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This volume aims to return to the starting point of the fields of
infinite dimensional analysis and quantum probability, fields that
are growing rapidly at present, and to seriously attempt mutual
interaction between the two, with a view to enumerating and solving
the many fundamental problems they entail. For such a purpose, we
look for interdisciplinary bridges in mathematics including
classical probability and to different branches of physics, in
particular, research for new paradigms for information science on
the basis of quantum theory.
This volume is to pique the interest of many researchers in the
fields of infinite dimensional analysis and quantum probability.
These fields have undergone increasingly significant developments
and have found many new applications, in particular, to classical
probability and to different branches of physics. These fields are
rather wide and are of a strongly interdisciplinary nature. For
such a purpose, we strove to bridge among these interdisciplinary
fields in our Workshop on IDAQP and their Applications that was
held at the Institute for Mathematical Sciences, National
University of Singapore from 3-7 March 2014. Readers will find that
this volume contains all the exciting contributions by well-known
researchers in search of new directions in these fields.
This volume is based on the fifth international conference of
quantum bio-informatics held at the QBI Center of Tokyo University
of Science.This volume provides a platform to connect mathematics,
physics, information and life sciences, and in particular, research
for new paradigm for information science and life science on the
basis of quantum theory.The following topics are discussed:
This volume contains the current research in quantum probability,
infinite dimensional analysis and related topics. Contributions by
experts in these fields highlight the latest developments and
interdisciplinary connections with classical probability,
stochastic analysis, white noise analysis, functional analysis and
quantum information theory.This diversity shows how research in
quantum probability and infinite dimensional analysis is very
active and strongly involved in the modern mathematical
developments and applications.Tools and techniques presented here
will be of great value to researchers.
The purpose of this proceedings volume is to return to the starting
point of bio-informatics and quantum information, fields that are
growing rapidly at present, and to seriously attempt mutual
interaction between the two, with a view to enumerating and solving
the many fundamental problems they entail. For such a purpose, we
look for interdisciplinary bridges in mathematics, physics,
information and life sciences, in particular, research for new
paradigm for information science and life science on the basis of
quantum theory.
This volume seeks to return to the starting point of
bio-informatics and quantum information, where these fields are
constantly engaged in explosive advancements, and to seriously
attempt mutual interaction between the two fields, with a view to
enumerating and solving the many encountered fundamental problems.
For such a purpose, we look for interdisciplinary bridges in
mathematics, physics, information and life sciences, in particular,
the research for a new paradigm for information science and life
science on the basis of quantum theory.
Recent Developments in Infinite-Dimensional Analysis and Quantum
Probability is dedicated to Professor Takeyuki Hida on the occasion
of his 70th birthday. The book is more than a collection of
articles. In fact, in it the reader will find a consistent
editorial work, devoted to attempting to obtain a unitary picture
from the different contributions and to give a comprehensive
account of important recent developments in contemporary white
noise analysis and some of its applications. For this reason, not
only the latest results, but also motivations, explanations and
connections with previous work have been included. The wealth of
applications, from number theory to signal processing, from optimal
filtering to information theory, from the statistics of stationary
flows to quantum cable equations, show the power of white noise
analysis as a tool. Beyond these, the authors emphasize its
connections with practically all branches of contemporary
probability, including stochastic geometry, the structure theory of
stationary Gaussian processes, Neumann boundary value problems, and
large deviations.
The subject of this book is a new mathematical technique, the stochastic limit, developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules"), which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution, and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques.
Recent Developments in Infinite-Dimensional Analysis and Quantum
Probability is dedicated to Professor Takeyuki Hida on the occasion
of his 70th birthday. The book is more than a collection of
articles. In fact, in it the reader will find a consistent
editorial work, devoted to attempting to obtain a unitary picture
from the different contributions and to give a comprehensive
account of important recent developments in contemporary white
noise analysis and some of its applications. For this reason, not
only the latest results, but also motivations, explanations and
connections with previous work have been included. The wealth of
applications, from number theory to signal processing, from optimal
filtering to information theory, from the statistics of stationary
flows to quantum cable equations, show the power of white noise
analysis as a tool. Beyond these, the authors emphasize its
connections with practically all branches of contemporary
probability, including stochastic geometry, the structure theory of
stationary Gaussian processes, Neumann boundary value problems, and
large deviations.
These proceedings of the workshop on quantum probability held in
Heidelberg, September 26-30, 1988 contains a representative
selection of research articles on quantum stochastic processes,
quantum stochastic calculus, quantum noise, geometry, quantum
probability, quantum central limit theorems and quantum statistical
mechanics.
This volume, the fourth of the quantum probability series, collects
part of the contributions to the Year of Quantum Probability
organized by the Volterra Center of University of Rome II. The
intensive communication among researchers during this Year allowed
several open problems to be solved and several inexpected
connections to be revealed.
These proceedings of the first Quantum Probability meeting held in
Oberwolfach is the fourth in a series begun with the 1982 meeting
of Mondragone and continued in Heidelberg ('84) and in Leuven
('85). The main topics discussed were: quantum stochastic calculus,
mathematical models of quantum noise and their applications to
quantum optics, the quantum Feynman-Kac formula, quantum
probability and models of quantum statistical mechanics, the notion
of conditioning in quantum probability and related problems
(dilations, quantum Markov processes), quantum central limit
theorems. With the exception of K mmerer's review article on
Quantum Markov Processes, all contributions are original research
papers.
This proceedings volume gathers selected, peer-reviewed papers
presented at the 41st International Conference on Infinite
Dimensional Analysis, Quantum Probability and Related Topics (QP41)
that was virtually held at the United Arab Emirates University
(UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021.
The works cover recent developments in quantum probability and
infinite dimensional analysis, with a special focus on applications
to mathematical physics and quantum information theory. Covered
topics include white noise theory, quantum field theory, quantum
Markov processes, free probability, interacting Fock spaces, and
more. By emphasizing the interconnection and interdependence of
such research topics and their real-life applications, this reputed
conference has set itself as a distinguished forum to communicate
and discuss new findings in truly relevant aspects of theoretical
and applied mathematics, notably in the field of mathematical
physics, as well as an event of choice for the promotion of
mathematical applications that address the most relevant problems
found in industry. That makes this volume a suitable reading not
only for researchers and graduate students with an interest in the
field but for practitioners as well.
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