Markovian master equations

We give a rigorous proof that under certain technical conditions the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit. This is sufficient to show that a number of open systems obey an exponential decay law in the weak coupling limit for a rescaled time variable. The theory is applied to a fairly general finite dimensional system weakly coupled to an infinite free heat bath.     

Reaction-rate approach to impurity dipole reorientation in RbBr:Ag+

The temperature dependence of optical relaxation time of impurity dipoles (Ag⁺ in RbBr) is calculated using the quantum-mechanical theory of reaction rates in condensed media. A good agreement between theory and experiment is found.     

Recursion operators, higher-order symmetries and superintegrability in quantum mechanics

A connection between the theory of superintegrable quantum-mechanical systems, which admit a maximal number of integrals of motion, and the standard Lie group theory is established. It is shown that the flows generated by first- and second-order Lie symmetries of the bidimensional Schrödinger equation can be classified and interpreted as quantum-mechanical operators which commute with integrable or superintegrable Hamiltonians. In this way, all known superintegrable potentials in the plane are naturally obtained and slightly more general integrals of motion are found.     

Trace formulas for time delay and the second virial coefficient

A high-temperature expansion for the quantum-mechanical second virial coefficient is derived using newly developed trace formulas for time delay in scattering theory. The known cancellation between the bound state and continuum contributions is explained in this general framework. The method cam be extended to higher virial coefficients.     

超导电性的量子特征

大量实验事实及量子力学理论已证明微观粒子的运动会表现出一系列量子化特征．因此,过去人们通常认为量子效应是微观粒子所独有的．在本文中,我们通过超导体的一些奇特现象,论述了超导电性的量子特征;阐明在一定条件下由大量微观粒子组成的宏观物体也具有量子化效应,宏观可测量也可以是量子化的,这种宏观量子效应仍可用量子力学理论来研究．     

On the theory of the spontaneous magnetization of thin films. Part I

Conclusion From (3) it is seen that the quantum-mechanical theory of thin films leads to quite analogous results as for massive specimens. It is obvious that we should arrive at the same results as in (3) if from the very beginning we solved the whole problem by means of the theory of molecular fields putting the molecular fields of the individual atomic planes proportional to their magnetization. We shall therefore make use of this fact in the future by working with the method of molecular fields which permits of a somewhat more flexible procedure than the quantum-mechanical solution. At the same time, however, there appear in the equations constants of the molecular fields which are not more closely defined and which, as we know, are proportional to the exchange interaction energy between neighbours but with the present state of the theory this is not a disadvantage in comparison with the quantum-mechanical procedure, since the exchange integrals have not yet been calculated.A comparison of (3) with experiment will be left to the second part of this paper, where we shall compare the results of measurement with the equivalent equations in the molecular-field form.This paper was read at the international conference on magnetic phenomena in Moscow, 1956.     

Strong-coupling approximations

Standard path-integral techniques such as instanton calculations give good answers for weak-coupling problems, but become unreliable for strong-coupling. Here we consider a method of replacing the original potential by a suitably chosen harmonic oscillator potential. Physically this is motivated by the fact that potential barriers below the level of the ground-state energy of a quantum-mechanical system have little effect. Numerically, results are good, both for quantum-mechanical problems and for massive φ⁴ field theory in 1+1 dimensions.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

The role of homophase and heterophase interfaces on transport properties in structured materials

In structured or self-organized materials spatial confinement effects lead to structure- and interface-controlled modifications of the bulk transport properties. In part, such modifications can be accounted for by a classical master equation approach for the transport of the different charge carrier species. The rather large quantity of parameters, which enter such an approach, can more or less easily be adjusted to the dimensional characteristics, local potential changes at interfaces, and the electronic settings of the system as well as to temperature effects. On the other hand, a microscopically more detailed and mostly parameter-free picture is obtained from a quantum-mechanical treatment on the basis of the density-functional theory. An extension by a Green’s function formalism allows the determination and analysis of electronic transport through contacted nanostructures. Examples will be given to demonstrate the applicability of the different approaches for dissipative and hopping transport through a regular array of nanostructures, for a mechanically triggered metal-insulator transition in nanowires, and for the enhanced conductivity at multiferroic domain walls.     

Reservoir as a source of probability in quantum mechanics

The concept of the theory of measurement and choice of quantum alternative is considered, according to which the outcome of a particular measurement is determined by the reservoir (detector) state. The way of deducing standard (probabilistic) quantum-mechanical interpretation rules is discussed, with special emphasis on the theoretical demonstration of the wave-function reduction phenomenon. The method of resolving the “Schrodinger cat” paradox is suggested. The interrelation between the mechanisms of formation of shot and flicker noises and the role of reservoir in the formation of quantum-mechanical probability is discussed.     

Scattering quantum random walk

Random processes are of interest not only from the theoretical point of view but also for practical use in algorithms for investigating large combinatorial structures. The theory of quantum computing requires implementation of classical algorithms using quantum-mechanical devices, and random walk is an obvious candidate. We present a model for quantum random walk that is based on an interferometric analogy, can be easily implemented, and is a generalization of a former model of quantum random walk proposed by Aharonov and colleagues.     

An impact theory for Doppler and pressure broadening—I. General theory

A quantum-mechanical impact theory for the combined effects of Doppler and pressure broadening is developed from quantum radiation theory. The results are compared with other semiclassical theories and certain simplifying approximations relevant to cases of experimental and theoretical interest are discussed.     

Cramér-Rao inequalities for operator-valued measures in quantum mechanics

The theory of estimation of parameters of quantum-mechanical density operators is expressed in terms of the measurement of operator-valued measures. Lower bounds on mean-square errors of parameter estimates are set by two quantum-mechanical forms of the Cramér-Rao inequality of classical statistics, derived here in terms of such measures. The results are exemplified by the simultaneous estimation of the real and imaginary parts of the complex amplitude of a coherent oscillation in the presence of thermal noise.This research was supported by grant NSF GK-33811 from the National Science Foundation.     

Theory of inelastic scattering of slow electrons by molecules absorbed on metal surfaces

This paper presents a quantum-mechanical theory of the inelastic scattering of slow electrons by molecules adsorbed on metal surfaces. The differential cross section for vibrational excitation of one single molecule is computed.     

A second order full coulomb relaxation theory of spectral line broadening in plasmas

A second-order, quantum-mechanical relaxation theory of spectral line broadening in plasmas that uses a full Coulomb potential to describe the radiator-perturbing electron interactions is presented. A Fourier representation of the interaction is used rather than a multipole expansion. The results for the Lyman-alpha transition in hydrogen are compared with experimental data and with a corresponding relaxation theory computation that uses a dipole approximation.     

Interference and interaction in Schrödinger's wave mechanics

Reminiscing on the fact that E. Schrödinger was rooted in the same physical tradition as M. Planck and A. Einstein, some aspects of his attitude to quantum mechanics are discussed. In particular, it is demonstrated that the quantum-mechanical paradoxes assumed by Einstein and Schrödinger should not exist, but that otherwise the epistemological problem of physical reality raised in this context by Einstein and Schrödinger is fundamental for our understanding of quantum theory. The nonexistence of such paradoxes just shows that quantum-mechanical effects are due to interference and not to interaction. This line of argument leads consequently to quantum field theories with second quantization, and accordingly quantum theory based both on Planck's constant h and on Democritus's atomism.