3,076 research outputs found
Classical Aspects of Quantum Walls in One Dimension
We investigate the system of a particle moving on a half line x >= 0 under
the general walls at x = 0 that are permitted quantum mechanically. These
quantum walls, characterized by a parameter L, are shown to be realized as a
limit of regularized potentials. We then study the classical aspects of the
quantum walls, by seeking a classical counterpart which admits the same time
delay in scattering with the quantum wall, and also by examining the
WKB-exactness of the transition kernel based on the regularized potentials. It
is shown that no classical counterpart exists for walls with L < 0, and that
the WKB-exactness can hold only for L = 0 and L = infinity.Comment: TeX, 21 pages, 4 figures. v2: some parts of the text improved, new
and improved figure
Theory of RIXS in strongly correlated electron systems: Mott gap excitations in cuprates
We theoretically examine the momentum dependence of resonant inelastic x-ray
scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates
based on the single-band Hubbard model with realistic parameter values. The
spectrum is calculated by using the numerical diagonalization technique for
finite-size clusters. We focus on excitations across the Mott gap and clarify
spectral features coming from the excitations as well as the physics behind
them. Good agreement between the theoretical and existing experimental results
clearly demonstrates that the RIXS is a potential tool to study the
momentum-dependent charge excitations in strongly correlated electron systems.Comment: 9 pages, 8 figures, Proceedings of 5th International Conference on
Inelastic X-ray Scattering (IXS 2004
Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
The Schroedinger operator with point interaction in one dimension has a U(2)
family of self-adjoint extensions. We study the spectrum of the operator and
show that (i) the spectrum is uniquely determined by the eigenvalues of the
matrix U belonging to U(2) that characterizes the extension, and that (ii) the
space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius
strip with boundary. We employ a parametrization of U(2) that admits a direct
physical interpretation and furnishes a coherent framework to realize the
spectral duality and anholonomy recently found. This allows us to find that
(iii) physically distinct point interactions form a three-parameter quotient
space of the U(2) family.Comment: 16 pages, 2 figure
Quantum contact interactions
The existence of several exotic phenomena, such as duality and spectral
anholonomy is pointed out in one-dimensional quantum wire with a single defect.
The topological structure in the spectral space which is behind these phenomena
is identified.Comment: A lecture presented at the 2nd Winter Institute on Foundations of
Quantum Theory and Quantum Optics (WINST02), Jan. 2-11, 2002, S.N.Bose
Institute, Calcutta, India: 8 pages latex with Indian Acad. Sci. style fil
Exact diagonalization study of optical conductivity in two-dimensional Hubbard model
The optical conductivity \sigma(\omega) in the two-dimensional Hubbard model
is examined by applying the exact diagonalization technique to small square
clusters with periodic boundary conditions up to \sqrt{20} X \sqrt{20} sites.
Spectral-weight distributions at half filling and their doping dependence in
the 20-site cluster are found to be similar to those in a \sqrt{18} X \sqrt{18}
cluster, but different from 4 X 4 results. The results for the 20-site cluster
enable us to perform a systematic study of the doping dependence of the
spectral-weight transfer from the region of the Mott-gap excitation to
lower-energy regions. We discuss the dependence of the Drude weight and the
effective carrier number on the electron density at a large on-site Coulomb
interaction.Comment: 5 pages, 5 figure
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