### Résumés CEMPI seminar day

D. Agafontsev

Integrable turbulence and formation of rogue waves

In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable turbulence" [V.E. Zakharov, Turbulence in integrable systems, Stud. in Appl. Math. 122, no. 3, 219-234, (2009)]. We study the time evolution of it's major characteristics averaged across realizations of initial data - the condensate solution seeded by small random noise with fixed statistical properties. The measured quantities are: (1) wave-action spectrum and spatial correlation function, (2) the probability density function (PDF) of wave amplitudes and their momenta, and (3) kinetic and potential energies.

Integrable turbulence and formation of rogue waves

In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable turbulence" [V.E. Zakharov, Turbulence in integrable systems, Stud. in Appl. Math. 122, no. 3, 219-234, (2009)]. We study the time evolution of it's major characteristics averaged across realizations of initial data - the condensate solution seeded by small random noise with fixed statistical properties. The measured quantities are: (1) wave-action spectrum and spatial correlation function, (2) the probability density function (PDF) of wave amplitudes and their momenta, and (3) kinetic and potential energies.

D. Horoshko

Quantum superpositions of two-mode coherent states: creation, entropic measures and entanglement.

We consider two harmonic oscillators (modes of optical field) in a joint non-factoring pure state, known as entangled state. We study a special class of such entangled states represented by quantum superpositions of classical (two-mode coherent) states. We consider their creation on a beam-splitter by means of splitting a single-mode superposition of coherent states, which is known to be produced in non-linear optical processes. We discuss various measures of entanglement, like von Neumann entropy and quantum Renyi entropy of the partial density matrix of one mode, and show the advantages of either for the considered class of states. We calculate an exact analytic expression for the entanglement of formation in the case where the initial set of single-mode coherent states is equidistant on the circle with linear relative phase, for any number of components in the superposition, generalizing the expressions, well known for two components.

Quantum superpositions of two-mode coherent states: creation, entropic measures and entanglement.

We consider two harmonic oscillators (modes of optical field) in a joint non-factoring pure state, known as entangled state. We study a special class of such entangled states represented by quantum superpositions of classical (two-mode coherent) states. We consider their creation on a beam-splitter by means of splitting a single-mode superposition of coherent states, which is known to be produced in non-linear optical processes. We discuss various measures of entanglement, like von Neumann entropy and quantum Renyi entropy of the partial density matrix of one mode, and show the advantages of either for the considered class of states. We calculate an exact analytic expression for the entanglement of formation in the case where the initial set of single-mode coherent states is equidistant on the circle with linear relative phase, for any number of components in the superposition, generalizing the expressions, well known for two components.

C. Mejia-Monasterio

From Hamilton to Boltzmann: The scattering road to equilibrium

Can Hamiltonian dynamics explain the ubiquity of the Boltzmann factor? In this talk we explore this question and study the convergence toward thermal equilibrium of Hamiltonian (and mechanical) systems of interacting particles in contact to a bath of other systems. We focus on interactions that occur through collisions and explore the conditions in which the system reaches equilibrium after repeated interactions with the bathÕs degrees of freedom, even when the later is out of equilibrium.

From Hamilton to Boltzmann: The scattering road to equilibrium

Can Hamiltonian dynamics explain the ubiquity of the Boltzmann factor? In this talk we explore this question and study the convergence toward thermal equilibrium of Hamiltonian (and mechanical) systems of interacting particles in contact to a bath of other systems. We focus on interactions that occur through collisions and explore the conditions in which the system reaches equilibrium after repeated interactions with the bathÕs degrees of freedom, even when the later is out of equilibrium.

P.E. Parris

Models versus Materials: How well do disorder based transport theories actually describe charge transport in real molecularly doped polymers?

There has been extensive theoretical and experimental investigation of photo-injected charge carriers in amorphous molecularly-doped polymers, due to their ubiquitous use as charge transport layers in electro-photographic and optoelectronic devices. Molecularly-doped polymers have also motivated the development of general theories of high field transport in energetically disordered solids. The high-field mobility, e.g., displays a universal ÒPoole-FrenkelÓ field dependence (exponential in the square root of the electric field) believed to arise from a spatially-correlated Gaussian energy distribution of transport sites encountered by charges moving through the material. The observed universality of time-of-flight (TOF) transients and a metal-insulator like transition to ÒdispersiveÓ transport, on the other hand, have traditionally been explained by Òmultiple-trappingÓ models that postulate an uncorrelated exponential distribution of low energy trap sites. So which is it? In this talk, we review the successes and failures of different transport models that have been developed for these materials over the years and present recent theoretical work that actually supports the initially suspect idea that in these materials both kinds of disorder might coexist.

Models versus Materials: How well do disorder based transport theories actually describe charge transport in real molecularly doped polymers?

There has been extensive theoretical and experimental investigation of photo-injected charge carriers in amorphous molecularly-doped polymers, due to their ubiquitous use as charge transport layers in electro-photographic and optoelectronic devices. Molecularly-doped polymers have also motivated the development of general theories of high field transport in energetically disordered solids. The high-field mobility, e.g., displays a universal ÒPoole-FrenkelÓ field dependence (exponential in the square root of the electric field) believed to arise from a spatially-correlated Gaussian energy distribution of transport sites encountered by charges moving through the material. The observed universality of time-of-flight (TOF) transients and a metal-insulator like transition to ÒdispersiveÓ transport, on the other hand, have traditionally been explained by Òmultiple-trappingÓ models that postulate an uncorrelated exponential distribution of low energy trap sites. So which is it? In this talk, we review the successes and failures of different transport models that have been developed for these materials over the years and present recent theoretical work that actually supports the initially suspect idea that in these materials both kinds of disorder might coexist.