6,930 research outputs found
Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number
We present numerical simulations of three-dimensional thermal convective
flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann
(LB) method. The thermal LB model is based on double distribution function
approach, which consists of a D3Q19 model for the Navier-Stokes equations to
simulate fluid flows and a D3Q7 model for the convection-diffusion equation to
simulate heat transfer. Relaxation parameters are adjusted to achieve the
isotropy of the fourth-order error term in the thermal LB model. Two types of
thermal convective flows are considered: one is laminar thermal convection in
side-heated convection cell, which is heated from one vertical side and cooled
from the other vertical side; while the other is turbulent thermal convection
in Rayleigh-B\'enard convection cell, which is heated from the bottom and
cooled from the top. In side-heated convection cell, steady results of
hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers
of and , and Prandtl number of 0.71, where the mesh sizes are up
to ; in Rayleigh-B\'enard convection cell, statistical averaged results
of Reynolds and Nusselt numbers, as well as kinetic and thermal energy
dissipation rates are presented at Rayleigh numbers of , ,
and , and Prandtl numbers of 0.7 and 7, where the nodes within thermal
boundary layer are around 8. Compared with existing benchmark data obtained by
other methods, the present LB model can give consistent results.Comment: 33 pages, 8 figure
Approximated seventh order calculation of vacuum wave function of 2+1 dimensional SU(2) lattice gauge theory
Using the coupled cluster expansion with the random phase approximation, we
calculate the long wavelength vacuum wave function and the vacuum energy of 2+1
dimensional Hamiltonian SU(2) lattice gauge theory (LGT) up to the seventh
order. The coefficients , of the vacuum wave function show good
scaling behavior and convergence in high order calculations
Revisiting 1-Dimensional Double-Barrier Tunneling in Quantum Mechanics
This paper revisited quantum tunneling dynamics through a square
double-barrier potential. We emphasized the similarity of tunneling dynamics
through double-barrier and that of optical Fabry--Prot (FP)
interferometer. Based on this similarity, we showed that the well-known
resonant tunneling can also be interpreted as a result of matter multi-wave
interference, analogous to that of FP interferometer. From this analogy, we
also got an analytical finesse formula of double-barrier. Compared with that
obtained numerically for a specific barrier configuration, we found that this
formula works well for resonances at "deep tunneling region". Besides that, we
also calculated standing wave spectrum inside the well of double barriers and
phase time of double-barrier tunneling. The wave number spectrums of standing
wave and phase time show another points of view on resonance. From
semi-numerical calculations, we interpreted the peak of phase time at resonance
as resonance life time, which coincides at least in order of magnitude with
that obtained from uncertainty principle. Not to our surprise, phase time of
double-barrier tunneling also saturates at long barrier length limit
as that of tunneling through a single barrier, and the
limits are the same.Comment: 14 pages, 18 figure
Prediction of interface states in liquid surface waves with one-dimensional modulation
We theoretically studied the interface states of liquid surface waves
propagating through the heterojunctions formed by a bottom with one-dimensional
periodic undulations. Via considering the periodic structure as a homogeneous
one, our systematic study shows that the signs of the effective depth and
gravitational acceleration are opposite within the band gaps no matter the
structure is symmetric or asymmetric. Those effective parameters can be used to
predict the interface states which could amplify the amplitudes of liquid
surface waves. These phenomena provide new opportunities to control the
localization of water-wave energy.Comment: 5 pages, 4 figure
On Quantum Entanglement in Topological Phases on a Torus
In this paper we study the effect of non-trivial spatial topology on quantum
entanglement by examining the degenerate ground states of a topologically
ordered system on torus. Using the string-net (fixed-point) wave-function, we
propose a general formula of the reduced density matrix when the system is
partitioned into two cylinders. The cylindrical topology of the subsystems
makes a significant difference in regard to entanglement: a global quantum
number for the many-body states comes into play, together with a decomposition
matrix which describes how topological charges of the ground states
decompose into boundary degrees of freedom. We obtain a general formula for
entanglement entropy and generalize the concept of minimally entangled states
to minimally entangled sectors. Concrete examples are demonstrated with data
from both finite groups and modular tensor categories (i.e., Fibonacci, Ising,
etc.), supported by numerical verification.Comment: v2. more references added; v3: submitted versio
Irreducible bases in icosahedral group space
The irreducible bases in the icosahedral group space are calculated
explicitly by reducing the regular representation. The symmetry adapted bases
of the system with {\bf I} or {\bf I} symmetry can be calculated easily
and generally by applying those irreducible bases to wavefunctions of the
system, if they are not vanishing. As examples, the submatrices of the
H\"{u}ckel Hamiltonians for Carbon-60 and Carbon-240 are re-calculated by the
irreducible bases.Comment: Revtex 16 page
Correlations of spin states for icosahedral double group
The irreducible bases of the group space of the icosahedral double groups
{\bf I'} and {\bf I} are calculated explicitly. Applying those bases on
the spin states , we present a simple formula to combine the spin
states into the symmetrical adapted bases, belonging to a given row of a given
irreducible representations of {\bf I'} and {\bf I}.Comment: latex file 11 pages, send the figure to person who wants to need,
submitted to Chemical Phys. Lette
Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
Based on the tensor network state representation, we develop a nonlinear
dynamic theory coined as network contractor dynamics (NCD) to explore the
thermodynamic properties of two-dimensional quantum lattice models. By invoking
the rank- decomposition in the multi-linear algebra, the NCD scheme makes
the contraction of the tensor network of the partition function be realized
through a contraction of a local tensor cluster with vectors on its boundary.
An imaginary-time-sweep algorithm for implementation of the NCD method is
proposed for practical numerical simulations. We benchmark the NCD scheme on
the square Ising model, which shows a great accuracy. Besides, the results on
the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice are disclosed in
good agreement with the quantum Monte Carlo calculations. The
quasi-entanglement entropy , Lyapunov exponent and loop character
are introduced within the dynamic scheme, which are found to display
the ``nonlocality" near the critical point, and can be applied to determine the
thermodynamic phase transitions of both classical and quantum systems.Comment: 8 pages, 9 figure
Electromagnetic Response for High-Frequency Gravitational Waves in the GHz to THz Band
We consider the electromagnetic (EM) response of a Gaussian beam passing
through a static magnetic field to be the high-frequency gravitational waves
(HFGW) as generated by several devices discussed at this conference. It is
found that under the synchroresonance condition, the first-order perturbative
EM power fluxes will contain a ''left circular wave'' and a ''right circular
wave'' around the symmetrical axis of the Gaussian beam. However, the
perturbative effects produced by the states of + polarization and \times
polarization of the GW have a different physical behavior. For the HFGW of
, (which corresponds to the power flux density ) to , (which corresponds to the
power flux density ) expected by the HFGW generators
described at this conference, the corresponding perturbative photon fluxes
passing through a surface region of would be expected to be
. They are the orders of magnitude of the
perturbative photon flux we estimated using typical laboratory parameters that
could lead to the development of sensitive HFGW receivers. Moreover, we will
also discuss the relative background noise problems and the possibility of
displaying the HFGW. A laboratory test bed for juxtaposed HFGW generators and
our detecting scheme is explored and discussed.Comment: 19 pages, 3 figure
Irreducible bases and correlations of spin states for double point groups
In terms of the irreducible bases of the group space of the octahedral double
group {\bf O'}, an analytic formula is obtained to combine the spin states
into the symmetrical adapted bases, belonging to a given row
of a given irreducible representation of {\bf O'}. This method is effective for
all double point groups. However, for the subgroups of {\bf O'}, there is
another way to obtain those combinations. As an example, the correlations of
spin states for the tetrahedral double group {\bf T'} are calculated
explicitly.Comment: Latex file 16 pages,no figur
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