Coupled physical systems

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.Dedicated to Professor Peter Mittelstaedt.     

States of physical systems

States of physical systems may be represented by states onB*-algebras, satisfying certain requirements of physical origin. We discuss such requirements as are associated with the presence of unbounded observables or invariance under a group. It is possible in certain cases to obtain a unique decomposition of states invariant under a group into extremal invariant states. Our main results is such a decomposition theorem when the group is the translation group in dimensions and theB*-algebra satisfies a certain locality condition. An application of this theorem is made to representations of the canonical anticommutation relations.     

On transformations of physical systems

A universal, unified theory of transformations of physical systems based on the propositions of probabilistic physics is developed. This is applied to the treatment of decay processes and intramolecular rearrangements. Some general features of decay processes are elucidated. A critical analysis of the conventional quantum theories of decay and of Slater's quantum theory of intramolecular rearrangements is given. It is explained why, despite the incorrectness of the decay theories in principle, they can give correct estimations of decay rate constants. The reasons for the validity of the Arrhenius formula for the temperature dependence of an intramolecular rearrangement rate constant are discussed. A criterion for the possibility of a proper intramolecular rearrangement is given. The issue of causality in quantum physics is settled.     

The physical states of Fermi systems

A classification of all translationally invariant states over the algebra of anticommutation relations which satisfy criteria of finite mean density, finite mean kinetic energy, and finite mean entropy is given. It is demonstrated that these concepts can be discussed in terms of affine, semi-continuous, functionals which respect the barycentric decompositions of invariant states. Many other pertinent results, both local and global, are derived.     

Description of quantum systems by the collective behavior method

Optics and Spectroscopy - We develop the constructive viewpoint to quantum theory, which means the using of constructive mathematics as the basic formalism. It is shown how the heuristic of...     

Algebraic implications of composability of physical systems

From classical and quantum mechanics we abstract the concept of a two-product algebra. One of its products is left unspecified; the other is a Lie product and a derivation with respect to the first. From composition of physical systems we abstract the concept of composition classes of such two-product algebras, each class being a semigroup with a unit. We show that the requirement of mutual consistency of the algebraic and the semigroup structures completely determines both the composition classes and the two-product algebras they consist of. The solutions are labelled by a single parameter which in the physical case is proportional to the square of the quantum of action.     

Classical and quantum q-deformed physical systems

On the basis of non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under the action of the q-symplectic group of transformations. Within this framework we introduce the q-deformed Hamilton equations and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion, is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the standard canonical quantization rule, we compare the well-known q-deformed Heisenberg algebra with the algebra generated by the q-deformed Poisson bracket. PACS 02.45.Gh, 45.20.-d, 03.65.-w, 02.20.Uw     

Description of uniform many-particle systems in density operator function space

Assuming the ground state wavefunction, ψ₀, of a boson fluid is known, and writing the excited state wavefunctions in the form Fψ₀, a linear eigenvalue equation of the form $\text{H}\text{F = EF}$ is obtained, where E₀ + $\text{E}$ is the excited state energy, E₀ is the ground state energy, and H is a non-hermitian operator which depends in a simple way upon U ≡ ln ψ₀² instead of the potential energy function. An extremum principle is derived in terms of an auxiliary hermitian Hamiltonian operator, H′. The many-body boson plane-wave basis, ?_n(k₁ … k_n) is used to express U in terms of its Fourier components (ordered conveniently in terms of the number of nonzero arguments), making it possible to calculate matrix elements of ovcirc|H and H′ in that basis. A perturbation theory similar to Brillouin-Wigner perturbation theory is developed for the non-hermitian eigenvalue problem. Nonorthogonal perturbation theory is developed for the correlated basis ?_nψ₀. The requirement that these two perturbation theories be consistent produces useful relationships between the components of U and the static structure functions of ψ₀. These relationships are shown to reduce to previous results in the extreme case of low density and weak interactions.     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

Evidence for consciousness-related anomalies in random physical systems

Speculations about the role of consciousness in physical systems are frequently observed in the literature concerned with the interpretation of quantum mechanics. While only three experimental investigations can be found on this topic in physics journals, more than 800 relevant experiments have been reported in the literature of parapsychology. A well-defined body of empirical evidence from this domain was reviewed using meta-analytic techniques to assess methodological quality and overall effect size. Results showed effects conforming to chance expectation in control conditions and unequivocal non-chance effects in experimental conditions. This quantitative literature review agrees with the findings of two earlier reviews, suggesting the existence of some form of consciousness-related anomaly in random physical systems.     

基于物理混沌的混合图像加密系统研究

初步实现了基于物理混沌的混沌和数据加密标准算法级联的混合图像加密系统,基于该系统研究了级联加密与单级加密的抗统计分析能力,以及不可预测性强弱不同的混沌信号在该系统中应用时密文特性的不同.这种利用物理混沌不可预测性的混合加密系统,不存在确定的明文密文映射关系,而且密文统计特性也应优于(或大致相当)其他加密系统.数值结果支持这一结论,同时表明不可预测性较强的混沌系统其加密产生的密文相关性较弱.     

Transformation of quantum correlations between systems of different physical nature

Using the general equation for two independent two-level atoms in a broadband two-component entangled bath, the problem of transforming quantum correlations from light to atoms is considered. To identify the transfer of inseparability, it is proposed to choose an adequate observable. Finally, we consider the average fidelity, which is a characteristic of the channel in the teleportation process.     

A new physical characterisation of classical systems in quantum mechanics

A physical characterisation of classical systems in quantum mechanics is given in terms of the set of ensembles in contrast to the well-known characterisations concerning the effects or observables: A quantum mechanical system is classical if and only if each two decompositions of every ensemble are compatible.