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A quantum central limit theorem for interacting many particle systems and its applications

Michael J. Hartmann, G. Mahler, Ortwin G. Hess

Verhandlungen der Deutschen Physikalischen GesellschaftJan 1, 20050 citations

Central limit theorem for locally interacting Fermi gas

Vojkan Jakšić, Yan Pautrat, Claude‐Alain Pillet

We consider a locally interacting Fermi gas in its natural non-equilibrium steady state and prove the Quantum Central Limit Theorem (QCLT) for a large class of observables. A special case of our results concerns finitely many free Fermi gas reservoirs coupled by local interactions. The QCLT for flux observables, together with the Green-Kubo formulas and the Onsager reciprocity relations previously established [JOP4], complete the proof of the Fluctuation-Dissipation Theorem and the development of linear response theory for this class of models. Central limit theorem for locally interacting Fermi gas 2 1We consider a locally interacting Fermi gas in its natural non-equilibrium steady state and prove the Quantum Central Limit Theorem (QCLT) for a large class of observables. A special case of our results concerns finitely many free Fermi gas reservoirs coupled by local interactions. The QCLT for flux observables, together with the Green-Kubo formulas and the Onsager reciprocity relations previously established [JOP4], complete the proof of the Fluctuation-Dissipation Theorem and the development of linear response theory for this class of models. Central limit theorem for locally interacting Fermi gas 2 1

Jan 1, 20070 citations

Experiments with Interacting Fermi Gases

John E. Thomas

Bulletin of the American Physical SocietyMay 22, 20090 citations

On the Algebra of Fluctuation in Quantum Spin Chains.

Taku Matsui

We present a proof of the central limit theorem for a pair of mutually noncommuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction of the time evolution of the algebra of normal fluctuation for Gibbs states of finite range interactions on a one-dimensional lattice. We show that the state of the algebra of normal fluctuation satisfies the β-KMS condition if the microscopic state is a β-KMS state. We show that any mixing finitely correlated state satisfies our assumption for the central limit theorem. KEY WORDS: central limit theorem; KMS states; quantum spin chainWe present a proof of the central limit theorem for a pair of mutually noncommuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction of the time evolution of the algebra of normal fluctuation for Gibbs states of finite range interactions on a one-dimensional lattice. We show that the state of the algebra of normal fluctuation satisfies the β-KMS condition if the microscopic state is a β-KMS state. We show that any mixing finitely correlated state satisfies our assumption for the central limit theorem. KEY WORDS: central limit theorem; KMS states; quantum spin chain

Jan 1, 200219 citations

Markov limit for a quantum particle interacting with a Fermi gas

A. Sh. Domnenkov

Theoretical and Mathematical PhysicsMay 1, 19891 citation

A convergent virial expansion for the quantum Lorentz gas with point interactions

C Carvalho

The author studies the quantum Lorentz gas with point interactions. The author uses the explicit form of the resolvent of this system to set up an expansion for the pressure and the central limit theorem to sum the many random contributions to the scattering of the light particle due to the heavy particles. The author also discusses the convergence of the expansion.

Journal of Physics A Mathematical and GeneralMar 21, 19901 citation

Central Limit Theorem for Locally Interacting Fermi Gas

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