Quantum theory as the most robust description of reproducible experiments

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.     

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.     

Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, described by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the phase-space dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity can arise as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.     

Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

Quantum kinetic Boltzmann equation taking into account the resonant exchange of excitations

A derivation of the quantum Boltzmann equation is given for identical particles with internal degrees of freedom. It is shown that the off-diagonal (with respect to the internal degrees of freedom) term of the equation contains an energy pole term, which is not present in the most commonly used kinetic equation, known as the Waldmann-Snider equation. The physical conditions underlying the occurrence of the pole term in the quantum kinetic equation are analyzed. Zh. éksp. Teor. Fiz. 111, 831–837 (March 1997)     

General Requirements for a Relativistic Quantum Theory

The equations of a relativistic quantum theory for two or more particles should satisfy at least the following criteria. (1) They should be Poincaré invariant. (2) The cluster property should hold. (3) Causality should not be violated over distances much larger than the Compton wavelengths of the particles involved. (4) The electromagnetic interaction between charged particles should be formulated in a gauge-invariant way. (5) If, for a two-particle system, one of the masses becomes infinitely large, the equations should reduce to the relevant relativistic equation for the other particle. (6) In the nonrelativistic limit the equation should reduce to the Schr?dinger equation. In this paper it will be shown how a quasi-potential theory, which was introduced many years ago [1] and which was applied to a number of systems [2–12], meets all these requirements. Received March 25, 1997; revised July 15, 1997; accepted for publication March 18, 1998     

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be satisfied by the general equation of motion which is yet to be discovered.Part I of this paper appeared inFound. Phys. 6(1), 15 (1976). Part IIa appeared inFound. Phys. 6(2), 127 (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part IIa.     

Interference effects in the scattering of identical atoms in a laser radiation field

The properties of the collision integral in a quantum Boltzmann-type kinetic equation are studied under the conditions of spatially nonuniform distributions of colliding particles interacting with an external electromagnetic field. The components of the nonlinear resonances and the velocity distribution of the excited atoms, which are due to polarization transitions, are determined on the basis of the Kazantsev collision integral.     

Depth distributions of implanted atoms under the influence of surface erosion and diffusion

Shallow range distributions are altered significantly by diffusion and surface erosion. It will be shown here that the simultaneous processes of implantation, diffusion, and surface erosion can be described by a second order differential equation which is mathematically tractable and yields general results in terms of analytical functions. The resulting depth distributions depend on one parameter only which is a combination of the mean particle range, the diffusion coefficient, and the velocity of surface erosion (e.g. sputtering). The theory is applied to practical cases, e.g. implantation of plasma particles in the wall of fusion reactors, or solar wind ions in the surface of meteorite materials.     

Stochastic electrodynamics. III. Statistics of the perturbed harmonic oscillator-zero-point field system

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field.     

Tempered distributions in infinitely many dimensions

The space of testing functions for tempered distributions is characterized in an abstract way as the maximal space in a certain class of locally convex topological vector-spaces. The main characteristic of this class is stability under the differentiation and multiplication operators.The ensuing characterization of tempered distributions may readily be generalized to the case of infinitely many dimensions, and a certain class of such generalizations is studied. The spaces of testing elements are required to be stable under the action of the canonical field operators of the quantum theory of free fields, and it is shown that extreme spaces of testing elements exist and have simple properties. In fact, the maximal space is a Montel space, and the minimal complete space is a direct sum of such spaces.The formalism is applied to the problem of extending the canonical field operators, and a number of extension theorems are derived. In a forthcoming paper the theory of tempered distributions in infinitely many variables will be applied to a structurally simple linear operator equation.     

Covariant Relativistic Statistical Mechanics of Many Particles

In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ. The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (concatenations) particle properties such as the equation of state may be obtained. We further reconsider the generalized quantum equilibrium ensemble theory and the free event case of the Fermi-Dirac and Bose-Einstein distributions, and some consequences. The ultra-relativistic limit differs from the non-covariant theory and is a test of this point of view.     

甚长波量子阱红外探测器的暗电流特性研究

基于载流子在量子结构中的输运理论研究了甚长波量子阱红外探测器(峰值响应波长15μm，量子阱个数大于40)的载流子的输运性质.研究结果表明，在甚长波量子阱红外探测器中，电流密度一般很低，暗电流主要来源于能量高于势垒边的热激发电子.通过薛定谔方程和泊松方程以及电流的连续性方程的自洽求解，发现外加偏压下电子浓度在甚长波器件各量子阱的分布发生较大变化，电场在整个器件结构上呈非均匀分布，靠近发射极层的势垒承担的电压远远高于均匀分布的情形.平带模型假定电压在器件体系上均匀分布，导致小偏压下的理论计算值远远低于实验值. 关键词： 甚长波量子阱红外探测器 量子波输运 暗电流     

Quantum nature of ROT and TRI asymmetries in the ternary fission of nuclei

Effects of T-odd asymmetry in ternary-nuclear-fission reactions induced by polarized cold neutrons are considered within quantum theory. It is shown that the asymmetry coefficient can be expressed in terms of experimental angular distributions of third particles in reactions induced by unpolarized neutrons. The explicit form of this coefficient makes it possible to explain the difference in the magnitudes and signs of the TRI and ROT effects observed experimentally for different targets.     

Beltrami-de Sitter时空中标量和旋量粒子的量子理论

参照在Minkowski时空中,从粒子的相对论性经典理论过渡到量子理论,建立标量粒子和旋量粒子的相对论性波动方程的方案,在Beltrami-de Sitter时空中建立了de Sitter不变的标量粒子和旋量粒子的相对论性量子力学的基本方程,它们恰恰分别是Beltrami-de Sitter时空中的Klein-Gordon方程和Dirac方程。在Beltrami-anti de Sitter时空的同时类空超曲面簇上求解了这些方程,得到了分立的本征值和相应的本征函数。 关键词：     

Nonminimal particle-like solutions in cubic scalar field theory

The cubic scalar field theory admits the bell-shaped solitary wave solutions which can be interpreted as a massive Bose particles. We rule out the nonminimal p-brane action for such a solution as the point particle with curvature. When quantizing it as the theory with higher derivatives, it is shown that the corresponding quantum equation has SU(2) dynamical symmetry group realizing the exact spin-coordinate correspondence. Finally, we calculate the quantum corrections to the mass of the bell boson which can not be obtained by means of the perturbation theory starting from the vacuum sector.