# Theme « Quantic dynamic of complex systems »

## Researchers :

*Dominique Boosé, Olivier Brodier, Amaury Mouchet, Jérémy Le Deunff.*

/~mouchet/

http://www.lmpt.univ-tours.fr/~brodier/

For a presentation aimed to a broad audience, see :

/~mouchet/vulgarisation/cq_deug/cq_deug.html

##

Presentation (for specialists) :

Research of D. Boosé stands in the frame of quantum transport and disordered systems, in particular a) study of transmission through unidimensional disordered systems modelised by probabilistic laws with infinite first momentum, or infinite first and second momenta, and, b) study of multiple scattering in disordered tridimensional systems with finite size. D. Boosé and collaborators have identified three new localization regimes in unidimensional disordered systems, namely, a superlocalization regime, a sublocalization regime, and a fluctuating localization regime; these three new regimes can be distinguished from Anderson's localization in that they cannot be attributed a Lyapunov exponent. They also showed evidences for a new quantum phenomenon which manifests itself as a significant increase of transmission when dephasing induced by scatterers decreases; this new phenomenon, whose origin is simply multiple scattering between scatterers in space, is the third known example of a quantum mechanism which increases transmission, after resonant scattering and superrariance.

Research of Olivier Brodier deals with quantum decoherence, a fundamental question in the field of quantum information. Although decoherence is well understood theoretically, its precise effect is difficult to evaluate for it requires to know precisely the environment of the system and how it interacts with it, which is either anavailable or impossible to compute. Exact calculations often restrict to coupled harmonic oscillators, which is an extremely simplified situation. However, a generic formalism able to describe the evolution of a system coupled to an unknown environment exists in the Markovian case. System's evolution is then described by a partial differential equation called Lindblad equation, which has generally no analytical solution. The research of O. Brodier between 2006 and 2009 was to built, in collaboration with A. M. Ozorio de Almeida, a semiclassical theory of the Lindblad equation. The purpose of this theory is to provide tools to analyse the generic behaviour of the solutions of this equation, and particularly decoherence, when dynamics is nonlinear. In certain conditions it is possible to write the solution as a WKB ansatz, and to understand, in terms of classical dynamics, the competition between quantum correlation induced by the nonlinearity of the system, and decoherence induced by the environment.

Research of A. Mouchet deals mainly with tunneling in complex systems. Tunneling, which accounts for classically forbidden quantum phenomena, is difficult to study as soon as the underlying classical dynamics is sufficiently rich. In particular, paradoxical as it may seem, whether the Hamiltonian dynamics is regular or chaotic has a great influence on tunneling, by several orders of magnitude. Theoretical predictions and experimental control remain rather unsatisfactory. Collaboration of A. Mouchet with C. Eltschka and P. Schlagheck allowed to precise (quantitatively and qualitatively) the crucial role of resonances in the giant fluctuations (by several orders of magnitude) of characteristic tunneling times. The partial Wick rotation introduced by A. Mouchet allowed to retain only the main resonances, which notably simplifies the semiclassical approach of tunneling. In the simplest cases, J. Ledeunff and A. Mouchet showed that their approach, which refreshes the old instanton idea, can reconstitute the peaks "à la Fabry-Perot" due to a single resonance. An other aspect of A. Mouchet's work is about developing new methods to approximate the spectrum of an operator. The differential method, in certain N-bodies problems, can produce exact boundaries which are comparable, if not better, than the ones obtained from traditional (variational and perturbative) methods. It has been generalized with H. Giacomini to get precise forbidden bands which can discriminate between the different eigenvalues.

**Group's scientific production (2006-2010) :**

**1. Articles with lecture commity:**

D. BOOSÉ, J.-M. LUCK,

*Statistics of quantum transmission in one dimension with broad disorder*,

Journal of Physics A 40 14045 (2007)

A. M. OZORIO DE ALMEIDA, O. BRODIER,

*Phase space propagators and quantum operators,*Annals of Physics 321 1790 (2006)

A. R. R. CARVALHO, M. BUSSE, O. BRODIER, C. VIVIESCAS, and A. BUCHLEITNER,

*Optimal dynamical characterization of entanglement*, Physical Review Letters 90 190501 (2007)

A. M. OZORIO DE ALMEIDA, P. de M. RIOS, O. BRODIER,

*Semiclassical evolution of dissipative Markovian systems*, Journal of Physics A 42 065306 (2009)

A. MOUCHET,

*Bounding the ground-state energy of a many-body system with the differential method*, Nuclear Physics A 765 (2006) 319.

A. MOUCHET,

*Upper and lower bounds for an eigenvalue associated with a positive eigenvector*, Journal of Mathematical Physics 47 022109 (2006).

A. MOUCHET, C. ELTSCHKA & P. SCHLAGHECK,

*Influence of classical resonances on chaotic tunnelling*, Physical Review E 74 026211 (2006).

H. GIACOMINI, A. MOUCHET,

*Finding gaps in a spectrum*, Journal of Physics A 40 F921 (2007)

A. MOUCHET,

*Importance of the Wick rotation on tunnelling*, Journal of Physics A 40 F663 (2007)

A. MOUCHET,

*Interaction with a field: a simple integrable model with backreaction*, European Journal of Physics 29 1033 (2008)

A. MOUCHET,

*A mechanical model of tunnelling*, European Journal of Physics 30, L1 (2009)

O. BRODIER, A. M. OZORIO DE ALMEIDA,

*Markovian evolution of Gaussian states in the semiclassical limit*, Physics Letters A 374, 2315-2323 (2010)

**2. HDR & defended thesis:**

A. MOUCHET,

*Effet tunnel chaotique - Méthode différentielle,*Mémoire d'Habilitation à Diriger des Recherche (7 décembre 2006), Université François Rabelais.

**3. Invitations to national and international conferences :**

O. BRODIER,

*Decoherence and nonlinearity*, Tunneling and Scattering in Complex Systems - From Single to Many Particle Physics (TSICS09), International Seminar and Workshop - September 07 - 25, 2009 (Max Planck Institut of Dresden)

A. MOUCHET,

*Tunnelling and complex time paths*, Tunneling and Scattering in Complex Systems - From Single to Many Particle Physics (TSICS09), International Seminar and Workshop - September 07 - 25, 2009 (Max Planck Institut of Dresden)

A. MOUCHET,

*Quantum billiards*, Atelier Maths et Billards, march 25 and 26, 2008 (FDP, Orléans)

**4. Posters in national and international conferences:**

J. LEDEUNFF, A. MOUCHET

*Tunnelling and instantons*, Tunneling and Scattering in Complex Systems - From Single to Many Particle Physics (TSICS09), International Seminar and Workshop - September 07 - 25, 2009 (Max Planck Institut of Dresden)

**5. Research valorisation: publications and conferences for a broad audience:**

A. MOUCHET,

*L'étrange subtilité quantique, Quintessence de poussières*. Dunod (avril 2010)

coll. UniverSciences.

**6. To be published:**

D. BOOSÉ J.-Y. FORTIN, J.-M. LUCK,

*Exact quantum multiple scattering in disordered systems of spherical shape,*Journal of Physics A (2009)

O. BRODIER, A. M. OZORIO DE ALMEIDA,

*Complex WKB evolution of Markovian open systems*, Journal of Physics A (2010)

J. LE DEUNFF, A. MOUCHET,

*Instantons re-examined: Dynamical tunneling and resonant tunneling*, Physical Review E (2010)

A. MOUCHET P. SCHLAGHECK, D. ULLMO

*Resonant Tunneling*, chapter from the book ``Dynamical Tunneling - Theory and Experiment" edited by SRIHARI KESHAVAMURTHY et PETER SCHLAGHECK (2010)