Statistical problem of ideal gas in general 2-dimensional regions

In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general 2-dimensional regions. We consider some examples and the numerical results and fitting results are given. We also give the thermodynamic quantities of the general 2-dimensional regions, and compare the thermodynamic quantities of the different regions.Comment: 16 pages, 10 figures, 3 table

Experimental implementation of high-fidelity unconventional geometric quantum gates using NMR interferometer

Following a key idea of unconventional geometric quantum computation developed earlier [Phys. Rev. Lett. 91, 197902 (2003)], here we propose a more general scheme in such an intriguing way: $\gamma_{d}=\alpha_{g}+\eta \gamma _{g}$, where $\gamma_{d}$ and $\gamma_{g}$ are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with $\eta$ as a constant and $\alpha_{g}$ being dependent only on the geometric feature of the operation. More arrestingly, we demonstrate the first experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.Comment: 4 pages, 3 figure

Probability Thermodynamics and Probability Quantum Field

In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented

Discovering New Gauge Bosons of Electroweak Symmetry Breaking at LHC-8

We study the physics potential of the 8TeV LHC (LHC-8) to discover, during its 2012 run, a large class of extended gauge models or extra dimensional models whose low energy behavior is well represented by an SU(2)^2 x U(1) gauge structure. We analyze this class of models and find that with a combined integrated luminosity of 40-60/fb at the LHC-8, the first new Kaluza-Klein mode of the W gauge boson can be discovered up to a mass of about 370-400 GeV, when produced in association with a Z boson.Comment: PRD final version (only minor refinements showing the consistency with new LHC data), 11 pages, 5 Figs, 2 Table