What is the limit ℏ→0\hbar \to 0 of quantum theory ?

An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown that Schr\"odinger's equation for a single particle moving in an external potential $V$ does not, except in special cases, lead, in this limit, to Newton's equation of motion for the particle. This shows that classical mechanics cannot be regarded as emerging from quantum mechanics-at least in this sense-upon straightforward application of the limit $\hbar \to 0$.Comment: 12 pages, no figure

Berry phase, topology, and diabolicity in quantum nano-magnets

A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.Comment: 4 pages, 3 figure

Relationship between brachycephalic airway syndrome and gastrointestinal signs in three breeds of dog

Objectives: To assess the breed-specific prevalence of, and effects of corrective airway surgery on, gastrointestinal signs in French bulldogs, English bulldogs and pugs presenting with brachycephalic airway syndrome to a referral teaching hospital. Materials and Methods: In this retrospective study, ptyalism, regurgitation and vomiting were graded at presentation using a previously established scoring system. Staphylectomy and nares resection were performed on all dogs. Gastrointestinal signs were re-assessed via telephone follow-up at least 6 weeks after surgery. Results: Ninety-eight dogs were included: French bulldogs (n=43), English bulldogs (n=12) and pugs (n=43). Overall population prevalence of all gastrointestinal signs was 56%. Breed-specific prevalence for French bulldogs was 93%, English bulldogs 58% and pugs 16%. There was post-surgical clinical improvement in gastrointestinal signs for the whole study population, especially in French bulldogs. Clinical Significance: The prevalence of gastrointestinal signs in dogs presenting with brachycephalic airway syndrome and improvement in these clinical signs following corrective surgery may vary between breeds

Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models

We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of non-interacting Brownian particles in steady flow.Comment: 6 pages, submitted to PR

Number-of-particle fluctuations in systems with Bose-Einstein condensate

Fluctuations of the number of particles for the dilute interacting gas with Bose-Einstein condensate are considered. It is shown that in the Bogolubov theory these fluctuations are normal. The fluctuations of condensed as well as noncondensed particles are also normal both in canonical and grand canonical ensembles.Comment: Latex file, 12 page

Relative momentum for identical particles

Possible definitions for the relative momentum of identical particles are considered

Spectroscopy on two coupled flux qubits

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a $\sigma_1^z\sigma_2^z$ interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the magnetic field applied we observe the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance

Optimal trap shape for a Bose gas with attractive interactions

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.Comment: Latex file, 21 page

Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.Comment: 4 pages, 1 figure, 1 tabl