈΡ ΠΈΠ·Π²Π΅ΡΡΠ½Ρ: ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΡΡΠ΅Π΄Ρ Π² Π°ΠΊΡΠΈΠ²Π½ΡΡ ΡΠΎΡΠΌΡ (Π. Π’Π΅ΡΠ»Π°, Π.Π. Π¦ΠΈΠΎΠ»ΠΊΠΎΠ²ΡΠΊΠΈΠΉ, Π.Π.ΠΡΠ΅ΠΏΠΊΠΎΠ² ΠΈ Π΄Ρ.) Π±ΡΠ»ΠΈ Π·Π°Π±Π»ΠΎΠΊΠΈΡΠΎΠ²Π°Π½Ρ ΠΈ ΠΎΠ±ΡΡΠ²Π»Π΅Π½Ρ Π»ΠΆΠ΅Π½Π°ΡΠΊΠΎΠΉ, ΠΈ ΡΠ΅Π»ΠΎΠ²Π΅ΡΠ΅ΡΡΠ²ΠΎ ΠΊ ΠΊΠΎΠ½ΡΡ Π²Π΅ΠΊΠ° ΠΎΠΊΠ°Π·Π°Π»ΠΎΡΡ Π½Π° Π³ΡΠ°Π½ΠΈ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΊΠ°ΡΠ°ΡΡΡΠΎΡΡ. Π Π΅Π°Π»ΡΠ½ΡΠΉ ΠΏΡΡΡ ΠΊ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ, ΠΊΠ°ΠΊ Π²ΠΈΠ΄Π½ΠΎ ΠΈΠ· ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠ°Π±ΠΎΡΡ, Π»Π΅ΠΆΠΈΡ ΡΠ΅ΡΠ΅Π· ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ, Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΠ΅ Π½Π° ΡΠΎΠ·Π΄Π°Π½ΠΈΠ΅ Π°ΠΊΡΠΈΠ²Π½ΡΡ
Π’Π β ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π½ΠΎΠ²ΡΡ
ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈ ΡΠΈΡΡΡΡ
ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ² ΡΠ½Π΅ΡΠ³ΠΈΠΈ
Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs
We give sufficient conditions for essential self-adjointness of magnetic
Schr\"odinger operators on locally finite graphs. Two of the main theorems of
the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as
follows: the ordering of presentation has been modified in several places,
more details have been provided in several places, some notations have been
changed, two examples have been added, and several new references have been
inserted. The final version of this preprint will appear in Integral
Equations and Operator Theor
Time, what is it? Dynamical Properties of Time 1
Abstract. The phenomenon of local dynamical inhomogeneity of time is predicted, which implies that the course of time along the trajectory of motion of a particle in the inertial reference frames moving relative to each other depends on the state of motion of the particle under the influence of a force field. As is seen from the results obtained, the ability to influence the course of time represents one of the most fundamental properties of any material system intrinsically inherent in it by the very nature of things, which manifests itself when the system interacts with force fields. The inferences of the paper are not based on the use of any hypotheses and strictly follow from relativistic equations of motion. The dependence of the course of time upon the behaviour of physical system is, thus, a direct consequence of causality principle, relativity principle and the pseudoeuclidity of space-time. The results obtained confirm the Kozyrev hypothesis that time has physical properties and open up radically new opportunities for the efficient control of physical processes. It is demonstrated with point particle that the change in the course of time results in the appearance of an additional force acting on the particle. A general conclusion is drawn on the basis of the theory advanced that relativistic equations of motion for any kind of matter contain information about the physical properties of time, which are, thus, of dynamical nature
Numerical study of oil spill in the Patos lagoon under flood and ebb conditions
Facing great obstacles to eradicate environmental hazards generated by oil spills, it is crucial to establish actions against such accidents. In this context, the focus of this study is to analyze oil spills at the harbor region of Rio Grande, Rio Grande do Sul. The Easy Coupling Oil System (ECOS) model was used to model the oil spills under different environmental conditions simulated by the hydrodynamic model Telemac-3D, with the intention to identify the main forces controlling the movement of the oil slicks over a year of averaged hydrodynamic conditions from 2003 to 2015. The computational domain comprises the Patos Lagoon, the harbor area of Rio Grande and the Southern Brazilian Shelf. For the oil spill simulations, eight distinct events were defined considering both flood and ebb conditions in the estuarine region of the Patos Lagoon. The oil spill simulations showed that, in ebb conditions, the oil slick movement is mainly ruled by the currents, moving towards the outflow. After a few hours, the wind action makes the slick move towards the margins of the waterway. In flood conditions, on the other hand, the oil slick drifts to the interior of the estuary, following the dominant currents and the local winds
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