On the stueckelberg formula for non-adiabatic transitions

The phase corrected Stueckelberg and Landau-Zener formulae for the non-adiabatic transition probability in a two state problem are compared. It is shown that validity criteria on the derivation of the former imply precise equivalence between the two formulations for the linear curve crossing problem; but the Stueckelberg approach is seen to have greater flexibility. A proposed uniformization of the Stueckelberg form for use at low velocities is shown to be incorrect.     

再谈洛伦兹变换的推导

评论了仅仅依据光速不变假设和相对性原理推导洛伦兹变换公式的方法.     

Comments on the derivation of the Ott relativistic temperature transformation

Ter Haar and Wergeland obtained the Ott temperature transformation from the Gibbs equilibrium conditions. Newburgh based his derivation on the Lorentz invariance of both radiated power and entropy. The two derivations are shown to be equivalent.     

洛伦兹速度变换的一种直接推导方法

用光速不变原理直接导出洛伦兹速度变换式，并证明相对论性速度构成双曲几何的Beltrami-Klein模型。     

On the derivation of effective interactions by matrix diagonalization methods

A technique is developed which in certain cases allows the derivation of a completely linked two body effective interaction for two particles beyond a closed shell using matrix diagonalization methods. In particular this applies to a space consisting of 0 and $\text{2}\text{h}\text{?}\text{ω}$ excitations.     

A microscopic derivation of macroscopic sharp interface problems involving phase transitions

Macroscopic free boundary problems involving phase transitions (e.g., the classical Stefan problem or its modifications) are derived in a unified way from a Hamiltonian based on a general set of microscopic interactions. A Hamiltonian of the form + _x,x J(x–x)(x)(x) leads to differential equations as a result of Fourier transforms. Expanding the Fourier transform ofJ in powers ofq (the wave number), one can truncate the series at anarbitrary orderM, and thereby obtainMth-order differential equations. An asymptotic analysis of these equations in various scalings of the physical parameters then implies limits which are the standard macroscopic models for the dynamics of phase boundaries.     

Electronic phase transitions in the spinless Falicov-Kimball model

We have studied thedV/dI vs.V characteristics of point contacts between the heavy fermion superconductor URu₂Si₂ and the conventional superconductors Zn and NbTi. Contacts between URu₂Si₂ and Zn do not show Josephson effects; instead Andreev reflection type structures occur, which are related to both, the heavy fermion and the conventional superconductor. In contrast, contacts between URu₂Si₂ and NbTi become superconducting at low currents. A closed-loop setup with two NbTi contacts on URu₂Si₂ showed SQUID oscillations in a small magnetic field. Our data give evidence that the contacts should be described as superconductor/normal/superconductor junctions with a thick normal layer on the URu₂Si₂ side of the contact with proximity induced superconductivity in theN-layer in the case of NbTi. With such a model the occurrence or absence of superconductivity can be explained and also the suppression of Andreev-scattering which is frequently observed for contacts between heavy fermion superconductors and normal metals.     

Electronic structure and phase transitions of MnAs

On the basis of a two center tight binding approach the recursion method of Haydock et al. was applied for MnAs to calculate non-polarized and spin polarized local densities of states, magnetic moments and band energies for two different B8₁ crystal structures and two B31 structures. The itineracy of the Mn 3d-states was implied by allowing for hybridization of p-states centred at the As-sites with d-states centred at the Mn-sites. Self-consistency procedures were applied to determine the relative position of the paramagnetic p- and d-band centers (E_p - E_d = - 1 eV), and to calculate the magnetic moments (3.27 μ_B for the low temperature B8₁ phase and 3.14 μ_B for the corresponding B31 phase). Because of the similarities of the electronic structures of both phases it is argued that for the first-order B8₁ [rlarr2] B31 phase transition the usually applied model of a high spin-low spin transition of the Mn³⁺ ion is basically wrong. Instead of such an ionic model it is suggested to adopt an itinerant d-electron concept within that both phases are closely related but the B8₁ phase is favoured above a certain critical magnetic moment as supported by a very recent study of Kato et al. For the high temperature B8₁ phase occurring after the second-order B31 → B8₁ phase transition a magnetic moment of 3.37 μ_B was obtained.     

Exact density matrix of an oscillator-bath system: Alternative derivation

Starting from a total Lagrangian describing an oscillator-bath system, an alternative derivation of exact quantum propagator is presented. Having the quantum propagator, the exact density matrix, reduced density matrix of the main oscillator and thermal equilibrium fixed point are obtained. The modified quantum propagator is obtained in the generalised case where the main oscillator is under the influence of a classical external force. By introducing auxiliary classical external fields, the generalised quantum propagator or generating functional of position correlation functions is obtained.     

Shape transformation transitions of a tethered surface model

A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in the Hamiltonian. We find that the model has a large variety of phases; the spherical phase, the planar phase, the long linear phase, the short linear phase, the wormlike phase, and the collapsed phase. Almost all two neighboring phases are separated by discontinuous transitions. It is also remarkable that no surface fluctuation can be seen in the surfaces both in the spherical phase and in the planar phase.     

An alternative derivation of dynamic admittance matrix of piezoelectric cantilever bimorph

In this paper, the derivation method used in (J. Microelectromech. Systems 3 (1994) 105) and the solutions of dynamic admittance matrix of a piezoelectric device derived from the method are reviewed. By solving the problem of dynamic responses of a piezoelectric cantilever bimorph with mode analysis method, an alternative approach in the derivation of the dynamic admittance matrix and other related parameters of a piezoelectric system, which can be expressed explicitly in terms of series resonance characteristics of the structure, is presented. It is shown that this form of solutions may offer some conveniences in studying mechanical and electrical properties of the system in the vicinity of resonance frequencies.     

Free energy and structural phase transitions in mixed crystals: A microscopic derivation

We consider mixed crystals of the form(MY) _x (MX) _1–x , whereY is an active component which drives a structural phase transition, while the componentX has no active internal degree of freedom. We describe this system by a compressible Ising model, including the dilution of the spinsY and the elastic strain fields caused by the componentX. We derive a Landau expansion of the free energy for this system, within molecular field theory. The coefficients of this expansion depend on temperature, pressure, spin concentrationx and the strain fields. This simple model exhibits a rich phase diagram. At sufficiently high concentrationsx, the phase transition is first order. Decreasingx, the transition passes through a tricritical point and eventually becomes second order. For lowx or high strain fields, no transition occurs.     

电磁能量-动量转化和守恒定律四维形式的一种推导

定义了电磁场的四维动量流密度张量,并将电磁能量转化和守恒定律及动量转化和守恒定律写成了四维协变形式,给出了三维电磁能量密度、能流密度、动量密度和动量流密度关于两个惯性系之间的变换关系,还给出了四维动量流密度张量与四维电磁场张量之间的依赖关系。     

Limiting transitions in the Tolman solution of the equations of general relativity

The paper considers the limiting transitions to special relativity and the Newtonian theory of gravitation in the Tolman solutions of the Einstein equations. It is shown that elliptical systems do not have an analog in the special theory. The analogs for hyperbolic and parabolic systems are the noninertial Robertson and the special-theory inertial systems, respectively. It is shown that a transition to the Newtonian theory of gravitation can be made for any type of Tolman coordinate system.