Quantum monodromy and semi-classical trace formulæ
نویسندگان
چکیده
منابع مشابه
Quantum Monodromy and Semi-classical Trace Formulæ
Trace formulæ provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is described in terms of closed orbits of the corresponding classical Hamiltonian. In algebraic situations, such as the original Selberg trace formula, the identities ar...
متن کاملQuantum Monodromy and Semi–Classical Trace Formulae
Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is described in terms of closed orbits of the corresponding classical Hamiltonian. In algebraic situations, such as the original Selberg trace formula, the identities a...
متن کاملSemi-classical trace formulas and heat expansions
There is a strong similarity between the expansions of the heat kernel as worked out by people in Riemannian geometry in the seventies (starting with the famous “Can one hear the shape of a drum” by Mark Kac [Kac], the Berger paper [Berger] and the Mc-Kean-Singer paper [McK-Si]) and the so-called semi-classical trace formulas developed by people in semi-classical analysis (starting with Helffer...
متن کاملMonodromy and geometric phases in classical and quantum mechanics
Stuart Althorpe Geometric phase effects in reaction dynamics If a reaction path follows a closed loop that encircles a conical intersection (electronic degeneracy), then the path will acquire a geometric phase. This talk will describe recent work aimed at finding out what (if any) is the effect of this phase on the mechanism and rate of a chemical reaction. First, we discuss systems in which th...
متن کاملSemi - Classical Trace Formula , Isochronous Case
Under conditions of clean flow we compute the leading term in the STF when the set of periods of the energy surface is discrete. Comparing to the case of non-degenerate periodic orbits, we obtain a supplementary term which is given in terms of the linearized flow. As particular cases, we give a STF for quadratic Hamiltonians and we obtain the Berry-Tabor formula for integrable systems. For cons...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2002
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(01)01230-2