Eigenstate thermalization and ensemble equivalence in few-body fermionic systems.

We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature obtained from a thermodynamic relation in a wide energy range, (iii) it is independent of details of the coupling between the two systems in a finite parameter range, (iv) it satisfies the transitivity condition underlying the zeroth law of thermodynamics, and (v) it is consistent with Carnot's theorem.

Noise-induced desynchronization and stochastic escape from equilibrium in complex networks.

Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, they can push the system from an initial stable equilibrium point, over a nearby saddle point, outside of the basin of attraction of the stable point.

Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices.

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector.

Spin transistor action from hidden Onsager reciprocity.

We investigate generic Hamiltonians for confined electrons with weak inhomogeneous spin-orbit coupling. Using a local gauge transformation we show how the SU(2) Hamiltonian structure reduces to a U(1)×U(1) structure for spinless fermions in a fictitious orbital magnetic field, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry or opening additional transport terminals, thus allowing one to switch the generated spin current on or off.

Geometric correlations and breakdown of mesoscopic universality in spin transport.

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects into the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order.

Scattering theory of current-induced spin polarization.

We construct a novel scattering theory to investigate magnetoelectrically induced spin polarizations. Local spin polarizations generated by electric currents passing through a spin-orbit-coupled mesoscopic system are measured by an external probe. The electrochemical and spin-dependent chemical potentials on the probe are controllable and tuned to values ensuring that neither charge nor spin current flow between the system and the probe, on time average.

Controlling the sign of magnetoconductance in Andreev quantum dots.

We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign.

Electrical probing of the spin conductance of mesoscopic cavities.

We investigate spin-dependent transport in multiterminal mesoscopic cavities with spin-orbit coupling. Focusing on a three-terminal set-up we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. When the injected current is a pure spin current, a single measurement allows us to extract the spin conductance of the cavity.

Macroscopic resonant tunnelling through Andreev interferometers.

We investigate the conductance through and the spectrum of ballistic chaotic quantum dots attached to two s-wave superconductors, as a function of the phase difference phi between the two order parameters. A combination of analytical techniques-random matrix theory, Nazarov's circuit theory and the trajectory-based semiclassical theory-allows us to explore the quantum-to-classical crossover in detail. When the superconductors are not phase-biased, phi = 0, we recover known results that the spectrum of the quantum dot exhibits an excitation gap, while the conductance across two normal leads carrying N(N) channels and connected to the dot via tunnel contacts of transparency Gamma(N) is [Formula: see text].

Superconductivity-induced macroscopic resonant tunneling.

We show analytically and by numerical simulations that the conductance through pi-biased chaotic Josephson junctions is enhanced by several orders of magnitude in the short-wavelength regime. We identify the mechanism behind this effect as macroscopic resonant tunneling through a macroscopic number of low-energy quasidegenerate Andreev levels.

Mesoscopic spin Hall effect.

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average.

Lyapunov generation of entanglement and the correspondence principle.

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit.

Quantum reversibility and echoes in interacting systems.

In echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity M(B)(t), the Boltzmann echo, where only part of the system's degrees of freedom can be time reversed. We present a semiclassical calculation of M(B)(t).

Shot noise in semiclassical chaotic cavities.

We construct a trajectory-based semiclassical theory of shot noise in clean chaotic cavities. In the universal regime of vanishing Ehrenfest time tau(E), we reproduce the random matrix theory result and show that the Fano factor is exponentially suppressed as tau(E) increases. We demonstrate how our theory preserves the unitarity of the scattering matrix even in the regime of finite tau(E).

Microscopic theory for the quantum to classical crossover in chaotic transport.

We present a semiclassical theory for the scattering matrix S of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multibounce expansion, we show how the Liouville conservation of phase-space volume decomposes S as S=S(cl) plus sign in circle S(qm). The short-time, classical contribution S(cl) generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution S(qm).

Semiclassical time evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems.

Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix rho(1), obtained by integrating out the degrees of freedom of one of the particles. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics.

Breakdown of universality in quantum chaotic transport: the two-phase dynamical fluid model.

We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic classical dynamics, and result from the separation of the quantum phase space into a stochastic and a deterministic phase. Consequently, sample-to-sample conductance fluctuations lose their universality, while the persistence of a finite stochastic phase protects the universality of conductance fluctuations under variation of a quantum parameter.

Quantum Andreev map: a paradigm of quantum chaos in superconductivity.

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations.

Decay of the Loschmidt echo for quantum states with sub-planck-scale structures.

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than variant Planck's over 2pi [W. H. Zurek, Nature (London) 412, 712 (2001)]].