Decoherence and the conditions for the classical control of quantum systems

We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalisation is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are similar in structure to recently proposed models for consistently combining quantum and classical stochastic dynamics

Lower limit on the achievable temperature in resonator-based sideband cooling

A resonator can be effectively used as a cooler for another linear oscillator with a much smaller frequency. A huge cooling effect, which could be used to cool a mechanical oscillator below the energy of quantum fluctuations, has been predicted by several authors. However, here we show that there is a lower limit T* on the achievable temperature that was not considered in previous works and can be higher than the quantum limit in realistic experimental realizations. We also point out that the decay rate of the resonator, which previous studies stress should be small, must be larger than the decay rate of the cooled oscillator for effective cooling.Comment: 6 pages, 4 figures, uses psfra

Survival of a diffusing particle in an expanding cage

We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We calculate the joint probability density, p(r,t|r_0), that the particle survives until time t, and is at a distance r from the centre of the sphere, given that it started at a distance r_0 from the centre.Comment: 5 page

Time-resolved noise of adiabatic quantum pumps

We investigate quantum-statistical correlation properties of a periodically driven mesoscopic scatterer on a time-scale shorter than the period of a drive. In this limit the intrinsic quantum fluctuations in the system of fermions are the main source of a noise. Nevertheless the effect of a slow periodic drive is clearly visible in a two-time current-current correlation function as a specific periodic in time modulation. In the limit of a strong drive such a modulation can change the sign of a current correlation function.Comment: 11 pages, 10 figure

Smooth potentials with prescribed boundary behaviour

This paper examines when it is possible to find a smooth potential on a $C^{1}$ domain $D$ with prescribed normal derivatives at the boundary. It is shown that this is always possible when $D$ is a Liapunov-Dini domain, and this restriction on $D$ is essential. An application concerning $C^{1}$ superharmonic extension is given

The dynamics of loop formation in a semiflexible polymer

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical/experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study (K. P. Santo and K. L. Sebastian, Phys. Rev. E, \textbf{73}, 031293 (2006)), we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit, based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain which leads to results that are physically expected. Such a multidimensional analysis leading to these results does not seem to exist in the literature so far.Comment: 37 pages 4 figure

Dynamical instabilities of Bose-Einstein condensates at the band-edge in one-dimensional optical lattices

We report on experiments that demonstrate dynamical instability in a Bose-Einstein condensate at the band-edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and perform numerical modeling of the experiments using both a mean-field and beyond mean-field approach. We compare our numerical results to the experimental data, and find that the Gross-Pitaevskii equation is not able to describe this experiment. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and thermalization that are observed in the laboratory, and we find good agreement with the experimental results.Comment: v2: Added several reference

Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear in Advances in Physic

Cooperative Jahn-Teller Distortion in PrO2

We report neutron diffraction data on single crystal PrO2 which reveal a cooperative Jahn-Teller distortion at TD = 120 +/- 2 K. Below this temperature an internal distortion of the oxygen sublattice causes the unit cell of the crystallographic structure to become doubled along one crystal axis. We discuss several possible models for this structure. The antiferromagnetic structure below TN = 13.5 K is found to consist of two components, one of which shares the same doubled unit cell as the distorted crystallographic structure. We also present measurements of the magnetic susceptibility, the specific heat capacity and the electrical conductivity of PrO2. The susceptibility data show an anomaly at a temperature close to TD. From the specific heat capacity data we deduce that the ground state is doubly degenerate, consistent with a distortion of the cubic local symmetry. We discuss possible mechanisms for this. The conductivity shows an activated behaviour with an activation energy Ea = 0.262 +/- 0.003 eV.Comment: 12 pages, 14 figures, 2 tables. Additional suggested structure in v