15,381 research outputs found
Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
We clearly refine the fundamental framework of the thin-layer quantization
procedure, and further develop the procedure by taking the proper terms of
degree one in ( denotes the curvilinear coordinate variable
perpendicular to curved surface) back into the surface quantum equation. The
well-known geometric potential and kinetic term are modified by the surface
thickness. Applying the developed formalism to a toroidal system obtains the
modification for the kinetic term and the modified geometric potential
including the influence of the surface thickness.Comment: 9 pages, 3 figure
Algebraic Characterizations of Consensus Problems for Networked Dynamic Systems
In this paper, we study the consensus problem for networked dynamic systems
with arbitrary initial states, and present some structural characterization and
direct construction of consensus functions. For the consensus problem under
similar transformation, we establish some necessary and sufficient conditions
by exploiting the structure of consensus functions. Finally, we discuss the
consensus problem for dynamic systems under switching by using the common
Lyapunov function method
A two-level atom coupled to a controllable squeezed vacuum field reservoir
The dissipative and decoherence properties of the two-level atom interacting
with the squeezed vacuum field reservoir are investigated based on the
nonautonomous master equation of the atomic density matrix in the framework of
algebraic dynamics. The nonautonomous master equation is converted into a
Schr\"{o}dinger-like equations and its dynamical symmetry is found based on the
left and right representations of the relevant algebra. The time-dependent
solution and the steady solution are obtained analytically. The asymptotic
behavior of the solution is examined and the approach to the equilibrium state
is proved. Based on the analytic solution the response of the system to the
squeezed vacuum field reservoir is studied numerically.Comment: 8 pages, 6 figure
What can We Learn from Triple Top-Quark Production?
Different from other multiple top-quark productions, triple top-quark
production requires the presence of both flavor violating neutral interaction
and flavor conserving neutral interaction. We describe the interaction of
triple top-quarks and up-quark in terms of two dimension-6 operators; one can
be induced by a new heavy vector resonance, the other by a scalar resonance.
Combining same-sign top-quark pair production and four top-quark production, we
explore the potential of the 13 TeV LHC on searching for the triple top-quark
production
Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
Investigating the geometric effects resulting from the detailed behaviors of
the confining potential, we consider square and circular confinements to
constrain a particle to a space curve. We find a torsion-induced geometric
potential and a curvature-induced geometric momentum just in the square case,
while a geometric gauge potential solely in the circular case. In the presence
of electromagnetic field, a geometrically induced magnetic moment couples with
magnetic field as an induced Zeeman coupling only for the circular confinement,
also. As spin-orbit interaction is considered, we find some additional terms
for the spin-orbit coupling, which are induced not only by torsion, but also
curvature. Moreover, in the circular case, the spin also couples with an
intrinsic angular momentum, which describes the azimuthal motions mapped on the
space curve. As an important conclusion for the thin-layer quantization
approach, some substantial geometric effects result from the confinement
boundaries. Finally, these results are proved on a helical wire.Comment: 7 pages, 2 figure
Coherent electron transport in a helical nanotube
The quantum dynamics of carriers bound to helical tube surfaces is
investigated in a thin-layer quantization scheme. By numerically solving the
open-boundary Schrdinger equation in curvilinear coordinates,
geometric effect on the coherent transmission spectra is analysed in the case
of single propagating mode as well as multimode. It is shown that, the coiling
endows the helical nanotube with different transport properties from a bent
cylindrical surface. Fano resonance appears as a purely geometric effect in the
conductance, the corresponding energy of quasibound state is obviously
influenced by the torsion and length of the nanotube. We also find new plateaus
in the conductance. The transport of double-degenerate mode in this geometry is
reminiscent of the Zeeman coupling between the magnetic field and spin angular
momentum in quasi-one-dimensional structure.Comment: 11 pages, 9 figure
Characterizing vortex beam with angular-double-slit interference
The Fraunhofer diffraction intensity distribution of Laguerre-Gaussian beam
is studied in an angular-double-slit interferometer. We demonstrate that the
spiral phase structure of vortex light can be clearly revealed in this
interference geometry, and it gives us an efficient way to distinguish
different order of Laguerre-Gaussian beams. This angular-double-slit
interference gives us a better understanding to the nature of orbital angular
momentum and the interpretation of vortex beams interference phenomenon.Comment: 4 pages, 5 figure
Electromagnetic wave propagating along a space curve
Using the thin-layer approach, we derive the effective equation for the
electromagnetic wave propagating along a space curve. We find intrinsic
spin-orbit, extrinsic spin-orbit and extrinsic orbital angular momentum and
intrinsic orbital angular momentum couplings induced by torsion, which can lead
to geometric phase, spin and orbital Hall effects. And we show the helicity
inversion induced by curvature that can convert the right-handed circularly
polarized electromagnetic wave into left-handed polarized one, vice verse.
Finally, we demonstrate that the gauge invariance of the effective dynamics is
protected by the geometrically induced gauge potential
Evaluating Laguerre-Gaussian beams with an invariant parameter
We define a new parameter about Laguerre-Gaussian (LG) beams, named
, which is only related to mode indices and . This parameter
is able to both evaluate and distinguish LG beams. The values are
first calculated theoretically and then measured experimentally for several
different LG beams. Another mode quality parameter, value, is also
measured. The comparison between and shows same trend for
the quality of LG mode, while the measurement of is much easier
than .Comment: 3.1 pages, 4 figures, 1 tabl
Curvature-induced bound states and coherent electron transport on the surface of a truncated cone
We study the curvature-induced bound states and the coherent transport
properties for a particle constrained to move on a truncated cone-like surface.
With longitudinal hard wall boundary condition, the probability densities and
spectra energy shifts are calculated, and are found to be obviously affected by
the surface curvature. The bound-state energy levels and energy differences
decrease as increasing the vertex angle or the ratio of axial length to bottom
radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with
this geometric structure, an estimation of the ground-state energy shift of
ballistic transport electrons induced by the geometric potential (GP) is
addressed, which shows that the fraction of the ground-state energy shift
resulting from the surface curvature is unnegligible under some region of
geometric parameters. Furthermore, we model a truncated cone-like junction
joining two cylinders with different radii, and investigate the effect of the
GP on the transmission properties by numerically solving the open-boundary 2D
Schr\"odinger equation with GP on the junction surface. It is shown that the
oscillatory behavior of the transmission coefficient as a function of the
injection energy is more pronounced when steeper GP wells appear at the two
ends of the junction. Moreover, at specific injection energy, the transmission
coefficient is oscillating with the ratio of the cylinder radii at incoming and
outgoing sides.Comment: 8pages, 9figure
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