Related papers: Upper and Lower Bounds for The Quantum Dynamics of…
This work investigates the quantum transport in a narrow constriction acted upon by a finite-range transversely polarized time-dependent electric field. A generalized scattering-matrix method is developed that has incorporated a…
Transport through two quantum dots laterally embedded in Aharonov-Bohm interferometry with infinite intradot and arbitrary interdot Coulomb repulsion is analyzed in the weak coupling and Coulomb blockade regime. By employing the modified…
We prove two-sided inequalities for the $L^p$-norm of a pushforward or pullback (with respect to an orientation-preserving diffeomorphism) on oriented volume and Riemannian manifolds. For a function or density on a volume manifold, these…
We discuss a method by which quantum fluctuations can be included in microscopic transport models based on wave packets that are not energy eigenstates. By including the next-to-leading order term in the cumulant expansion of the…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
We have calculated the admittance of a two-dimensional quantum point contact (QPC) using a novel variant of the Wigner distribution function (WDF) formalism. In the semiclassical approximation, a Boltzman-like equation is derived for the…
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used…
We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange…
Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary…
In this paper we study one-dimensional Jacobi operators on the lattice with a potential given by the skew shift. We show that the large deviation theorem takes place for Diophantine frequency and sufficiently large disorder. Combining the…
In this work, we study the relativistic quantum kinetic equations in 2+1 dimensions from Wigner function formalism by carrying out a systematic semi-classical expansion up to $\hbar$ order. The derived equations allow us to explore…
Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called…
Time-resolved electron transport in nano-devices is described by means of a time-nonlocal quantum master equation for the reduced density operator. Our formulation allows for arbitrary time dependences of any device or contact parameter.…
We study the differential conductance in the Kondo regime of a quantum dot coupled to multiple leads. When the bias is applied symmetrically on two of the leads ($V$ and $-V$, as usual in experiments), while the others are grounded, the…
We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered…
The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
Topological quantum phases of matter are characterized by an intimate relationship between the Hamiltonian dynamics away from the edges and the appearance of bound states localized at the edges of the system. Elucidating this correspondence…