Appendix: A connection between quantum systems and stochastic processes

1984 ◽  
pp. 206-209
Author(s):  
Luigi Accardi ◽  
Alberto Frigerio ◽  
Vittorio Gorini
Keyword(s):  
Stochastic Processes ◽  
Quantum Systems

Can One Validly Use Classical Statistical Inference in Open Quantum Systems?

2010 ◽  
Vol 17 (04) ◽  
pp. 311-330
Author(s):  
Mallén Arenas ◽  
Rolando Rebolledo
Keyword(s):  
Stochastic Processes ◽  
Statistical Inference ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Measurement Process ◽  
Suitable Choice ◽  
Markov Semigroups ◽  
Open Quantum ◽  
Classical Reduction ◽  
Consistent Approach

A major problem to perform statistical inference in open quantum systems is the perturbation induced by the measurement process. However, at least theoretically, a suitable choice of the measurement process could provide a consistent approach through classical stochastic processes. This work proposes a method to perform statistical inference on open quantum systems represented by quantum Markov semigroups having a suitable classical reduction. The method is based on measurements associated to observables generating invariant abelian algebras.

BOOK REVIEW: "AN INTRODUCTION TO THE MATHEMATICAL STRUCTURE OF QUANTUM MECHANICS, A SHORT COURSE FOR MATHEMATICIANS", BY F. STROCCHI

2009 ◽  
Vol 07 (03) ◽  
pp. 697-700
Author(s):  
WAYNE LAWTON
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Mathematical Structure ◽  
Quantum Systems ◽  
Quantum Theories ◽  
Algebra Of Observables ◽  
Short Course ◽  
Specific Quantum

This book provides a concise introduction to quantum mechanics for students versed in mathematics and mechanics. Dr Strocchi imparts a holistic perspective of the quantum landscape by focussing on three concepts: the algebra of observables, basic quantum systems, and stochastic processes. After mastering these concepts, readers are prepared to study specific quantum theories of information, statistical mechanics, and fields.

scholarly journals Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems

2010 ◽  
Vol 105 (1) ◽  
Author(s):  
H.-P. Stimming ◽  
N. J. Mauser ◽  
J. Schmiedmayer ◽  
I. E. Mazets
Keyword(s):  
Stochastic Processes ◽  
Quantum Systems ◽  
Many Body ◽  
One Dimensional

scholarly journals Quantum systems for Monte Carlo methods and applications to fractional stochastic processes

2019 ◽  
Vol 534 ◽  
pp. 121901
Author(s):  
Sebastian F. Tudor ◽  
Rupak Chatterjee ◽  
Lac Nguyen ◽  
Yuping Huang
Keyword(s):  
Monte Carlo ◽  
Stochastic Processes ◽  
Monte Carlo Methods ◽  
Quantum Systems

scholarly journals Investigating Information Geometry in Classical and Quantum Systems through Information Length

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 574 ◽  
Author(s):  
Eun-jin Kim
Keyword(s):  
Stochastic Processes ◽  
Information Geometry ◽  
Quantum Systems ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Density Functions ◽  
Mathematical Tool ◽  
Initial Condition ◽  
Disciplinary Boundaries ◽  
Information Change

Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.

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