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The Schrodinger-like Equation for a Nonrelativistic Electron in a Photon Field of Arbitrary Intensity
The ordinary Schrodinger equation with minimal coupling for a nonrelativistic
electron interacting with a single-mode photon field is not satisfied by the
nonrelativistic limit of the exact solutions to the corresponding Dirac
equation. A Schrodinger-like equation valid for arbitrary photon intensity is
derived from the Dirac equation without the weak-field assumption. The
"eigenvalue" in the new equation is an operator in a Cartan subalgebra. An
approximation consistent with the nonrelativistic energy level derived from its
relativistic value replaces the "eigenvalue" operator by an ordinary number,
recovering the ordinary Schrodinger eigenvalue equation used in the formal
scattering formalism. The Schrodinger-like equation for the multimode case is
also presented.Comment: Tex file, 13 pages, no figur
Snyder's Quantized Space-time and De Sitter Special Relativity
There is a one-to-one correspondence between Snyder's model in de Sitter
space of momenta and the \dS-invariant special relativity. This indicates that
physics at the Planck length and the scale should be
dual to each other and there is in-between gravity of local \dS-invariance
characterized by a dimensionless coupling constant .Comment: 8 page
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A Body-Nonlinear Green's Function Method with Viscous Dissipation Effects for Large-Amplitude Roll of Floating Bodies
A novel time-domain body-nonlinear Greenâs function method is developed for evaluating large-amplitude roll damping of two-dimensional floating bodies with consideration of viscous dissipation effects. In the method, the instantaneous wetted surface of floating bodies is accurately considered, and the viscous dissipation effects are taken into account based on the âfairly perfect fluidâ model. As compared to the method based on the existing inviscid body-nonlinear Greenâs function, the newly proposed method can give a more accurate damping coefficient of floating bodies rolling on the free surface with large amplitudes according to the numerical tests and comparison with experimental data for a few cases related to ship hull sections with bilge keels
Non-Arrhenius modes in the relaxation of model proteins
We have investigated the relaxational dynamics for a protein model at various
temperatures. Theoretical analysis of this model in conjunction with numerical
simulations suggests several relaxation regimes, including a single
exponential, a power law and a logarithmic time dependence. Even though a
stretched exponential form gives a good fit to the simulation results in the
crossover regime between a single exponential and a power law decay, we have
not been able to directly deduce this form from the theoretical analysis.Comment: 5 figures, 12 page
Three Kinds of Special Relativity via Inverse Wick Rotation
Since the special relativity can be viewed as the physics in an inverse Wick
rotation of 4-d Euclid space, which is at almost equal footing with the 4-d
Riemann/Lobachevski space, there should be important physics in the inverse
Wick rotation of 4-d Riemann/Lobachevski space. Thus, there are three kinds of
special relativity in de Sitter/Minkowski/anti-de Sitter space at almost equal
footing, respectively. There is an instanton tunnelling scenario in the
Riemann-de Sitter case that may explain why \La be positive and link with the
multiverse.Comment: 3 pages, no figures, to appear in Chin. Phys. Let
The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction
The renormalisation group approach is applied to the study of the short-time
critical behaviour of the -dimensional Ginzburg-Landau model with long-range
interaction of the form in momentum space. Firstly the
system is quenched from a high temperature to the critical temperature and then
relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws
and the initial slip exponents and of the order
parameter and the response function respectively, are calculated to the second
order in .Comment: 18 pages, 4 figures, 1 tabl
Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System
We study the Hilbert expansion for small Knudsen number for the
Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term
takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi
\theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\
}\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).t=0u_00\leq t\leq \varepsilon
^{-{1/2}\frac{2k-3}{2k-2}},\rho_{0}(t,x) u_{0}(t,x)\gamma=5/3$
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