Dr. Christopher Gaul email cgaul (at) fis.ucm.es tel +34 91 394 44 96 post Universidad Complutense Departamento de Física de Materiales Avenida Complutense s/n E-28040 Madrid 2nd floor, Room 117   groups    Campus de Excelencia Internacional (CEI) Moncloa Quantum Nanosystems Group (QNG) Grupo Interdisciplinar de Sistemas Complejos (GISC) Quantum Transport of Light and Matter (QTLM)

Transport under the Influence of Quantum Statistics, Interactions, and Randomness

Electronic transport in graphene

Graphene is a unique two-dimensional material of great mechanical strenght and with very high electron mobility. Graphene's honeycomb lattice has a two-atomic basis, thus, the spectrum of the p electrons form two bands. Due to symmetries, the bands touch at the so-called Dirac points, and the dispersion relation is linear, just like for superrelativistic fermions.

Currently, I am interested in two fields of problems:

• Electronic transport in graphene nanoribbons
• Interaction effects in graphene

Bogoliubov Excitations of Disordered Bose-Einstein Condensates

Bose-Einstein condensates are efficiently described with the Bogoliubov ansatz, i.e., as a macroscopically populated condensate mode plus quantized fluctuations. The first effect of an external disorder potential is deforming the condensate on the mean-field level. Certainly this affects the (quantum) excitations of the condensate. By a saddle-point expansion of the many-body Hamiltonian around the deformed mean-field ground state, the Hamiltonian for the quantum fluctuations is found. Furthermore, a suitable basis for the following disorder perturbation theory is needed. In particular, the basis should not depend on the particular realization of the disorder, and it must respect certain orthogonality relations with respect to the condensate [2].

Then, the question can be addressed, how the excitation spectrum and Bose-Einstein condensation itself are affected. We have computed:

• the renormalized excitation dispersion relation, i.e., the speed of sound and mean free paths [2]
• the quantum depletion of the condensate, i.e. the fraction of particles outside the condensate mode [1]

Bloch Oscillations of a Bose-Einstein Condensate with Time-Dependent Nonlinearity

In this project, Bloch oscillations of Bose-Einstein condensates in presence of time-dependent interactions are considered. In general, the interaction leads to dephasing and destroys the Bloch oscillation. Feshbach resonances allow the atom-atom interaction to be manipulated as function of time. In particular, modulations around zero interaction are considered. Different modulations lead to very different behavior: either the wave packet evolves periodically with time or it decays rapidly. The former is explained by a periodic time-reversal argument. The decay in the other cases can be described by a dynamical instability with respect to small perturbations, which are similar to Bogoliubov excitations.

References:
C. Gaul, E. Díaz, R. P. A. Lima, F. Domínguez-Adame, C. A. Müller, Phys. Rev. A 84 053627 (2011)
E. Díaz, C. Gaul, R. P. A. Lima, F. Domínguez-Adame, C. A. Müller, Phys. Rev. A 81 051607(R) (2010)
C. Gaul, R. P. A. Lima, E. Díaz, C. A. Müller, F. Domínguez-Adame, Phys. Rev. Lett. 102, 255303 (2009)

Quantum heat conduction in disordered chains

Fourier's law states that heat flows contrarily to the temperature gradient, such that temperature differences tend to level out. Moreover, the magnitude of the heat flux is proportional to the temperature gradient. On macroscopic scales, this law is very intuitive and well tested. On the microscopic level, however, things are not so clear. In chains of coupled harmonic oscillators (and also in some nonlinear generalizations like the Fermi-Pasta-Ulam chain) the heat transport is ballistic and the temperature gradient vanishes inside the chain. Apart from the introduction of nonlinearities, also disorder can lead to a finite temperature gradient in such systems, because the eigenstates of the chain become localized.

With the quantum-mechanical Langevin method, the heat flux and the temperature temperature profiles of a chain connected to two heat baths can be computed. Indeed, a finite temperature gradient due to disorder is found. However, the heat resistance is not extensive, i.e., the heat resistance grows more slowly than the length of the chain. Both features have been known from classical chains before. But now, also intrinsic quantum phenomena, like entanglement between parts of the chain, and freezing of the heat conductivity (Bose statistics of phonons) can be studied.

Reference:
C. Gaul and H. Büttner, Phys. Rev. E 76, 011111 (2007)

Publications