Showing papers on "Open quantum system published in 1968"
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01 Jan 1968
TL;DR: In this paper, the Logic of a Quantum Mechanical System (LMS) and Logics Associated with Hilbert Spaces (LAS) are used to describe the properties of a quantum mechanical system.
Abstract: Boolean Algebras on a Classical Phase Space.- Projective Geometries.- The Logic of a Quantum Mechanical System.- Logics Associated with Hilbert Spaces.- Measure Theory on G-Spaces.- Systems of Imprimitivity.- Multipliers.- Kinematics and Dynamics.- Relativistic Free Particles.
1,031 citations
354 citations
TL;DR: In this article, the statistical predictions of quantum mechanics for infinite ensembles are derived from its assertions for individual systems, and a discussion of the meaning of the state of an individual quantum mechanical system is given, and an application is made to clarify some of the paradoxical features of the theory.
Abstract: A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for individual systems. A discussion of the meaning of the “state” of an individual quantum mechanical system is given, and an application is made to the clarification of some of the paradoxical features of the theory.
282 citations
161 citations
TL;DR: The theory of Baer *-semigroups provides mathematical constructs utilized in the quantum logic approach to the mathematical foundations of quantum physics as discussed by the authors, and there exists a remarkable connection between the mathematical theories of orthomodular ortholattices and Baer*-Semigroups.
Abstract: The theory of orthomodular ortholattices provides mathematical constructs utilized in the quantum logic approach to the mathematical foundations of quantum physics There exists a remarkable connection between the mathematical theories of orthomodular ortholattices and Baer *-semigroups; therefore, the question arises whether there exists a phenomenologically interpretable role for Baer *-semigroups in the context of the quantum logic approach Arguments, involving the quantum theory of measurements, yield the result that the theory of Baer *-semigroups provides the mathematical constructs for the discussion of “operations” and conditional probabilities
119 citations
TL;DR: In this paper, the relations among the statistical ensembles, systems, and states (pure and mixed) of quantum theory are explored. But the conceptual gulf between classical states and quantum states is wider than commonly assumed.
Abstract: This paper carefully explores the relations among the statistical ensembles, systems, and states (pure and mixed) of quantum theory. By systematically contrasting the classical and quantal realizations of a general paradigm for a probabilistic physics, important distinctions are exposed both in statics and dynamics. Included are observations concerning the intrinsic ambiguity of the quantum-state concept and the peculiarly quantum property of dynamic indivisibility. It is concluded that the conceptual gulf between classical states and quantum “states” is wider than commonly assumed.
TL;DR: In this article, the authors apply quantum mechanics to the problem of a particle bound in an external gravitational potential, and find the following results which violate one's classical conception of the principle of weak equivalence: radii, frequencies, etc., depend on the mass of the bound particle; the binding energy has the wrong mass dependence; inertial forces do not look like gravitational forces; and there are mass-dependent interference effects.
TL;DR: A good deal of the opinions expressed in this article on the problem of quantal measurements is misleading or incorrect, as it will be shown in the present note as discussed by the authors, as well as the present paper.
TL;DR: In this paper, the general forms of such semiclassical descriptions are discussed and conditions for the two descriptions to be equivalent are examined, and the general form of such descriptions is discussed.
Abstract: In the semiclassical descriptions, it is usual to describe a quantum‐mechanical system in a classical language with (i) a correspondence between classical functions and operators of quantum mechanics and (ii) with a real, but not necessarily positive, probability density function in phase space corresponding to a particular quantum‐mechanical state. The general forms of such semiclassical descriptions is discussed. The conditions for the two descriptions to be equivalent are also examined.
TL;DR: In this article, it was shown that the *-algebra of test-functions for a quantum field is reduced, i.e. for eachb∈ R,b≠ 0, there exists a positive continuous linear functionalW(a) onR withW(b)≠0.
Abstract: It is shown that the *-algebraR of test-functions for a quantum field is reduced, i.e. for eachb∈R,b≠0, there exists a positive continuous linear functionalW(a) onR withW(b)≠0.
TL;DR: In this paper, the authors give new formulae permitting the calculation of time ordered but otherwise arbitrary correlation functions of electromagnetic field operators in terms of a class of quantum mechanical quasi-probability distribution functions.
Abstract: We give new formulae permitting the calculation of time ordered but otherwise arbitrary correlation functionsK of electromagnetic field operators in terms of a class of quantum mechanical quasi-probability distribution functions This class contains among others the socalledQ- andP-functions as well as the Wigner function
TL;DR: In this paper, the authors argue that attempts to set up on an axiomatic basis an abstract "theory of measurement" in quantum mechanics lead to imaginary difficulties and suggest speculations about non-physical effects which have no objective justification.
01 Jan 1968
01 Jan 1968
TL;DR: In this paper, the problem of the reduction of the wave function in quantum theory is treated from a new standpoint, by combining Heisenberg's uncertainty relations with gravitation, quantitative limi tations on the sharpness of the structure of space-time are derived.
Abstract: The problem of the reduction of the wave function in quantum theory is treated from a new standpoint. First, by combining Heisenberg's uncertainty relations with gravitation, quantitative limi tations on the sharpness of the structure of space-time are derived. Second, the resulting uncertainty in space-time structure is incorporated into the equations for the propagation of the quantum-mechanical wave amplitudes. In the resulting theory an initially pure wave function generally develops in time into a mixture. A single pure wave function survives only as long as it corresponds to a sufficiently small spread in the position of any massive part of the system under investigation. Quantitative relations between the mass and the maximum coherent spread in the center-of-mass wave function of a single body are obtained.
TL;DR: In this paper, the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containing multiple modes, and the results obtained are used for the superposition of coherent and thermal fields.
Abstract: The relations between the probability distributionp
n
vt
of the number of photonsn
vt
in a volumeV at timet and the probability distributions PN(W) and PA(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn
vt
, PN(W) and PA(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn
vt
, PN(W) and PA(W) become equal.