16 research outputs found
Quantum NOT operation and integrability in two-level systems
No full textAbstract We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different ''average'' systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps
Onsager’s inequality, the Landau–Feynman ansatz and superfluidity
No full textWe revisit an inequality due to Onsager, which states that the (quantum) liquid structure factor has an upper bound of the form (const) × |k|, for not too large modulus of the wave vector k. This inequality implies the validity of the Landau criterion in the theory of superfluidity with a definite, nonzero critical velocity. We prove an auxiliary proposition for general Bose systems, together with which we arrive at a rigorous proof of the inequality for one of the very few solvable examples of an interacting Bose fluid, Girardeau’s model. The latter proof demonstrates the importance of the thermodynamic limit of the structure factor, which must be taken initially at k = 0. It also substantiates very well the heuristic density functional arguments, which are also shown to hold exactly in the limit of large wavelengths. We also briefly discuss which features of the proof may be present in higher dimensions, as well as some open problems related to superfluidity of trapped gases. PACS numbers: 67.40.−w, 67.40.Db 1
Upper quantum Lyapunov exponent and parametric oscillators
No full textInternational audienceWe introduce a definition of upper Lyapunov exponent for quantum systems in the Heisenberg representation, and apply it to parametric quantum oscillators. We provide a simple proof that the upper quantum Lyapunov exponent ranges from zero to a positive value, as the parameters range from the classical system’s region of stability to the instability region. It is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum Anosov relations defined by Emch, Narnhofer, Sewell, and Thirring
A Trotter-Kato product formul for a class of non-autonomous evolution equations
No full textInternational audienc
CAUSAL APPROACH TO (2+1)-DIMENSIONAL QED
No full textIt is shown that the causal approach to (2 + 1)-dimensional quantum electrodynamics yields a well-defined perturbative theory. In particular, and in contrast to renormalized perturbative quantum field theory, it is free of any ambiguities and ascribes a nonzero value to the dynamically generated, nonperturbative photon mass. (C) 1994 Academic Press, Inc.UNESP,INST FIS TEOR,BR-01405 SAO PAULO,BRAZILUNIV SAO PAULO,INST FIS,BR-01498 SAO PAULO,BRAZILUNESP,INST FIS TEOR,BR-01405 SAO PAULO,BRAZI
