Research

Research activities and interest

Non-perturbative properties of energy eigenfunctions: studied by a generalized Brillouin-Wigner perturbation theory.

Energy eigenstates as pointer states in systems with weak coupling to environment:Proof is given for a generic coupling and a generic chaotic environment.

A semiclassical approach to the sensitivity of quantum motion near quantum phase transitions

Quantum Loschmidt echo or fidelity decay in classically chaotic and regular systems.Main achievements: a uniform semiclassical approach to fidelity decay in systems with weak chaos in the classical limit, a general semiclassical expression for fidelity
decay in the Lyapunov regime of systems with chaotic classical limit, semiclassical expressions of fidelity decay in regular systems.

A generalized perturbation theory and its application to energy eigenfunctions (EFs)and to local spectral density of states (LDOS) in classically chaotic and mixed-type systems. Including: separation of EFs into non-perturbative and perturbative (tail) parts, statistics of EFs in their non-perturbative parts, dynamical localization, and renormalized Hamiltonians for the non-perturbative parts of EFs; structural properties and a scaling property of LDOS.
Universal statistics for ratios of components of energy eigenfunctions in disordered and classically chaotic systems. Manifestations of the destruction of integrability, in particular in the neighborhood of avoided level crossings.

Study of decoherence and pointer states of systems in relatively weak interaction withenvironments, Natural Science Foundation of China, No. 10975123, 2010-2012.

Study of solid-state quantum computation based on the control of nuclear spin , subtopic:Study of quantum computation of solid-state ensemble based on the coherenceof nuclear and electron spins , the National Fundamental Research Programme of China Grant No.2007CB925200, 2007-2012.

Stability of the motion of quantum regular systems under small perturbation, Natural Science Foundation of China, No. 10775123, 2008-2010.

Division of energy eigenfunctions into perturbative and nonperturbative parts and their properties, Natural Science Foundation of China, No. 10275011, 2003-2005.

Chaos and related dynamics, National Basic Research Project, “Nonlinear Science”,China, 1997-2000.

Stability of Quantum Motion: Beyond Fermi-golden-rule, contributed talk, at “Dynamics Days Asia-Pacific 2004: 3rd International Conference on Nonlinear Science”,Singapore, June 2004.

Stability of the evolution of a Bose-Einstein condensation, contributed talk, at “1st International Workshop on transmission of information and energy in nonlinear and complex systems”, Singapore, August, 2006.

Stability of quantum motion under small perturbation: decoherence and energy eigenstates,invited talk, at “2007 autumn conference of Chinese physical society”, Nanjing,China, September 2007.

Decoherence, energy eigenstates, and foundations of statistical physics, invited talk,at “the 3rd Cross-Strait Conference on Statistical Physics”, Hangzhou, China, November 2007.

Study of a problem in the foundations of statistical physics from the viewpoint of decoherence, invited talk, at “2008 autumn conference of Chinese physical society”,Jinan, China, September 2008.

A quantum theory for a total system including a measuring apparatus, contributedtalk, at “The International Conference on Quantum Foundation and Technology:Frontier and Future”, Shanghai, China, July 2009.