Grant: Discovery Grants Program - Individual
Memorial University of Newfoundland
$14,500.00
Mathematics of open quantum systems
EF 2011-12
Résumé
Any quantum mechanical system must be regarded as being in constant interactions with an environment. This is due to two facts: Firstly, it is impossible to isolate completely a system from its surroundings (which cannot be controlled in general, and which influence the system in a non-negligible way). Secondly, any observation of a quantum mechanical system is brought about by an interaction with an environment (measuring device). It is therefore not surprising that the theory of open quantum systems, which analyzes environment-induced effects on systems, receives much attention in mathematical physics.
The rigorous theory of open quantum systems is currently experiencing significant progress. The main driving force is the development of suitable modern mathematical tools. Those tools are situated at the intersection of spectral theory of evolution groups, the theory of operator algebras, scattering theory, the theory of quantum resonances, and quantum field theory. Modern applications are found in quantum computing, quantum information theory and the theory of quantum measurement.
A recently developed, new approach to the topic has allowed us to obtain a precise, quantifyable description of the process of return to equilibrium (stability of equilibria), and it has explained the emergence and the properties of asymptotic states far from equilibrium. An important achievement of this theory for physics is the derivation of macroscopic laws of thermodynamics and electricity, starting from a microscopic, hamiltonian quantum statistical description of the system. These laws are expressed as relations bewteen quantities such as temperature, entropy, density, and fluxes of heat and of charge.
The research proposed in this project will further develop, extend and solidify the mathematical theory of open quantum systems. This is done by considering new classes of physical models and by developing new mathematical techniques. The results are of interest to a wide variety of mathematicians and physicists.
Programme
Discovery Grants Program - Individual
Bénéficiaire
Emplacement
Newfoundland and Labrador, Canada
Type de bénéficiaire
Academia
Type
Grant
Source
NSERC's Awards Data
Tel que publié
Application id
341184-2007
Name nom
Merkli, Marco
Department département
Mathematics and Statistics
Organization id
89
Institution établissement
Memorial University of Newfoundland
Province en
Newfoundland and Labrador
Province fr
Terre-Neuve-et-Labrador
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2011
Competition year année de concours
2007
Award amount
14500
Program id
RGPIN
Program nane en
Discovery Grants Program - Individual
Program name fr
Programme de subventions à la découverte - individuelles
Group en
Discovery grants programs
Group fr
Programmes de subventions à la découverte
Committee code
337
Committee name en
Pure & Applied Maths - B
Committee name fr
Maths pures et appliquées - B
Area of application code
1205
Area of application group en
Advancement of knowledge
Area of application group fr
Avancement des connaissances
Area of application en
Mathematical sciences
Area of application fr
Sciences mathématiques
Research subject code
2958
Research subject group en
Applied mathematics
Research subject group fr
Mathématiques appliquées
Research subject en
Mathematical physics
Research subject fr
Mathématiques de la physique
Partie
5
Nb partie
5
Application title
Mathematics of open quantum systems
Keyword
NSERC
Application summary
Any quantum mechanical system must be regarded as being in constant interactions with an environment. This is due to two facts: Firstly, it is impossible to isolate completely a system from its surroundings (which cannot be controlled in general, and which influence the system in a non-negligible way). Secondly, any observation of a quantum mechanical system is brought about by an interaction with an environment (measuring device). It is therefore not surprising that the theory of open quantum systems, which analyzes environment-induced effects on systems, receives much attention in mathematical physics.
The rigorous theory of open quantum systems is currently experiencing significant progress. The main driving force is the development of suitable modern mathematical tools. Those tools are situated at the intersection of spectral theory of evolution groups, the theory of operator algebras, scattering theory, the theory of quantum resonances, and quantum field theory. Modern applications are found in quantum computing, quantum information theory and the theory of quantum measurement.
A recently developed, new approach to the topic has allowed us to obtain a precise, quantifyable description of the process of return to equilibrium (stability of equilibria), and it has explained the emergence and the properties of asymptotic states far from equilibrium. An important achievement of this theory for physics is the derivation of macroscopic laws of thermodynamics and electricity, starting from a microscopic, hamiltonian quantum statistical description of the system. These laws are expressed as relations bewteen quantities such as temperature, entropy, density, and fluxes of heat and of charge.
The research proposed in this project will further develop, extend and solidify the mathematical theory of open quantum systems. This is done by considering new classes of physical models and by developing new mathematical techniques. The results are of interest to a wide variety of mathematicians and physicists.
