4,228 research outputs found
Mean-field approximation for the chiral soliton in a chiral phase transition
In the mean-field approximation we study the chiral soliton within the linear
sigma model in a thermal vacuum. The chiral soliton equations with different
boundary conditions are solved at finite temperatures and densities. The
solitons are discussed before and after the chiral restoration. We find that
the system has soliton solutions even after the chiral restoration and they are
very different from those before the chiral restoration, which indicates that
the quarks are still bounded after the chiral restoration.Comment: 9 pages, 11 figures. Some sentences and words have been correcte
Oblique Klein tunneling in 8-Pmmn borophene p-n junctions
The 8-\textit{Pmmn} borophene is one kind of new elemental monolayer, which
hosts anisotropic and tilted massless Dirac fermions (MDF). The planar
\textit{p-n} junction (PNJ) structure as the basic component of various novel
devices based on the monolayer material has attracted increasing attention.
Here, we analytically study the transport properties of anisotropic and tilted
MDF across 8-\textit{Pmmn} borophene PNJ. Similar to the isotropic MDF across
graphene junctions, perfect transmission exists but its direction departures
the normal direction of borophene PNJ induced by the anisotropy and tilt, i.e.,
oblique Klein tunneling. The oblique Klein tunneling does not depend on the
doping levels in \textit{N} and \textit{P} regions of PNJ as the normal Klein
tunneling but depends on the junction direction. Furthermore, we analytically
derive the special junction direction for the maximal difference between
perfect transmission direction and the normal direction of PNJ and clearly
distinguish the respective contribution of anisotropy and tilt underlying the
oblique Klein tunneling. In light of the rapid advances of experimental
technologies, we expect the oblique Klein tunneling to be observable in the
near future.Comment: 7 pages, 3 figure
Space-filling curves of self-similar sets (I): Iterated function systems with order structure
This paper is the first paper of three papers in a series, which intend to
provide a systematic treatment for the space-filling curves of self-similar
sets.
In the present paper, we introduce a notion of \emph{linear graph-directed
IFS} (linear GIFS in short). We show that to construct a space-filling curve of
a self-similar set, it is amount to explore its linear GIFS structures. Some
other notions, such as chain condition, path-on-lattice IFS, and visualizations
of space-filling curves are also concerned.
In sequential papers \cite{Dai15} and \cite{RZ14}, we obtain a universal
algorithm to construct space-filling curves of self-similar sets of finite
type, that is, as soon as the IFS is given, the computer will do everything
automatically.
Our study extends almost all the known results on space-filling curves.Comment: 24 pages, 14 figure
Space-filling curves of self-similar sets (III): Skeletons
Skeleton is a new notion designed for constructing space-filling curves of
self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of
self-similar sets (II): Edge-to-trail substitution
rule,https://doi.org/10.1088/1361-6544/ab1275] that for a connected
self-similar set, space-filling curves can be constructed provided that it
possesses a skeleton. In this paper, we give a criterion of existence of
skeletons by using the so-called neighbor graph of a self-similar set. In
particular, we show that a connected self-similar set satisfying the finite
type condition always possesses skeletons: an algorithm is obtained here
Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions
We develop an analytical mode-matching technique for the tight-binding model
to describe electron transport across graphene P-N junctions. This method
shares the simplicity of the conventional mode-matching technique for the
low-energy continuum model and the accuracy of the tight-binding model over a
wide range of energies. It further reveals an interesting phenomenon on a sharp
P-N junction: the disappearance of the well-known Klein tunneling (i.e.,
perfect transmission) at normal incidence and the appearance of perfect
transmission at oblique incidence due to trigonal warping at energies beyond
the linear Dirac regime. We show that this phenomenon arises from the
conservation of a generalized pseudospin in the tight-binding model. We expect
this effect to be experimentally observable in graphene and other Dirac
fermions systems, such as the surface of three-dimensional topological
insulators.Comment: 11 pages, 11 figure
The baryon mass calculation in the chiral soliton model at finite temperature and density
In the mean-field approximation, we have studied the soliton which is
embedded in a thermal medium within the chiral soliton model. The energy of the
soliton or the baryon mass in the thermal medium has been carefully evaluated,
in which we emphasize that the thermal effective potential in the soliton
energy should be properly treated in order to derive a finite and well-defined
baryon mass out of the thermal background. The result of the baryon mass at
finite temperatures and densities in chiral soliton model are clearly
presented.Comment: 7 pages, 4 figures, 1 tabl
Velocity-determined anisotropic behaviors of RKKY interaction in 8-\textit{Pmmn} borophene
As a new two-dimensional Dirac material, 8-\textit{Pmmn} borophene hosts
novel anisotropic and tilted massless Dirac fermions (MDFs) and has attracted
increasing interest. However, the potential application of 8-\textit{Pmmn}
borophene in spin fields has not been explored. Here, we study the long-range
RKKY interaction mediated by anisotropic and tilted MDFs in magnetically-doped
8-\textit{Pmmn} borophene. To this aim, we carefully analyze the unique
real-space propagation of anisotropic and tilted MDFs with noncolinear momenta
and group velocities. As a result, we analytically demonstrate the anisotropic
behaviors of long-range RKKY interaction, which have no dependence on the Fermi
level but are velocity-determined, i.e., the anisotropy degrees of oscillation
period and envelop amplitude are determined by the anisotropic and tilted
velocities. The velocity-determined RKKY interaction favors to fully determine
the characteristic velocities of anisotropic and tilted MDFs through its
measurement, and has high tunability by engineering velocities shedding light
on the application of 8-\textit{Pmmn} borophene in spin fields.Comment: 8 pages, 5 figure
Deep Learning for Sequential Recommendation: Algorithms, Influential Factors, and Evaluations
In the field of sequential recommendation, deep learning (DL)-based methods
have received a lot of attention in the past few years and surpassed
traditional models such as Markov chain-based and factorization-based ones.
However, there is little systematic study on DL-based methods, especially
regarding to how to design an effective DL model for sequential recommendation.
In this view, this survey focuses on DL-based sequential recommender systems by
taking the aforementioned issues into consideration. Specifically,we illustrate
the concept of sequential recommendation, propose a categorization of existing
algorithms in terms of three types of behavioral sequence, summarize the key
factors affecting the performance of DL-based models, and conduct corresponding
evaluations to demonstrate the effects of these factors. We conclude this
survey by systematically outlining future directions and challenges in this
field.Comment: 36 pages, 17 figures, 6 tables, 104 reference
Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule
It is well-known that the constructions of space-filling curves depend on
certain substitution rules. For a given self-similar set, finding such rules is
somehow mysterious, and it is the main concern of the present paper. Our first
idea is to introduce the notion of skeleton for a self-similar set. Then, from
a skeleton, we construct several graphs, define edge-to-trail substitution
rules, and explore conditions ensuring the rules lead to space-filling curves.
Thirdly, we summarize the classical constructions of the space-filling curves
into two classes: the traveling-trail class and the positive Euler-tour class.
Finally, we propose a general Euler-tour method, using which we show that if a
self-similar set satisfies the open set condition and possesses a skeleton,
then space-filling curves can be constructed. Especially, all connected
self-similar sets of finite type fall into this class. Our study actually
provides an algorithm to construct space-filling curves of self-similar sets.Comment: 44 pages, 16 figure
Helical damping and anomalous critical non-Hermitian skin effect
Non-Hermitian skin effect and critical skin effect are unique features of
non-Hermitian systems. In this Letter, we study an open system with its
dynamics of single-particle correlation function effectively dominated by a
non-Hermitian damping matrix, which exhibits skin effect, and
uncover the existence of a novel phenomenon of helical damping. When adding
perturbations that break anomalous time reversal symmetry to the system, the
critical skin effect occurs, which causes the disappearance of the helical
damping in the thermodynamic limit although it can exist in small size systems.
We also demonstrate the existence of anomalous critical skin effect when we
couple two identical systems with skin effect. With the help of
non-Bloch band theory, we unveil that the change of generalized Brillouin zone
equation is the necessary condition of critical skin effect.Comment: 7+5 pages, 4+5 figure
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