Finite temperature spectral function of the σ meson from large <Emphasis Type="Italic">N</Emphasis> expansion

The spectral function of the scalar-isoscalar channel of the O(N) symmetric linear σ model is studied in the broken symmetry phase. The investigation is based on the leading order evaluation of the self-energy in the limit of large number of Goldstone bosons. We describe its temperature-dependent variation in the whole low temperature phase. This variation closely reflects the trajectory of the scalar-isoscalar quasi-particle pole. In the model with no explicit chiral symmetry breaking, we studied also the corresponding dynamical exponent near the critical point.     

Finite dimensional irreducible representations of Lie superalgebra D(2, 1; α)

This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2, 1; α). We explicitly construct the finite dimensional representations of the superalgebra D(2, 1; α) by using the shift operator and differential operator representations. Unlike ordinary Lie algebra representation, there are typical and atypical representations for most superalgebras. Therefore,its typical and atypical representation conditions are also given. Our results are expected to be useful ...     

Finite Temperature Schr?dinger Equation

We know Schr?dinger equation describes the dynamics of quantum systems, which don’t include temperature. In this paper, we propose finite temperature Schr?dinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shr?dinger equation.     

Limiting Temperatures for Finite Nuclear Systems

The mass dependence of the limiting temperatures for finite nuclear systems is investigated. Our study shows that the different parameter sets of Skyrme interaction and the form of surface tension can influence the limiting temperature obviously.     

Yangian Realisations from Finite ?-Algebras

We construct an algebra homomorphism between the Yangian Y(sl(n)) and the finite ª-algebras ª(sl(np),n.sl(p)) for any p. We show how this result can be applied to determine properties of the finite dimensional representations of such ª-algebras.     

Parity-Violating in <Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript> Scattering at Finite Temperature

Parity violation implies that physics laws are not invariant under spatial coordinate reversal. Electron-positron scattering is a process that displays parity violation. Using the Thermo Field Dynamics formalism this scattering at finite temperature is analyzed. The transition amplitude is calculated as a function of temperature. The parity violation at very high temperatures tend to go to zero.     

Finite Temperature Casimir Effect for Corrugated Plates

Using the path-integral method, the corrections to the Casimir energy due to the combined effect of surface roughness and the finite temperature are calculated. For the specific case of two sinusoidally corrugated plates, the lateral Casimir force at finite temperature is obtained. The amplitude of the lateral Casimir force has a maximum at an optimal wavelength of λ≈ 2H with the mean plate distance H. This optimal parameter relation is almost independent of temperature.     

Finite—Amplitude Vibration of a Bubble

The Rayleigh-Plesset equation for bubble vibration is modified.The numerical solution of new equation is obtained by means of the symbolic computation programme.The acceleration of the liquid on the surface of the bubble,or pressure in the bubble,displays much intenseδ-impulse with a very short duration from ns to ps.SUggestions for developing the measurements of sonoluminescence and cavitation fusion(if any) are presented.     

Conway–Kochen and the Finite Precision Loophole

Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In this paper I show that the finite precision loophole does not apply to the Conway–Kochen Theorem.     

The McKean–Vlasov Equation in Finite Volume

We study the McKean–Vlasov equation on the finite tori of length scale L in d-dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in Gates and Penrose (Commun. Math. Phys. 17:194–209, 1970) and Kirkwood and Monroe (J. Chem. Phys. 9:514–526, 1941). Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, θ ^? of the interaction parameter. We show that the uniform density (which may be interpreted as the liquid phase) is dynamically stable for θ<θ ^? and prove, abstractly, that a critical transition must occur at θ=θ ^? . However for this system we show that under generic conditions—L large, d≥2 and isotropic interactions—the phase transition is in fact discontinuous and occurs at some $\theta_{\text{T}}<\theta^{\sharp }$ . Finally, for H-stable, bounded interactions with discontinuous transitions we show that, with suitable scaling, the $\theta_{\text{T}}(L)$ tend to a definitive non-trivial limit as L→∞.     

One ρ-Meson Exchange Potential at Finite Temperature

By means of the imaginary-time Green function method in finite-temperature field theory,one ρ-meson exchange potential at finite temperature is obtained.It is found that ρ-meson become lighter in terms of temperature increasing.The result is in good agreement with that obtained from scalling property of QCD.It is also found that temperature dependence of ρ-meson coupling constants is similar to that of,σ-meson coupling constants.     

Capillary Adhesion of Microbeams： Finite Deformation Analysis

Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young＇s contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force.     

Symmetry Breaking in Finite Volume (Ⅱ)

Using a Hamiltonian approach and the adiabatic approximation, the low-lying spectrum of the lattice O (N) model in the broken phase is analyzed to the next to leading order. It is seen that these corrections appear as a systematic expansion in the inverse power of the lattice size L in the large volume limit.     

Quantum Electrodynamics of Čerenkov Radiation at Finite Temperature

An exact, to order , study of erenkov radiation in QEDis carried out at finitetemperatures T 0 in isotropic homogeneous media for the first time. By avoidingthe method of combining denominators of Feynman propagators in parametricform, which has led to approximations in the past due to the complexity of theresulting integrals, we use instead a complex integration method and automaticallyevaluate the h ²²/E ²contribution to the quantum power spectrum and settle theambiguity associated with this term which has been known to exist at T = 0.We show that complex integration over a so-called pinching singularity actuallysimplifies the problem tremendously over the usual method of combining thedenominators of the propagators. In particular, the imaginary part of the electronself-energy satisfies the correct underlying boundary condition and no contactterm is needed in its evaluation. QED, unlike its classical counterpart, introducesautomatically a cutoff for higher frequencies, emphasizing the importance of thequantum treatment.     

η-meson in the Pseudoscalar Coupling at Finite Temperature

By means of the imaginary-time Green's function method in the finite-temperature field theory, the η-meson and nucleons interaction coupling constant, the effective mass of η-meson and the one η-meson exchange potential for the pseudoscalarcoupling at finite temperature are given. The results are compared with that given by the pseudovector coupling case.     

Finite nuclei in the reggeon “toy model”

Hadron–nucleus amplitudes at high energies are studied in the “toy” Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and loses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprising result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.     

Finite size scaling at first order phase transitions?

It is demonstrated that finite size scaling at first order phase transitions is something basically very simple: As the number of particlesN in the system goes to infinity,s _N (), the entropy per particle, rapidly approaches its limiting behaviours (). Onces () has been determined, the thermal behaviour of the infinite system is completely known and in case of a first order phase transition the specific heat exhibitis a -function singularity. If, however, the specific heatc _N (T) per particle is calculated from the canonical partition functionZ _N ()=d exp {N[s _N ()-]}, then even ifs _N () is replaced by its limiting forms (),c _N (T) only exhibits a peak with a finite maximum value proportional toN which is due to the explicit factorN in front of the angular bracket in the exponent. This is theN-dependence which has recently been called finite size scaling at first order phase transitions. The entropys _N () can very efficiently be determined in the dynamical ensemble.     

The Donald–Flanigan Problem for Finite Reflection Groups

The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types B _n and D _n (whose rational group algebras are computed), leaving but six finite reflection groups with solutions unknown. We determine the structure of a wreath product of a group with a sum of central separable algebras and show that if there is a solution for H over k which is a sum of central separable algebras and if S _n is the symmetric group then (i) the problem is solvable also for the wreath product H S _n = H × ··· × H (n times) S _n and (ii) given a morphism from a finite Abelian or dihedral group G to S _n it is solvable also for H G. The theorems suggested by the Donald–Flanigan conjecture and subsequently proven follow, we also show, from a geometric conjecture which although weaker for groups applies to a broader class of algebras than group algebras.