We consider a three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point separating the magnetically ordered and the magnetically disordered phases. A specific example is TlCuCl 3 where the quantum phase transition can be driven by hydrostatic pressure and/or by external magnetic field. As expected, two transverse and one longitudinal magnetic excitations have been observed in the pressure-driven magnetically ordered phase. According to the experimental data, the longitudinal magnon has a substantial width, which has not been understood and has remained a puzzle. In the present work, we explain the mechanism for the width, calculate the width and relate the value of the width with the parameters of the Bose condensate of magnons observed in the same compound. The method of an effective quantum field theory is employed in the work.

We consider a 3-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter g. Starting from the magnetically ordered phase, the Néel temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behaviour near the QCP. We compare our results with available data for T lCuCl3.The subject of continuous Quantum Phase Transitions (QPT's) and the behaviour of quantum systems in the vicinity of the corresponding quantum critical points is a frontier area of research both in theory and in experiment. [1,2] A QPT is a transition at zero temperature, in the nature of the ground state, and is due to quantum fluctuations that can be enhanced or suppressed by varying some coupling constant. In real materials QPT's can be driven by pressure, by applied magnetic field, or by some other parameter.In the present work we consider an O(3) QPT which occurs between a magnetically ordered Néel phase and a magnetically disordered 'valence-bond-solid' (VBS) phase in a class of SU(2) invariant Heisenberg spin systems. This problem has attracted a great deal of attention in recent years, mainly in two-dimensional (2D) systems. It has been established that the interplay between quantum fluctuations and thermal fluctuations at low but finite temperatures influences the dynamics in the vicinity of a QPT in a highly nontrivial way [3,4]. However, in 2D systems there is no finite temperature magnetic order, due to the well known Mermin-Wagner theorem. One would expect that in 3D systems (3D + time) the presence of a finite Néel temperature and an extended region of magnetic order will affect the interplay between quantum and thermal fluctuations, and lead to new features not seen in 2D. An obvious question is the nature of the vanishing of the Néel temperature and its scaling with the magnetization and with the coupling constant as the QPT is approached. To the best of our knowledge the generic problem of the finite temperature behaviour of 3D systems in the vicinity of an O(3) QPT has not been previously considered. The present work addresses this question.Specifically, we discuss three aspects of this question. The first is to consider a general Landau-Ginzburg field theory, which is independent of the details of any microscopic model, and hence generic. The predictions of this approach are then compared with experimental results for the material TlCuCl 3 . Finally we present results obtained for a specific microscopic Heisenberg spin model, obtained using a variety of series-expansion methods. While the numerical precision close to the QPT is only moderate, the results are consistent with the field theory predictions, and reinforce our conclusion that the behaviour is universal.To develop a quantum field theoretic description we start from the standard effective Lagrangian describing an O(3) QPT, of the form [2,5,6].In...

The existing formula for the transfer matrix of conical elements assumes constant wave number, which is only valid for sufficiently short conical elements. In acoustic waveguides, the phase velocity, attenuation constant, and hence complex wave number depend on frequency and cross-section radius. As for conical waveguides, the cross-section radius is position dependent, the transfer matrix must allow for a position-dependent wave number. Taking this into account, this letter presents an analytic derivation of the transfer matrix for conical waveguides with any geometric parameters, which can be utilized to improve the method of computer modeling of complex waveguides.

A woodwind tone hole is often represented as a T-junction with a shunt and series impedance. We measured the frequency dependence of the series and shunt impedances of open and closed tone holes using a pair of impedance heads, one on either side of a symmetric section of short bore pipe with a finger hole, and each calibrated on resonance-free loads. The shunt impedance is most accurately measured when the hole is located at a pressure anti-node (speakers in phase) and the series impedance at a pressure node (speakers in anti-phase). We use both conditions, in this way, to measure series and shunt impedances for all frequencies studied. Pipes with the same length and diameter, but having wall thicknesses 1.5-5.0 mm and tone hole diameters 1.5-15.0 mm were used. For open holes, results are compared with calculations and results measured using other methods. The results for holes closed with fingers are also used to calculate the effective length of finger intrusion. Examples of the inclusion of the results into woodwind models are given.

The Virtual Flute is a popular web service that recommends alternative fingerings for difficult passages, timbre variations, intonations or multiphonics. Its database was generated by a machine-learned expert system analysing waveguide models for all 39,744 fingerings. The relatively simple geometry of the flute and its tone holes allowed a simple yet accurate model. The development of similar systems for other woodwinds faces greater modelling and computational challenges. For example, the clarinet has a more complex geometry, with tone holes whose radius and length vary by factors of 4.2 and 2.8. Further, it has several million different fingerings. To achieve the required accuracy, individual measurements of each hole separately and of mouthpiece and bell, as well as several dozen fingering examples, were used to determine parameters of a still simple waveguide model. The model uses conical and cylindrical segments with parallel and shunt impedances at junctions, representing tone holes. This approach of incrementally enhancing our waveguide model allows computational advantages: an efficient, woodwind-generic software framework is built that can adapt to the instrument of interest. We report interim results with such a system, with further potential applications in the design of woodwind instruments and other acoustic duct systems.