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in a dielectric nanowire in low temperature range [48]. They
showed that the presence of rough surface significantly decreases
the thermal conductance below the quantum value. Chen et al.
studied the influence of defects on the low temperature thermal
conductancecontributedfromseverallowesthorizontallypolarized
shear (SH) modes in the nanowire by using the scattering-matrix
method, and found an obvious decrease of the lattice thermal
conductance in the defective nanowires [51]. More recently, Peng
et al. calculated the thermal conductance associated with the
lowest six types ballistic phonon modes in quantum wire with
catenoidal contacts [54], and observed the destruction of the
quantum thermal conductance plateau and a decrease of thermal
conductance appeared in such a structure when the temperature is
su cientlylow.Inaddition,thedecreaseofthethermalconductance
was also analyzed in other quantum waveguide, such as stub
structures [55, 56], T-shaped quantum wires [57, 58], double-bend
nanowires [59, 60], and so on. From these results, one knows
that these inhomogeneities actually act as the thermal resistance,
which leads to decrease the phonon thermal conductance, and such
thermal resistance sensitively depends on the intrinsic properties
and sizesof configurations[55-61].
In spite of all these advancements mentioned above, a further
understanding of the ballistic thermal transport by phonons
remains to be important for both foundational significance and
applications in many nanodevices. Recently, Wang et al. presented
a review of the methods for thermal-transport calculations for
nanojunctions connected to two heat reservoirs [62], in which their
emphasis is on fundamental quantum theory and atomistic models.
Based on the single-particle scattering approach, non-equilibrium
Green's function formalism, molecular dynamics, etc., Dubi et al.
systematically review the thermal conductance, local temperature
and heating, and thermoelectricity in nanoscale systems, such as
molecularjunctions,suspendednanotubes,quantumpointcontacts,
and so on [63]. Similar to electrons, it is proved that phonons can
be put to beneficial use, such as to carry and process information.
In a recent colloquium, Li et al. discuss in detail the manipulation
of thermal flow on the nanoscale and the task of processing
information by utilizing phonons, and particularly focus on the
 
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