Abstract Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum (Lz) for an electron confined in quantum dots under a uniform magnetic field (UMF) and a static electric field (SEF). It finds that the eigenvalue of Lz just stands for the expectation value of a usual angular momentum lz in the eigen-state. It first obtains the matrix density for this system via directly calculating a transfer matrix element of operator $\exp( -\beta H$) in some representations with the technique of integral within an ordered products (IWOP) of operators, rather than via solving a Bloch equation. Because the quadratic homogeneity of potential energy is broken due to the existence of SEF, the virial theorem in statistical physics is not satisfactory for this system, which is confirmed through the calculation of thermal averages of physical quantities.
Received: 28 November 2005
Revised: 19 January 2006
Accepted manuscript online:
(Quantum computation architectures and implementations)
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 60374037 and
60574036), the Program for New Century Excellent Talents of High
Education of China(Grant No NCET 2005-290), The Special Research
Fund for the Doctoral Program of High Education of China (Grant No
20050055013).
Cite this article:
Pang Qian-Jun(庞乾骏) Density matrix for an electron confined in quantum dots under uniform magnetic field and static electrical field 2007 Chinese Physics 16 16
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