CLASSICAL ANALOG TO THE AIRY
WAVE PACKET
Algirdas Matulis
a and Artūras Acus
b
aSemiconductor Physics Institute, Center for
Physical Sciences and Technology, Saulėtekio 3, 10222 Vilnius,
Lithuania
bInstitute of Theoretical Physics and Astronomy,
Vilnius University, Saulėtekio 3, 10222 Vilnius, Lithuania
Emails: matulisalg@gmail.com; arturas.acus@tfai.vu.lt
Received 18 June 2019; accepted 25 June 2019
The solution of the Liouville equation for
the ensemble of free particles is presented and the classical
analog to the quantum accelerating Airy wave packet is
constructed and discussed. Considering the motion of various
classical packets – with an infinite and restricted
distribution of velocities of particles – and also the motion
of their fronts, we demonstrate in the simplest and most
definite way why the packet can display a more sophisticated
behaviour (even acceleration) as compared with a free
individual particle that moves at a fixed velocity. A
comparison of this classical solution with the quantum one in
the Wigner representation of quantum mechanics, which provides
the closest analogy, is also presented.
Keywords: Liouville
equation, accelerating front, density matrix in Wigner
representation
KLASIKINIS BANGINIO AIRY PAKETO ANALOGAS
Algirdas Matulisa, Artūras Acusb
aFizinių ir
technologijų mokslų centro Puslaidininkių fizikos institutas,
Vilnius, Lietuva
bVilniaus universiteto Teorinės fizikos ir
astronomijos institutas, Vilnius, Lietuva
Pateiktas Liuvilio lygties sprendinys,
aprašantis laisvų dalelių ansamblį, ir sukonstruotas bei
aptartas klasikinis kvantinio greitėjančio banginio Airy paketo
analogas. Sugretinus įvairius klasikinius begalinio ir riboto
dalelių greičių pasiskirstymų paketus, pačiu paprasčiausiu būdu
parodyta, kodėl iš laisvųjų dalelių, judančių pastoviu greičiu,
sudarytas paketas gali elgtis gana įvairiai (taip pat ir
greitėti). Šie klasikinio paketo judėjimo ypatumai palyginti su
kvantinę dalelę aprašančiais tankio matricos lygties
sprendiniais Vignerio vaizdavime, kur klasikinio bei kvantinio
aprašymų analogija yra ryškiausia.
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