A semiclassical study of the Jaynes-Cummings model

We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to the physics of cold atom systems, in non-equilibrium situations obtained by fast sweeping through a Feshbach resonance. We show that in this integrable system with two degrees of freedom, for any initial condition close to the unstable point, the classical dynamics is controlled by a singularity of the focus-focus type. In particular, it displays the expected monodromy, which forbids the existence of global action-angle coordinates. Explicit calculations of the joint spectrum of conserved quantities reveal the monodromy at the quantum level, as a dislocation in the lattice of eigenvalues. We perform a detailed semi-classical analysis of the associated eigenstates. Whereas most of the levels are well described by the usual Bohr-Sommerfeld quantization rules, properly adapted to polar coordinates, we show how these rules are modified in the vicinity of the critical level. The spectral decomposition of the classically unstable state is computed, and is found to be dominated by the critical WKB states. This provides a useful tool to analyze the quantum dynamics starting from this particular state, which exhibits an aperiodic sequence of solitonic pulses with a rather well defined characteristic frequency.Comment: pdfLaTeX, 51 pages, 19 figures, references added and improved figure captions. To appear in J. Stat. Mec

Polyakov conjecture and 2+1 dimensional gravity coupled to particles

A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical defects. Its relevance to the hamiltonian structure of 2+1 dimensional gravity in the maximally slicing gauge is stressed.Comment: Talk by P. Menotti at Int. Europhysics Conference on High Energy Physics, Budapest 12-18 July 2001, 5 pages late

Semiclassical and quantum Liouville theory

We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere on the background of three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and of the further perturbative corrections. The zeta function regularization provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseudosphere by Zamolodchikov and Zamolodchikov we obtain the correct quantum conformal dimensions from the one loop calculation and we show explicitly that the two loop corrections do not change such dimensions. We then apply the method to the case of the pseudosphere with one finite singularity and compute the exact value for the quantum determinant. Such results are compared to those of the conformal bootstrap approach finding complete agreement.Comment: 12 pages, 1 figure, Contributed to 5th Meeting on Constrained Dynamics and Quantum Gravity (QG05), Cala Gonone, Sardinia, Italy, 12-16 Sep 200

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the paper more concise (see v1 for the longer version), minor correction in a formula in the section on quantization, references added; results and conclusions unchange

Duration of remission after halving of the etanercept dose in patients with ankylosing spondylitis: a randomized, prospective, long-term, follow-up study

Fabrizio Cantini, Laura Niccoli, Emanuele Cassarà, Olga Kaloudi, Carlotta NanniniDivision of Rheumatology, Misericordia e Dolce Hospital, Prato, ItalyBackground: The aim of this study was to evaluate the proportion of patients with ankylosing spondylitis maintaining clinical remission after reduction of their subcutaneous etanercept dose to 50 mg every other week compared with that in patients receiving etanercept 50 mg weekly.Methods: In the first phase of this randomized, prospective, follow-up study, all biologic-naïve patients identified between January 2005 and December 2009 as satisfying the modified New York clinical criteria for ankylosing spondylitis treated with etanercept 50 mg weekly were evaluated for disease remission in January 2010. In the second phase, patients meeting the criteria for remission were randomized to receive subcutaneous etanercept as either 50 mg weekly or 50 mg every other week. The randomization allocation was 1:1. Remission was defined as Bath Ankylosing Spondylitis Disease Activity Index < 4, no extra-axial manifestations of peripheral arthritis, dactylitis, tenosynovitis, or iridocyclitis, and normal acute-phase reactants. The patients were assessed at baseline, at weeks 4 and 12, and every 12 weeks thereafter. The last visit constituted the end of the follow-up.Results: During the first phase, 78 patients with ankylosing spondylitis (57 males and 21 females, median age 38 years, median disease duration 12 years) were recruited. In January 2010, after a mean follow-up of 25 ± 11 months, 43 (55.1%) patients achieving clinical remission were randomized to one of the two treatment arms. Twenty-two patients received etanercept 50 mg every other week (group 1) and 21 received etanercept 50 mg weekly (group 2). At the end of follow-up, 19 of 22 (86.3%) subjects in group 1 and 19 of 21 (90.4%) in group 2 were still in remission, with no significant difference between the two groups. The mean follow-up duration in group 1 and group 2 was 22 ± 1 months and 21 ± 1.6 months, respectively.Conclusion: Remission of ankylosing spondylitis is possible in at least 50% of patients treated with etanercept 50 mg weekly. After halving of the etanercept dose, remission is maintained in a high percentage of patients during long-term follow-up, with important economic implications.Keywords: ankylosing spondylitis, anti-tumor necrosis factor, etanercept, remission, dose reductio

Algebraic Bethe Ansatz for the two species ASEP with different hopping rates

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans. We present also formulas for the total velocity of particles of a given type and their limit for large size of the system and finite densities of the particles.Comment: 14 page

First test of a high voltage feedthrough for liquid Argon TPCs connected to a 300 kV power supply

Voltages above a hundred kilo-volt will be required to generate the drift field of future very large liquid Argon Time Projection Chambers. The most delicate component is the feedthrough whose role is to safely deliver the very high voltage to the cathode through the thick insulating walls of the cryostat without compromising the purity of the argon inside. This requires a feedthrough that is typically meters long and carefully designed to be vacuum tight and have small heat input. Furthermore, all materials should be carefully chosen to allow operation in cryogenic conditions. In addition, electric fields in liquid argon should be kept below a threshold to reduce risks of discharges. The combination of all above requirements represents significant challenges from the design and manufacturing perspective. In this paper, we report on the successful operation of a feedthrough satisfying all the above requirements. The details of the feedthrough design and its manufacturing steps are provided. Very high voltages up to unprecedented voltages of -300 kV could be applied during long periods repeatedly. A source of instability was observed, which was specific to the setup configuration which was used for the test and not due to the feedthrough itself.Comment: 13 pages, 9 figure