Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

Irreversibility and the arrow of time in a quenched quantum system

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.Comment: 8 pages, 7 figures, RevTeX4-1; Accepted for publication Phys. Rev. Let

Antibonding Ground state of Adatom Molecules in Bulk Dirac Semimetals

The ground state of the diatomic molecules in nature is inevitably bonding, and its first excited state is antibonding. We demonstrate theoretically that, for a pair of distant adatoms placed buried in three-dimensional-Dirac semimetals, this natural order of the states can be reversed and an antibonding ground state occurs at the lowest energy of the so-called bound states in the continuum. We propose an experimental protocol with the use of a scanning tunneling microscope tip to visualize the topographic map of the local density of states on the surface of the system to reveal the emerging physics

Normalization procedure for relaxation studies in NMR quantum information processing

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a "loss of purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.Comment: 9 pages, 5 figures, to appear in QI