Dirac Equation at Finite Temperature

In this paper, we propose finite temperature Dirac equation, which can describe the quantum systems in an arbitrary temperature for a relativistic particle of spin-1/2. When the temperature T=0, it become Dirac equation. With the equation, we can study the relativistic quantum systems in an arbitrary temperature.     

Quasi-Periodic Solutions for Two-Level Systems

We consider the Schrödinger equation for a class of two-level atoms in a quasi-periodic external field in the case in which the spacing 2 between the two unperturbed energy levels is small, and we study the problem of finding quasi-periodic solutions of a related generalized Riccati equation. We prove the existence of quasi-periodic solutions of the latter equation for a Cantor set of values of around the origin which is of positive Lebesgue measure: such solutions can be obtained from the formal power series by a suitable resummation procedure. The set can be characterized by requesting infinitely many Diophantine conditions of Melnikov type.     

Properties of Proton Transfer in Hydrogen-Bonded Systems at Finite Temperature

The properties of proton transfer along hydrogen-bonded molecular systems are studied at finite temperature. The dynamic equations of the proton transport along the systems are obtained by using a completely quantum mechanics method. From the dynamic equations and its soliton solutions we find out specific heat arising from the motion of solitons in the systems with finite temperature and the critical temperature of the soliton in the protein molecules, which is about 318 K. This shows that we can continuously study some biological phenomena in the living systems by this model.     

Properties of Proton Transfer in Hydrogen-Bonded Systems at Finite Temperature

The properties of proton transfer along hydrogen-bonded molecular systems are studied at finite temperature. The dynamic equations of the proton transport along the systems are obtained by using a completely quantummechanics method. From the dynamic equations and its soliton solutions we find out specific heat arising from the motionof solitons in the systems with finite temperature and the critical temperature of the soliton in the protein molecules,which is about 318 K. This shows that we can continuously study some biological phenomena in the living systems bythis model.     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature

In this paper, using path integral techniques we derive a model-independent formula for the pressure density P（μ, T） （or equivalently the partition function） of Quantum Chromodynamics （QCD）, which gives the equation of state （EOS） of QCD at finite chemical potential and temperature. In this formula the pressure density P（μ, T） consists of two terms： the first term （p（μ, T）｜T=0） is a μ-independent （but T-dependent） constant; the second term is totally determined by G[μ, T]（p, ωn） （the dressed quark propagator at finite μ and finite T）, which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson-Schwinger （DS） approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ, T]（p,ωn） can be obtained from G[T]（p,ωn ） （the dressed quark propagator at μ= 0） by the substitution ωn →ωn ＋ iμ. This result facilitates numerical calculations considerably. By this result, once C [T] （p, ωn） is known, one can determine the EOS of QCD under the above approximations （up to the additive term p（μ, T）｜T=0）. Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation ρ（μ,T） =δp（μ,T）/δμ｜T.     

Bounds for Kac's Master Equation

Mark Kac considered a Markov Chain on the n-sphere based on random rotations in randomly chosen coordinate planes. This same walk was used by Hastings on the orthogonal group. We show that the walk has spectral gap bounded below by c/n ³. This and curvature information are used to bound the rate of convergence to stationarity. Received: 26 April 1999 / Accepted: 30 August 1999     

Geometric Phase for High-Temperature Master Equation

Geometric phase of mixed state is investigated for three-level system obeying a high-temperature master equation. The results show the Berry phase of mixed phase is strongly dependent on the initial condition. For the different initial angle, the turning region is different. In addition, the decrease of Berry phase is most slow around the coupling strength α=5 with an increasing of evolving time.     

Optimal Control for Quantum Driving of Two-Level Systems

In this paper, the optimal quantum control of two-level systems is studied by the decompositions of SU(2). Using the Pontryagin maximum principle, the minimum time of quantum control is analyzed in detail. The solution scheme of the optimal control function is given in the general case. Finally, two specific cases, which can be applied in many quantum systems, are used to illustrate the scheme, while the corresponding optimal control functions are obtained.     

有限温度下的Casimir效应

利用路径积分量子化方法,计算出两个平行的、理想的金属板之间,在有限温度下自由的量子电磁场和内部费米子单圈图对Casimir力的贡献.     

Ward-Takahashi Identity at Finite Temperature

A new real time formalism, based on the closed-time-path Green's function theory (CTPGF),is employed to obtain Ward-llfrkahashi identities of QED at finite temperature. It is shown that WT identity in coordinate space is of the same covariant form aa that in vacuum field theory. A perturbative check is provided to #how that in momentum spze, Takahashi's iden tities hold only in a weak sense.     

Weak-Coupling Theory for Low-Frequency Periodically Driven Two-Level Systems

We generalize the Wu-Yang strong-coupling theory to solve analytically periodically driven two-level systems in the weak-coupling and low-frequency regimes for single- and multi-period periodic driving of continuous-wave-type and pulse-type including ultrashort pulses of a few cycles. We also derive a general formula of the AC Stark shift suitable for such diverse situations.     

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$. These methods we studied provide an approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods can save a large amount of computational time.     

The Number of Master Integrals is Finite

For a fixed Feynman graph one can consider Feynman integrals with all possible powers of propagators and try to reduce them, by linear relations, to a finite subset of integrals, the so-called master integrals. Up to now, there are numerous examples of reduction procedures resulting in a finite number of master integrals for various families of Feynman integrals. However, up to now it was just an empirical fact that the reduction procedure results in a finite number of irreducible integrals. It this paper we prove that the number of master integrals is always finite.     

A Model Study of Equation of State of QCD at Finite Chemical Potential and Zero Temperature

In this paper, we give a direct method for calculating the partition function, and hence the equation of state （EOS） of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms： the first term P（μ）｜μ=0 （the pressure density at μ = 0） is a μ-independent constant; the second term, which is totally determined by G[μ] （p） （the dressed quark propagator at finite μ）, contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71 （2005） 015205], G[μ]（p） is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 67 （2003） 054019]. From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained （apart from the constant term P（μ）｜μ=0, which can in principle be caJculated from the CJT effective action）. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.     

Chiral Bag Model at Finite Temperature

By taking the thermodynamical contributions of the pion mesons cloud outside the bag into account,the chiral bag model is extended to finite temperature.The temperature dependence of the radius of the chiral bag and the critical temperature of quark deconfinement are given.     

Non-relativistic Quantum Theory at Finite Temperature

We propose the non-relativistic finite temperature quantum wave equations for a single particle and multiple particles. We give the relation between energy eigenvalues, eigenfunctions, transition frequency and temperature, and obtain some results: (1) when the degeneracies of two energy levels are same, the transition frequency between the two energy levels is unchanged when the temperature is changed. (2) When the degeneracies of two energy levels are different, the variance of transition frequency at two energy levels is direct proportion to temperature difference.