scholarly journals The von Neumann model of measurement in quantum mechanics

2014 ◽  
Author(s):  
Pier A. Mello
Keyword(s):  
Quantum Mechanics ◽  
Von Neumann ◽  
Neumann Model

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

The problem of measuring the quantity of output in the input–output model by W. Leontief in modeling the trends in economic reproduction of nations and regions

2021 ◽  
Vol 19 (8) ◽  
pp. 1568-1592
Author(s):  
Nikolai I. KURYSHEV
Keyword(s):  
Input Output ◽  
Von Neumann ◽  
Output Matrix ◽  
Production And Consumption ◽  
Production Quantity ◽  
Mathematical Analyses ◽  
Neumann Model ◽  
Product Output ◽  
The Relationship ◽  
Cost Characteristics

Subject. This article deals with the problem of constructing a Leontief's input–output matrix. Objectives. The article aims to determine the rules for constructing a Leontief's input–output matrix on the basis of data on production time and quantity of product output. Methods. For the study, I used the methods of logical and mathematical analyses. Results. The article formulates the rules for constructing a Leontief's input–output matrix, taking into account differences in the time of production, quantity of output, as well as the conditions for the reproduction of the resources expended. It summarizes these rules for the J. von Neumann model. Conclusions. The proposed approach to the analysis of the material mechanism of economic reproduction defines the relationship between the quantitative and cost characteristics of the production and consumption of products and resources. This relationship opens up new opportunities for the application of input–output models to create simple and accurate algorithms for identifying and predicting the macroeconomic trends.

The Standard Formulation of Quantum Mechanics

2019 ◽  
pp. 42-65
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computer ◽  
Mathematical Formalism ◽  
Standard Formulation ◽  
Central Importance ◽  
Conceptual History ◽  
Standard Interpretation ◽  
Linear Dynamics ◽  
Von Neumann ◽  
History Of

The standard von Neumann-Dirac formulation of quantum mechanics is presented as a set of five basic rules. We discuss each rule is discussed in turn paying particular attention to the conceptual history of the theory. Of central importance is the standard interpretation of states (the eigenvalue-eigenstate link) and the dynamical laws of the theory (the random collapse dynamics and the deterministic linear dynamics) and how the interpretation and dynamics work together to predict and explain the results of basic quantum experiments. While the focus is on the behavior of electrons, we also briefly consider how the theory uses the same mathematical formalism to treat other phenomena like the behavior of neutral K mesons and qbits in a quantum computer.

On a Generalized Von Neumann Model

1965 ◽  
Vol 6 (1) ◽  
pp. 115 ◽  
Author(s):  
Hanjiro Haga ◽  
Mikiro Otsuki
Keyword(s):  
Von Neumann ◽  
Neumann Model

scholarly journals Path Integrals, Spontaneous Localisation, and the Classical Limit

2020 ◽  
Vol 75 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Bhavya Bhatt ◽  
Manish Ram Chander ◽  
Raj Patil ◽  
Ruchira Mishra ◽  
Shlok Nahar ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Measurement Problem ◽  
Path Integrals ◽  
Path Integral Formulation ◽  
Von Neumann ◽  
Matrix Evolution ◽  
Grw Model

AbstractThe measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

scholarly journals Measurement theory in classical mechanics

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
So Katagiri
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Uncertainty Relation ◽  
Measurement Theory ◽  
Classical Mechanics ◽  
The State ◽  
Measurement Device ◽  
Von Neumann ◽  
Relative Interpretation ◽  
Classical And Quantum Mechanics

Abstract We investigate measurement theory in classical mechanics in the formulation of classical mechanics by Koopman and von Neumann (KvN), which uses Hilbert space. We show a difference between classical and quantum mechanics in the “relative interpretation” of the state of the target of measurement and the state of the measurement device. We also derive the uncertainty relation in classical mechanics.

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