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Andrei Khrennikov

Professor, Subject Representative
Department of Mathematics Faculty of Technology
+46 470 70 87 90
Hus B 2049
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Andrei Khrennikov is Professor of Mathematics at the Department of Mathematics at Linnaeus University. Andrei is also director of the research group International Center for Mathematical Modeling (ICMM) and organizer of some 20 conferences in the field of quantum theory at Linnaeus University.

My research activity can be characterized as extensively multi-disciplinary. (Sometimes I am surprised by myself that all these diverse studies covering so different areas of science were done by the same person.) The research activities are split in the basic disciplines: Mathematics, physics, and biology, cognition, psychology and behavioral economics.

Mathematics, pure and applied

  • Infinite-Dimensional Analysis and Feynman Integration
  • Functional Superanalysis
  • P-adic and non-Archimedean Analysis, the Q_p to Q_p
  • P-adic dynamical systems
  • P-adic and Ultrametric Analysis, Wavelets, Distributions, Pseudo-differential Operators, the Q_p to C case;
  • Foundations of Probability Theory

Physics, mathematical and theoretical

  • Quantization of systems with infinite number of degrees of freedom
  • Quantization of p-adic and non-Archimedean physical systems
  • Probabilistic foundations of quantum mechanics and Bell’s inequality
  • Classical random field model of quantum mechanics

Biology, cognition, psychology and behavioral economics

  • Quantum-like models: molecular biology, cognition, psychology, behavioral economics, social science
  • Econophysics: modeling of price dynamics on the basis of expectations of traders of the financial market
  • P-adic dynamical models of cognitive and biological processes

The quantum theory conferences in Växjö

The Växjö series of quantum theory conferences is arranged by ICMM, International Center for Mathematical Modeling in physics, engineering and cognitive sciences, at Linnaeus University in Växjö, Sweden. It is devoted to quantum foundations, information and novel quantum technologies (cryptography, random generators, imaging, computing) and probabilistic foundations. The main point is that quantum mechanics is essentially about a novel representation of probabilistic data and predictions about the results of random experiments.  

This is the longest continuous series of conferences on quantum foundations since the creation of quantum mechanics.  It was started in 2000 and goes on annually. This series was generated by the revolution in quantum information theory at the end of the 20th century.

The series of conferences can be characterized by two distinguishing features:

A). Openness for expression of opinions on the origin or problems of quantum mechanical foundations and their relation to the problems of probability theory and the possible ways of their resolution.

B). Creation of actively interacting mixture of top experts in theory and experiments and even a few philosophers.

From this viewpoint this conference-series is definitely unique. One cannot find anything similar anywhere in the world. At the first stage, I even try to involve pure mathematicians to create knowledge transfer between mathematics and physics.

More about the conference series

Experimenters working in quantum optics and neutron interferometry, quantum information technologies represent an important part of the team of invited speakers. In general, the conferences are planned as events unifying the efforts of experts in foundations, mathematical methods, and experimenters to clarify the fundamental questions of quantum theory and its future applications.

Historically, I can mention Christopher Fuchs as one of the creators of the series. In 2001 he came to Växjö with the great team, including Asher Pers, David Mermin, Daniel Greenberger, Lev Vaidman, Carlton Caves, Richard Josza, Lucien Hardy, Hery Folse, Arkady Plotnitsky and other bright physicists and philosophers. This event lifted the conference status enormously and attracted other top experts with the interest to quantum foundations, especially from USA. I also point to the "Austrian-branch" of the conference organizational efforts. Here Helmut Rauch and Gregor Weihs contributed a lot, during the last years the active participation of Anton Zeilinger and people from his lab also played the important role.

I also want to mention the stormy debates between Richard Gill and Jan-Åke Larsson from one side and Luigi Accardi and later also Karl Hess and Walter Philipp from another side during the initial stage of the conference series which were extremely important for clarification of positions of various groups of experts with respect the probabilistic structure of violations of Bell's inequality.

The participation of Gerard ´t Hooft supported essentially the position of researchers rejecting the conventional interpretation of quantum mechanics.

Växjö definitely played the crucial role in development of QBism. Here the Bayesian approach to quantum probabilities was actively advertised and debated.

Växjö-presentations also contributed a lot to development of the information approach to quantum theory by Mauro D'Ariano and his students.

I personally enjoyed lectures of Arkady Plotnitsky about views of Born, Heisenberg, and Schrödinger and recently Pauli. Nowadays not so many even experts read the original sources, so such lecturing is useful.

I really appreciate recent efforts of Alan Migdall and Sergey Polyakov from NIST, USA, to organize the top level experimental sessions.

Of course, the Växjö-series of conferences is the project of the great complexity and not without problems. For example, consider openness. Here I have to filter originality of mind from craziness. In some cases this is really a difficult task, because the difference is tinny, especially in the case of quantum foundations.

Another problem, at least for some physicists, that there are "too many philosophers". (In fact, they are one-three...) Some theoreticians are angry that there are too many experimental talks and so on. However, in general people are satisfied and many of them come to Växjö again and again.

Films from the conferences

Social laser in action: from color revolutions to brexit and Donald Trump

Presentation by Andrei Khrennikov (Linnaeus University, Sweden) from the Foundations of Quantum Mechanics and Technology 2017 conference

Note on entropy for quantum dynamical systems

Presentation by Noboru Watanabe (Tokyo University of Science, Japan) from the Foundations of Quantum Mechanics and Technology 2017 conference

Issues of quantum-inspired information access and retrieval

Presentation by Massimo Melucci (University of Padua, Italy) from the Foundations of Quantum Mechanics and Technology 2017 conference

Closing the door on Einstein and Bohr's quantum debate

Presentation by P Grangier (Quantum Optics, Lab. Charles Fabry, France) from the Quantum and Beyond 2016 conference

Violation of Bell's inequality under strict Einstein locality conditions

Presentation by G Weihs (University of Innsbruck, Austria) from the Quantum and Beyond 2016 conference

From the first loophole-free Bell test to a quantum Internet

Presentation by R Hanson (Delft University of Technology, the Netherlands) from the Quantum and Beyond 2016 conference

Significant loophole-free test of local realism with entangled photons

Presentation by M Giustina (University of Vienna/IQOQI Vienna, Austria) and M Versteegh (KTH Royal Institute of Technology, Sweden) from the Quantum and Beyond 2016 conference

A strong loophole-free test of Bell's inequalities

Presentation by K Shalm (National Institute of Standards and Technologies, USA) from the Quantum and Beyond 2016 conference

Event-ready loophole-free Bell test using heralded atom-atom entanglement

Presentation by H Weinfurter (LMU Munich, Germany) from the Quantum and Beyond 2016 conference

Violation of Bell's inequalities in a quantum realistic framework

Presentation by P Grangier, (CNRS, France) from the Quantum and Beyond 2016 conference

The future of Bell experiments

Presentation by A Zeilinger (Austrian Academy of Sciences, Austria) from the Quantum and Beyond 2016 conference


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