Quantum Cloning of Binary Coherent States - Optimal Transformations and Practical Limits

The notions of qubits and coherent states correspond to different physical systems and are described by specific formalisms. Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere. In contrast, the underlying Hilbert space of coherent states is infinite-dimensional and the states are typically represented in phase space. For the particular case of binary coherent state alphabets these otherwise distinct formalisms can equally be applied. We capitalize this formal connection to analyse the properties of optimally cloned binary coherent states. Several practical and near-optimal cloning schemes are discussed and the associated fidelities are compared to the performance of the optimal cloner.Comment: 12 pages, 12 figure

Quasi-deterministic transport of Brownian particles in an oscillating periodic potential

We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the diffusion coefficient. Furthermore we analyze the effect of the oscillating potential on the transport if additionally a constant force is applied. We show the existence of synchronization regimes at which the deterministic dynamics is in resonance with the potential oscillations giving rise to transport with extremely low dispersion. We distinguish slow and fast oscillatory driving and give analytical expressions for the mean velocity and effective diffusion.Comment: submitted: Feb 12th, 201

Symmetry defects and orbifolds of two-dimensional Yang-Mills theory

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted $G$-bundles, and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted $G$-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang-Mills theory but with gauge group given by an extension of $G$ by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang-Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras

Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems

The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC Lennard-Jones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure

Unusual electronic ground state of a prototype cuprate: band splitting of single CuO_2-plane Bi_2 Sr_(2-x) La_x CuO_(6+delta)

By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $\Gamma$M, giving the dispersion for the individual contributions. Since bi-layer effects can not be present in this single-layer material the results have to be discussed in the context of one-particle removal spectral functions derived from current theoretical models. The most prominent are microscopic phase separation including striped phase formation, coexisting antiferromagnetic and incommensurate charge-density-wave critical fluctuations coupled to electrons (hot spots) or even spin charge separation within the Luttinger liquid picture, all leading to non-Fermi liquid like behavior in the normal state and having severe consequences on the way the superconducting state forms. Especially the possibilty of observing spinon and holon excitations is discussed.Comment: 5 pages, 4 figure

Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page

Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential trap

We present a detailed theoretical analysis of micro-motion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time dependent behaviour of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular centre of mass motion in the lab frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.Comment: 12 pages, 2 figure