Showing papers on "Open quantum system published in 1981"
TL;DR: The form of the interaction Hamiltonian between the apparatus and its environment is sufficient to determine which observable of the measured quantum system can be considered "recorded" by the apparatus as mentioned in this paper.
Abstract: The form of the interaction Hamiltonian between the apparatus and its environment is sufficient to determine which observable of the measured quantum system can be considered "recorded" by the apparatus. The basis that contains this record---the pointer basis of the apparatus---consists of the eigenvectors of the operator which commutes with the apparatus-environment interaction Hamiltonian. Thus the environment can be said to perform a nondemolition measurement of an observable diagonal in the pointer basis.
1,326 citations
Book•
01 Jan 1981TL;DR: In this paper, the authors present a mathematical model for quantum probability theory based on the Hilbert-space formulation of quantum mechanics and a quantum logic of the physical system, which they call quantum logic quantum logic.
Abstract: Editor's statement Foreword Preface Part I. Hilbert-Space Quantum Mechanics 1. Static description of quantum mechanics 2. States 3. Physical quantities 4. Spin and motion 5. Superselection rules 6. Dynamical evolution 7. Compound systems 8. Elementary analysis of the measurement process 9. Mathematical structures emerging from the Hilbert-Space formulation of Quantum mechanics Part II. Basic Structures in the Description of Quantum Mechanics 10. The typical mathematical structure of propositions: orthomodular AC lattices 11. Probability measures on orthomodular posets and lattices 12. Characterization of commutativity 13. States and propositions of a physical system 14. Quantum-mechanical features in terms of the logic of the physical system 15. On the hidden-variable issue 16. Proposition-state structure and idealized measurements 17. Superpositions of states and closure spaces 18. Transition-probability spaces and quantum systems 19. On the convex-set approach 20. Introduction to a quantum logic Part III. Reconstruction of Hilbert-Space Quantum Mechanics 21. The coordinatization problem 22. Use of real and quaternionic Hibert Spaces: a simple example 23. Dynamics 24. Composition of physical systems 25. Hidden-variable theories and Gleason's Theorem 26. Introduction to quantum probability theory Appendices Subject index.
632 citations
TL;DR: In this article, it is demonstrated that the topological property that defines the atom determines the definition of its average properties, and that the quantum mechanics has been shown to account for the properties of isolated atoms and for the total properties of a molecular system.
Abstract: Publisher Summary This chapter deals with the quantum mechanical definition of the average properties of an atom. It is demonstrated that the topological property that defines the atom determines the definition of its average properties. It reviews only the basic topological properties of a charge distribution in this chapter. Their role in the definition of molecular structure and its change has been recently reviewed in detail. A bound atom is an example of an open quantum system. A quantum description of subsystems must be developed, free to exchange charge and momentum with their environment across boundaries that are defined in real space and that in general change with time. The chapter also reviews that the quantum mechanics has been shown to account for the properties of isolated atoms and for the total properties of a molecular system. The increased understanding that would result from the discovery of a firm theoretical basis for Dalton's theory has not been obtained because of a lack of a quantum definition of an atom in a molecule.
571 citations
TL;DR: In this paper, the ground state of a quantum mechanical antiferromagnetic model with next-nearest neighbor interactions was studied. But the results for the model were not exact.
Abstract: We present some exact results for the ground state of a quantum mechanical antiferromagnetic model in the two dimensions with next-nearest neighbor interactions.
509 citations
TL;DR: In this paper, the presence of unitary group generators in the time evolution of $N$-level quantum systems is shown to suggest a class of new nonlinear constants of motion, and to permit the description of the evolution in terms of the rotations of a real coherence vector.
Abstract: The presence of unitary group generators in the time evolution of $N$-level quantum systems is shown to suggest a class of new nonlinear constants of motion, and to permit the description of the evolution in terms of the rotations of a real coherence vector.
328 citations
TL;DR: In this paper, the authors present unambiguous evidence for dynamical tunneling in bound state quantum systems, where tunneling occurs between two distinct regions of classically trapped quasiperiodic motion.
Abstract: Tunneling involves an allowed quantum event which fails to take place classically. Dynamical tunneling is the subset of such events which do not involve a classically insurmountable potential barrier. In this paper, we present unambiguous evidence for dynamical tunneling in bound state quantum systems.The tunneling occurs between two distinct regions of classically trapped quasiperiodic motion. Close analogies are shown to exist between this situation and ordinary barrier penetration in a double minimum potential. In the cases we study, tunneling occurs between equivalent or nearly equivalent local mode motions, which have arisen out of a resonance between the symmetric and nonsymmetric stretch.
323 citations
TL;DR: In this paper, the quantum theory of photodetection from the point of view of quantum measurement has been considered, and it has been shown that the Mandel photon counting formula may lead to unphysical results such as negative probabilities, in some situations just because this modification is not incorporated into the model.
Abstract: We reconsider various approaches to the quantum theory of photodetection from the point of view of the quantum theory of measurement, and show that important differences between them depend upon the manner in which they take into account the modification of the field distribution produced by the presence of the detector. We show that the Mandel photon counting formula may lead to unphysical results, such as negative probabilities, in some situations just because this modification is not incorporated into the model. We also show that the recently developed quantum theory of continuous measurements provides a completely satisfactory framework for discussing photon counting experiments. As an illustration, an exact derivation of the photon statistics of a single-mode free field is presented, and some of the results are shown to be identical to those derived earlier by Mollow and others. We also indicate how our approach can be extended to discuss the photon statistics of fields in interaction with sources an...
241 citations
Book•
01 Jan 1981
TL;DR: The third volume of this textbook on mathematical physics is devoted to quantum mechanics and especially to its applications to atomic systems as mentioned in this paper, where the author builds the theory on an axiomatic basis and uses the functional analysis of unbounded operators to bridge the gap to physics and its experiments.
Abstract: The third volume of this textbook on mathematical physics is devoted to quantum mechanics and especially to its applications to atomic systems. The author builds the theory on an axiomatic basis and uses the functional analysis of unbounded operators to bridge the gap to physics and its experiments. Mathematics is shown to explain the axioms in depth and to provide the right tool for testing numerical data in experiments. The topics covered are Hilbert spaces, the theory of unbounded operators, scattering theory, atoms and molecules.
132 citations
TL;DR: In this paper, the structural similarity between physical optics and quantum mechanics is exploited and operators and fields that are unaltered by passage through an optical system are introduced and discussed. And the Fourier properties and imaging properties of an ideal lens are derived using operator algebraic methods.
Abstract: This paper is devoted to the exposition of operator algebraic methods that can be usefully applied to many areas of physical optics. These methods exploit the structural similarity between physical optics and quantum mechanics and make use of operator techniques widely used in quantum theory. We develop the basic approach here and illustrate its power by giving a compact derivation of the Fourier properties and the imaging properties of an ideal lens. We also use the operator approach to introduce and discuss operators and fields that are unaltered by passage through an optical system.
Book•
01 Jan 1981
TL;DR: In this paper, an approximation technique for integrals containing Fermi-Dirac function was proposed for integration of action integrals in the Actinide series of ac circuits.
Abstract: vector space, 27, 84, 350 ac circuits, 20 Actinide series, 131 Action integrals, 43 Alkali metals, 207 Alpha particle, 156,182 Alpha-particle emission, 108 Alpha-particle tunneling, 245 Aluminum (Al), 207 Ammonia clock, 115 Amorphous solids, 334-336 Angular momentum Bohr model, 41 electron in hydrogen atom, 123 operators, 54 quantum numbers, 119,123-125,127 Annihilation operator, 158 Anomalous skin effect, 405 Antisymmetry property of wave functions, 157,158 Approximation technique for integrals containing Fermi-Dirac function, 217-225 Argon (Ar), 344 Asymmetric potential well, 115 Atom, electron configurations, 128-130 Atomic orbital, 127 Average value of a physical observable, 74 Avogadro number, 173,413 Azimuthal quantum number, see Orbital quantum number
TL;DR: In this article, the authors propose a method to solve the problem of "uniformity" and "uncertainty" in the context of health care, and propose a solution.
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TL;DR: In this article, the polarization properties of light rays are investigated and the equations obeyed by the ray density function are deduced for homogeneous statistical wave fields, where the authors show that these properties have some relation with the phase-space picture of quantum mechanics.
Abstract: Stemming from the classic work of Planck, classical radiative transfer theory works with pencils of light rays streaming in straight lines in any homogeneous medium. But light is described by Maxwell's equations in classical and quantum electrodynamics, and so we need to find a bundle of rays equivalent to the electromagnetic waves. In this paper we realize such a pencils of light rays. Their properties and the equations obeyed by the ray density function are deduced. We need to generalize radiative transfer theory for this purpose appropriately. For homogeneous statistical wave fields radiative transfer theory obtains rigorously. Particular attention is paid to the polarization properties of light rays. These concepts have some relation with the phase-space picture of quantum mechanics. Also, other general questions including possible further developments are discussed.
TL;DR: In this article, a generalization of the canonical commutation relations of quantum mechanics is proposed, and a new uncertainly principle is obtained, as well as some results that may be connected with quark physics.
TL;DR: The nonrelativistic limit of a relativistic quantum mechanics of Stueckelberg type is studied in this paper, where a new degree of freedom, which is a purely quantum effect, emerges as a residue of the relativism theory; its role is to impose Galilean simultaneity.
Abstract: The nonrelativistic limit of a relativistic quantum mechanics of Stueckelberg type is studied. A new degree of freedom, which is a purely quantum effect, emerges as a residue of the relativistic theory; its role is to impose Galilean simultaneity. It is shown that the usual nonrelativistic Schr\"odinger equation is obtained as the asymptotic form of the relativistic evolution equation, and some new insight is provided into its interpretation from the point of view of the relativistic theory.
TL;DR: In this article, it was shown that the recent results and error trends of Lee and Scully and Brown and Heller are explicable in terms of the "dangerous cross term" analysis.
Abstract: It is shown that the recent results and error trends of Lee and Scully and Brown and Heller are explicable in terms of the ’’dangerous cross term’’ analysis. Extended quantum state suffer larger errors in the Wigner method.(AIP)
TL;DR: In this article, the existence problem of quasi-periodic states for quantum Hamiltonians periodic in time has been studied and some subtleties in the existence of such states have been pointed out.
Abstract: Points out some subtleties in the existence problem of quasi-periodic states for quantum Hamiltonians periodic in time.
TL;DR: In this article, it is shown that such a theory describes tachyons and that the quantum theory of tachyon should be a quaternionic one. But this theory needs fundamental changes in basic physical assumptions and in a sense it is complementary to known physics.
Abstract: The new approach to quaternion quantum mechanics is given. It is shown that such a theory describes tachyons and that the quantum theory of tachyons should be a quaternionic one. This theory needs fundamental changes in basic physical assumptions and in a sense it is complementary to known physics. An important analogy between the basic notions of quaternionic and complex quantum mechanics emerges from the new scheme. The consequences for the theory of quantum and classical tachyons seem to be very important.
TL;DR: In this article, the basic properties of nonrelativistic finite-dimensional quantum mechanics are presented, and a discrete quantum mechanics is developed and the symmetric and antisymmetric Fock spaces are discussed.
Abstract: The basic properties of nonrelativistic finite-dimensional quantum mechanics are presented A discrete quantum mechanics is developed Second quantization, the symmetric and antisymmetric Fock spaces are also discussed
TL;DR: In this paper, the authors discuss interpretational aspects of the concept of state in quantum mechanics which are related to the "ignorance inter? pretation of states" and to the problem of the completeness of describing states by state operators.
Abstract: In this paper we shall discuss some interpretational aspects of the concept of state in quantum mechanics which are related to the "ignorance inter? pretation of states" and to the problem of the completeness of describing states by state operators. All considerations are restricted to nonrelativistic systems with finitely many degrees of freedom. As a basis of our discussion we formulate two "rules of the game" which are intended to explain, at least partially, the author's conception of the notions "quantum system" and "state".
TL;DR: In this paper, the influence functional method was used to find the best possible classical description of a particle (system) interacting with a quantum system at a non-zero temperature, and it was found to be a stochastic one.