1,721,067 research outputs found
SUPERSELECTION RULES AND FLUCTUATIONS IN THE MANY-HILBERT-SPACES APPROACH TO QUANTUM MEASUREMENT
No full textThe interaction between a macroscopic detector and a quantum system is studied by means of a simple model in the context of the Many-Hilbert-Spaces approach, and it is shown that statistical fluctuations play a determinant role in the description of the detector. An order parameter is introduced, in terms of which a quantitative definition of wave-function collapse can be given. The meaning of the super-selection charges of the Many-Hilbert-Spaces is also clarified, and an inequivalent representation is given in the limit of infinite number of elementary constituents of the detector. Finally, this approach is compared to other proposals in the literature
MANY-HILBERT-SPACES APPROACH TO THE WAVE-FUNCTION COLLAPSE
No full textThe many-Hilbert-spaces approach to the measurement problem in quantum mechanics is reviewed, and the notion of wave function collapse by measurement is formulated as a dephasing process between the two branch waves of an interfering particle. Following the approach originally proposed in Ref. 1, we introduce a "decoherence parameter," which yields a quantitative description of the degree of coherence between the two branch waves of an interfering particle. By discussing the difference between the wave function collapse and the orthogonality of the apparatus' wave functions, we analyze critically two proposals, recently appeared in the literature,(2, 3) and argue that neither one describes a dephasing process. We conclude that the concept of "wave function collapse," according to the conventional Copenhagen interpretation, is to be replaced by that of a statistically defined dephasing process
WAVE-FUNCTION COLLAPSE BY MEASUREMENT AND ITS SIMULATION - REPLY
No full textWe discuss and clarify the concept of dephasing in the many-Hilbert-space approach to the quantum measurement problem. We argue that the phase randomization provoked by a detecting macroscopic device is responsible for the loss of quantum coherence, and that the ''collapse of the wave function'' is to be regarded as a statistical process for the accumulated distribution over many events. In stressing the fundamental differences between our approach and the Copenhagen interpretation, we counter the objections put forward by Johnston [preceding Comment, Phys. Rev. A 48, 2497 (1993)], whose stand-point is essentially similar to the Copenhagen one
MEANING OF THE DECOHERENCE PARAMETER IN THE MANY-HILBERT-SPACE APPROACH TO QUANTUM MEASUREMENTS
No full textWe discuss the role played by the decoherence parameter in the many-Hilbert-space approach to quantum measurements. Some criticisms recently put forward by de Muynck and Martens are analyzed, countered and shown to be flawed. It is clarified that a nonvanishing value of the decoherence parameter represents an irreversible loss of quantum-mechanical coherence
QUANTUM-THEORY OF MEASUREMENT BASED ON THE MANY-HILBERT-SPACE APPROACH
No full textWe review and develop the quantum theory of measurement along the line of thought of the many-Hilbert-space approach, originally proposed by Machida and Namiki some years ago. Our main interest is to analyze the mechanism of the wave-function collapse by measurement. We start by discussing the wave-particle dualism of quantum mechanical particles, as observed in a typical interference experiment of the Young type, and then analyze the quantum measurement process from a physical point of view. On the basis of these arguments, we reformulate the notion of wave-function collapse by measurement: We view the collapse as a dephasing process among the branch waves after they have undergone spectral decomposition, in opposition to the conventional Copenhagen interpretation. One of the most important points of the present approach is the introduction of an order parameter epsilon (named decoherence parameter) that ranges from 0 to 1 and quantitatively represents the degree of decoherence. In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus: The case of perfect decoherence, epsilon = 1, describes an apparatus by which we can perform perfect measurement, while the case of perfect coherence, epsilon = 0, describes an instrument by which we observe perfect interference. The intermediate values between 1 and 0 correspond to imperfect measurements or mesoscopic phenomena. From this point of view, we briefly give a critical review of some famous measurement theories. The present theory of measurement is also theoretically formulated in terms of density matrices within the mathematical framework of the continuous direct sum of many Hilbert spaces (the continuous-superselection-rule space). In order to show the characteristics of the theory, we introduce several solvable detector models and perform numerical simulations. Finally we analyze, by means of similar order parameters, miscellaneous related problems, including neutron and photon interference phenomena
MEASUREMENT-THEORETICAL ANALYSIS OF NEUTRON INTERFERENCE AT LOW TRANSMISSION PROBABILITY
No full textRecent experimental results of neutron interferometry at low transmission probability are analyzed when an absorber is present in one of the two routes of the interferometer. The process is regarded as a partial dephasing characterized by the decoherence parameter, along the same line of thought as in the many-Hilbert-space approach to the quantum measurement problem. It is shown that the density fluctuations of the elementary constituents of the absorber provoke a reduction of the visibility of the interference pattern. The effect is evaluated analytically in the case of Gaussian fluctuations, and found to be in agreement with the experimental data
EXPONENTIAL BEHAVIOR OF A QUANTUM SYSTEM IN A MACROSCOPIC MEDIUM
No full textAn exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling macroscopic limit. Some implications for the quantum measurement problems are discussed, in particular in connection with dissipation
WAVE-FUNCTION COLLAPSE BY MEASUREMENT AND ITS SIMULATION
No full textThe many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ''yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ''wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter epsilon that quantitatively describes the degree of decoherence. Its value ranges from epsilon = 0 (which describes the case in which the two waves are perfectly coherent) to epsilon = 1 (which describes the case in which coherence is totally lost); for this reason epsilon is named the ''decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex delta-potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit epsilon = 1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed
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