Classical states and the BRST charge

The role played by the BRST-charge in isolating the physical states in a classical first-class constrained system is analysed. Contrary to popular belief, the cohomological argument used to characterize the physical observables in such a system does not extend to the classical states. It is shown that, in order to recover the physical states, the BRST-charge must be augmented with a new charge, of ghost number minus one, constructed out of a set of gauge fixing conditions for the original constraints. The relevance of this construction to the quantum theory is discussed.     

Reconstruction theorems in quantum mechanics

Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means of well-motivated assumptions expressed in terms of a transition probability function defined on the set of all pure states of the system, we construct a system of elementary propositions, i.e., a complete orthomodular atomic lattice satisfying the covering law. We also study in this framework the important notion of compatibility of propositions, and we define the superpositions and the mixtures of the states of the physical system.     

Coherent and squeezed states on physical basis

A definition of coherent states is proposed as the minimum uncertainty states with equal variance in two hermitian non-commuting generators of the Lie algebra of the hamiltonian. That approach classifies the coherent states into distinct classes. The coherent states of a harmonic oscillator, according to the proposed approach, are shown to fall in two classes. One is the familiar class of Glauber states whereas the other is a new class. The coherent states of spin constitute only one class. The squeezed states are similarly defined on the physical basis as the states that give better precision than the coherent states in a process of measurement of a force coupled to the given system. The condition of squeezing based on that criterion is derived for a system of spins.     

Quantum States as Objective Informational Bridges

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.     

Properties and operational propositions in quantum mechanics

In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.     

Complexity of D-dimensional hydrogenic systems in position and momentum spaces

The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity is explicitly calculated and discussed by means of the quantum numbers and dimensionality. Finally, the position and momentum shape complexities are numerically discussed for various physical states and dimensionalities, and the dimensional and Rydberg energy limits as well as their associated uncertainty products are explicitly given. As a byproduct, it is shown that the shape complexity of the system in a stationary state does not depend on the strength of the Coulomb potential involved.     

一种直接用示波器观测单变量非线性系统状态的新方法

为解决用示波器观测单变量非线性系统难的问题, 本文提出了一种45°线法, 该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45°线上的点图, 并可用通用双踪示波器 (模拟或数字均可)直接显示出来, 从而达到直接方便地观测和分析单变量被测系统运行时的各种状态, 如周期稳定态, 局部和全局不稳定态. 文中详细阐述了该方法的机理. 同时, 研究和解决了设计实现该方法物理电路的关键问题, 即从连续变化的信号中提取出能反映系统状态的有用信号. 由于蔡氏电路是典型的非线性系统, 且能随参数的变化产生各种丰富的状态, 本文选用该电路作为被测系统进行了大量的物理实验, 实验结果证实了该方法的有效性和实用性. 关键词： 45°线法 单变量系统 系统状态 双踪示波器     

About a possibility of a decrease in the radiative width of excited levels of atoms and nuclei

The radiative width of quasi-energy states of a system, interacting with an external monochromatic field, is found in the present work. It is shown that a new physical effect — the formation of states with anomalous large life times — is possible in such systems.     

BRST Extension of Geometric Quantization

Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also BRST operators for many systems require regularization to be well-defined. In our more restricted context, we show that our treatment does not suffer from any of these difficulties.     

Enveloping subspaces and superposition of states

In the space of pure states of a generic physical system, a family ? of subsets is singled out and used to extend the quantum-mechanical notion of “superposition” of pure states. ? possesses a natural lattice structure and corresponds to the lattice of closed subspaces of Quantum Mechanics.     

Manipulation of multiple electromagnetically induced two-photon transparency in a six-level atomic system

In the five-level K-type atomic system, by using another control field to couple the excited level of the coupling transition to the sixth higher excited level, a six-level atomic system is constructed. In this system, the multiple electromagnetically induced two-photon transparency has been investigated. What is more, if choosing the parameters of the control fields properly the triple transparency window will reduce to a double one which means that the multiple electromagnetically induced two-photon transparency can be manipulated in this system. The physical interpretation of these phenomena is given in terms of the dressed states and the dark states.     

Constructive description of the compact set of states

We show a construction of the set of all pure states of any physical system. This set appears to be compact in a physically meaningful topology. The approach is based on quantum logic notions, but is “constructive” in the sense that we assume that our knowledge about a system increases when we perform more and more experiments and that the set of states is not given to us from the very beginning but is determined by our knowledge at any stage of investigations. The set of all states is obtained when all possible experiments are performed, which may require an infinite number of experiments. In such a situation the set of all states exists only on an abstract, purely theoretical level but nevertheless by our construction it is still compact.     

Practical implementation of multilevel quantum cryptography

The physical principles of a quantum key distribution protocol using four-level optical systems are discussed. Quantum information is encoded into polarization states created by frequency-nondegenerate spontaneous parametric down-conversion in collinear geometry. In the scheme under analysis, the required nonorthogonal states are generated in a single nonlinear crystal. All states in the selected basis are measured deterministically. The results of initial experiments on transformation of the basis polarization states of a four-level optical system are discussed.     

Epistemological and mathematical foundations of quantum mechanics

The concepts of measurement and measurable quantity are discussed. A probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given. The space of states of information about the physical system is Schwarz space rather than Hilbert space.     

Quantum theory and time asymmetry

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as ofinformation about physical states. The concept of relevance being used in all statistical theories of irreversible thermodynamics is demonstrated to be based on the same observer-relatedness. Quantum theories of irreversible processes implicitly use an objectivized process of state vector reduction. The conditions for the reduction are discussed, and it is concluded that the final (subjective) observer system may be carried by a space point.     

Metastability for Markov processes with detailed balance

We present a definition for metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance. In particular, we identify a crucial condition that distinguishes metastable states from other slow decaying modes and which allows us to show that our definition has several desirable properties similar to those postulated in the restricted ensemble approach. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible.     

Tracking controlled chaos: Theoretical foundations and applications

Tracking controlled states over a large range of accessible parameters is a process which allows for the experimental continuation of unstable states in both chaotic and non-chaotic parameter regions of interest. In algorithmic form, tracking allows experimentalists to examine many of the unstable states responsible for much of the observed nonlinear dynamic phenomena. Here we present a theoretical foundation for tracking controlled states from both dynamical systems as well as control theoretic viewpoints. The theory is constructive and shows explicitly how to track a curve of unstable states as a parameter is changed. Applications of the theory to various forms of control currently used in dynamical system experiments are discussed. Examples from both numerical and physical experiments are given to illustrate the wide range of tracking applications. (c) 1997 American Institute of Physics.