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Open Access Nano Express

Displacing, squeezing, and time evolution of quantum states for nanoelectronic circuits

Jeong Ryeol Choi1*, Byeong Jae Choi2 and Hyun Deok Kim3

Author Affiliations

1 Department of Radiologic TechnologyDaegu Health College, , Buk-gu, Daegu, 702-722, Republic of Korea

2 School of Electronics and Electrical EngineeringDaegu University, , Gyeongsan, Gyeongbuk, 712-714, Republic of Korea

3 School of Electronics Engineering, College of IT Engineering, Kyungpook National University, Daegu, 702-701, Republic of Korea

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Nanoscale Research Letters 2013, 8:30  doi:10.1186/1556-276X-8-30

Published: 15 January 2013

Abstract

The time behavior of DSN (displaced squeezed number state) for a two-dimensional electronic circuit composed of nanoscale elements is investigated using unitary transformation approach. The original Hamiltonian of the system is somewhat complicated. However, through unitary transformation, the Hamiltonian became very simple enough that we can easily treat it. By executing inverse transformation for the wave function obtained in the transformed system, we derived the exact wave function associated to the DSN in the original system. The time evolution of the DSN is described in detail, and its corresponding probability density is illustrated. We confirmed that the probability density oscillates with time like that of a classical state. There are two factors that drive the probability density to oscillate: One is the initial amplitude of complementary functions, and the other is the external power source. The oscillation associated with the initial amplitude gradually disappears with time due to the dissipation raised by resistances of the system. These analyses exactly coincide with those obtained from classical state. The characteristics of quantum fluctuations and uncertainty relations for charges and currents are also addressed.

Keywords:
Displaced squeezed number states; Electronic circuits; Nanoscale physics; Unitary transformation; Fluctuations of charges and currents