Learning About Classical Limit from an Integrable Two Spin System
نویسندگان
چکیده
It is shown how the simple two spin system viewed as a possible paradigm to study the properties of generic classical integrable systems with two degrees of freedom has quan tum characteristics that make it suitable to illustrate those properties also in the quantum domain We concentrate on quantum mechanical results and explore these characteristics to solve the problem to point out how this system permits a controllable approximation to the classical limit and to clarify some misleading associations concerning classical limit quantum numbers and energy levels
منابع مشابه
Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit
We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i. e. it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantisation without altering the classical limit of the dynamics on the torus, we numerically observe a transition...
متن کاملIntegrability and action operators in quantum Hamiltonian systems.
For a (classically) integrable quantum-mechanical system with two degrees of freedom, the functional dependence H=HQ(J1,J2) of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship H(p1,q1;p2,q2)=HC(J1,J2) in the classical limit of that system. The former converges toward the latter in some asymptotic regime associated with the ...
متن کاملLarge N Limit of Integrable Models
We consider a large N limit of the Hitchin type integrable systems. The first system is the elliptic rotator on GLN that corresponds to the Higgs bundle of degree one over an elliptic curve with a marked point. This system is gauge equivalent to the N -body elliptic Calogero-Moser system, that is derived from the Higgs bundle of degree zero over the same curve. The large N limit of the former s...
متن کاملDensity-functional theory simulation of large quantum dots
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electronelectron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particlein-the-box representation of the Kohn-Sham orbitals, an efficient conju...
متن کاملCritical behaviour of integrable mixed spins chains
We construct a mixed spin 1/2 and S integrable model and investigate its finite size properties. For a certain conformal invariant mixed spin system the central charge can be decomposed in terms of the conformal anomaly of two single integrable models of spin 1/2 and spin (S − 1/2). We also compute the ground state energy and the sound velocity in the thermodynamic limit. Published in J.Phys.A:...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007