A classical system, which is analogous to
the quantum one with a backflow of probability, is proposed.
The system consists of a chain of masses interconnected by
springs and attached by other springs to fixed supports.
Thanks to the last springs the cutoff frequency and dispersion
appears in the spectrum of waves propagating along the chain.
It is shown that this dispersion contributes to the appearance
of a backflow of energy. In the case of the interference of
two waves, the magnitude of this backflow is an order of
magnitude higher than the value of probability backflow in the
mentioned quantum problem. The equation of Green’s function is
considered and it is shown that the backflow of energy is also
possible when the system is excited by two consecutive short
pulses. This classical backflow phenomenon is explained by the
branching of energy flow to local modes that is confirmed by
the results for the forced damped oscillator. It is shown that
even in such a simple system the backflow of energy takes
place (both instantaneous and average).
Keywords: wave,
dispersion, energy, backflow, 1D lattice, oscillator
a Fizinių ir
technologijų mokslų centro Puslaidininkių fizikos institutas,
Vilnius, Lietuva
b Vilniaus universiteto Teorinės fizikos ir
astronomijos institutas, Vilnius, Lietuva
Aprašoma klasikinė sistema, kuri yra
kvantinės sistemos, pasižyminčios neigiamu tikimybės srautu,
analogas. Sistemą sudaro tarpusavyje spyruoklėmis sujungtų
rutuliukų grandinėlė, kurioje kiekvienas rutuliukas papildoma
spyruokle dar yra prijungtas prie fiksuotų atramų. Dėl
papildomai prijungtų spyruoklių atsiranda plintančių išilgai
grandinėlės bangų spektre draustinis dažnių ruožas ir
dispersija. Parodyta, kad tai lemia neigiamo bangos energijos
srauto atsiradimą. Dviejų interferuojančių bangų atveju šio
neigiamo srauto dydis visa eile viršija neigamo tikimybės
srauto dydį minėtame kvantiniame uždavinyje. Apskaičiuota
klasikinę sistemą aprašančių lygčių Gryno funkcija ir
parodyta, kad neigiamo energijos srauto atsiradimas įmanomas
ir tada, kai sistema žadinama dviem trumpais nuosekliais
impulsais. Ištirtoje klasikinėje sistemoje atsirandantis
neigiamo energijos srauto reiškinys aiškinamas energijos
išsišakojimu į lokalines modas. Tai patvirtina gauti žadinamo
išorine jėga disipacinio osciliatoriaus rezultatai. Parodyta,
kad net tokioje paprastoje sistemoje įmanomas atbulinis (tiek
momentinis, tiek ir vidutinis) energijos srautas.
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