About the use of entanglement in the optical implementation of quantum information processing

We review some applications of entanglement to improve quantum measurements and communication, with the main focus on the optical implementation of quantum information processing. The evolution of continuos variable entangled states in active optical fibers is also analyzed.Comment: 8pages, invited contribution to Quant. Interf. IV (ICTP Trieste 2002

An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects

As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of integrable dispersionless multidimensional PDEs is non-local, and the proper choice of integration constants should be the one dictated by the associated Inverse Scattering Transform (IST). Using the recently made rigorous IST for vector fields associated with the so-called Pavlov equation $v_{xt}+v_{yy}+v_xv_{xy}-v_yv_{xx}=0$, we have recently esatablished that, in the nonlocal part of its evolutionary form $v_{t}= v_{x}v_{y}-\partial^{-1}_{x}\,\partial_{y}\,[v_{y}+v^2_{x}]$, the formal integral $\partial^{-1}_{x}$ corresponding to the solutions of the Cauchy problem constructed by such an IST is the asymmetric integral $-\int_x^{\infty}dx'$. In this paper we show that this results could be guessed in a simple way using a, to the best of our knowledge, novel integral geometry lemma. Such a lemma establishes that it is possible to express the integral of a fairly general and smooth function $f(X,Y)$ over a parabola of the $(X,Y)$ plane in terms of the integrals of $f(X,Y)$ over all straight lines non intersecting the parabola. A similar result, in which the parabola is replaced by the circle, is already known in the literature and finds applications in tomography. Indeed, in a two-dimensional linear tomographic problem with a convex opaque obstacle, only the integrals along the straight lines non-intersecting the obstacle are known, and in the class of potentials $f(X,Y)$ with polynomial decay we do not have unique solvability of the inverse problem anymore. Therefore, for the problem with an obstacle, it is natural not to try to reconstruct the complete potential, but only some integral characteristics like the integral over the boundary of the obstacle. Due to the above two lemmas, this can be done, at the moment, for opaque bodies having as boundary a parabola and a circle (an ellipse).Comment: LaTeX, 13 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1507.0820

Kink Chains from Instantons on a Torus

We describe how the procedure of calculating approximate solitons from instanton holonomies may be extended to the case of soliton crystals. It is shown how sine-Gordon kink chains may be obtained from CP1 instantons on a torus. These kink chains turn out to be remarkably accurate approximations to the true solutions. Some remarks on the relevance of this work to Skyrme crystals are also made.Comment: latex 17 pages, DAMTP 94-7

Misfits in Skyrme-Hartree-Fock

We address very briefly five critical points in the context of the Skyrme-Hartree-Fock (SHF) scheme: 1) the impossibility to consider it as an interaction, 2) a possible inconsistency of correlation corrections as, e.g., the center-of-mass correction, 3) problems to describe the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, 4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE), and 5) a yet inappropriate trend in fission life-times when going to the heaviest SHE. While the first two points have more a formal bias, the other three points have practical implications and wait for solution.Comment: 9 pages, 4 figure

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the $x$-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of $N=1,2$ unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearence, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceeding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1708.00762 and substantial text overlap with arXiv:1707.0565

Thermoelectric properties of a weakly coupled quantum dot: enhanced thermoelectric efficiency

We study the thermoelectric coefficients of a multi-level quantum dot (QD) weakly coupled to two electron reservoirs in the Coulomb blockade regime. Detailed calculations and analytical expressions of the power factor and the figure of merit are presented. We restrict our interest to the limit where the energy separation between successive energy levels is much larger than the thermal energy (i.e., the quantum limit) and we report a giant enhancement of the figure of merit due to the violation of the Wiedemann-Franz law when phonons are frozen. We point out the similarity of the electronic and the phonon contribution to the thermal conductance for zero dimensional electrons and phonons. Both contributions show an activated behavior. Our findings suggest that the control of the electron and phonon confinement effects can lead to nanostructures with improved thermoelectric properties.Comment: 8 pages, 6 figure

Nonlocality and the inverse scattering transform for the Pavlov equation

As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of integrable dispersionless multidimensional PDEs is non-local, and the proper choice of integration constants should be the one dictated by the associated Inverse Scattering Transform (IST). Using the recently made rigorous IST for vector fields associated with the so-called Pavlov equation $v_{xt}+v_{yy}+v_xv_{xy}-v_yv_{xx}=0$, in this paper we establish the following. 1. The non-local term $\partial_x^{-1}$ arising from its evolutionary form $v_{t}= v_{x}v_{y}-\partial^{-1}_{x}\,\partial_{y}\,[v_{y}+v^2_{x}]$ corresponds to the asymmetric integral $-\int_x^{\infty}dx'$. 2. Smooth and well-localized initial data $v(x,y,0)$ evolve in time developing, for $t>0$, the constraint $\partial_y {\cal M}(y,t)\equiv 0$, where ${\cal M}(y,t)=\int_{-\infty}^{+\infty} \left[v_{y}(x,y,t) +(v_{x}(x,y,t))^2\right]\,dx$. 3. Since no smooth and well-localized initial data can satisfy such constraint at $t=0$, the initial ($t=0+$) dynamics of the Pavlov equation can not be smooth, although, as it was already established, small norm solutions remain regular for all positive times. We expect that the techniques developed in this paper to prove the above results, should be successfully used in the study of the non-locality of other basic examples of integrable dispersionless PDEs in multidimensions.Comment: 19 page

Droplets and the configurational entropy crisis for random first order transitions

We consider the effect of droplet excitations in the random first order transition theory of glasses on the configurational entropy. The contribution of these excitations is estimated both at and above the ideal glass transition temperature. The temperature range where such excitations could conceivably modify or `round-out' an underlying glass transition temperature is estimated, and found to depend strongly on the surface tension between locally metastable phases in the supercooled liquid. For real structural glasses this temperature range is found to be very narrow, consistent with the quantitative success of the theory. For certain finite-range spin-glass models, however, the surface tension is estimated to be significantly lower leading to much stronger entropy renormalizations, thus providing an explanation for the lack of a strict thermodynamic glass transition in simulations of these models.Comment: 5 page