11,419 research outputs found
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
Linear magnetoresistance in compensated graphene bilayer
We report a nonsaturating linear magnetoresistance in charge-compensated
bilayer graphene in a temperature range from 1.5 to 150 K. The observed linear
magnetoresistance disappears away from charge neutrality ruling out the
traditional explanation of the effect in terms of the classical random resistor
network model. We show that experimental results qualitatively agree with a
phenomenological two-fluid model taking into account electron-hole
recombination and finite-size sample geometry
Proton transport and torque generation in rotary biomotors
We analyze the dynamics of rotary biomotors within a simple
nano-electromechanical model, consisting of a stator part and a ring-shaped
rotor having twelve proton-binding sites. This model is closely related to the
membrane-embedded F motor of adenosine triphosphate (ATP) synthase, which
converts the energy of the transmembrane electrochemical gradient of protons
into mechanical motion of the rotor. It is shown that the Coulomb coupling
between the negative charge of the empty rotor site and the positive stator
charge, located near the periplasmic proton-conducting channel (proton source),
plays a dominant role in the torque-generating process. When approaching the
source outlet, the rotor site has a proton energy level higher than the energy
level of the site, located near the cytoplasmic channel (proton drain). In the
first stage of this torque-generating process, the energy of the
electrochemical potential is converted into potential energy of the
proton-binding sites on the rotor. Afterwards, the tangential component of the
Coulomb force produces a mechanical torque. We demonstrate that, at low
temperatures, the loaded motor works in the shuttling regime where the energy
of the electrochemical potential is consumed without producing any
unidirectional rotation. The motor switches to the torque-generating regime at
high temperatures, when the Brownian ratchet mechanism turns on. In the
presence of a significant external torque, created by ATP hydrolysis, the
system operates as a proton pump, which translocates protons against the
transmembrane potential gradient. Here we focus on the F motor, even though
our analysis is applicable to the bacterial flagellar motor.Comment: 24 pages, 5 figure
Quantum eigenstate tomography with qubit tunneling spectroscopy
Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has
recently become possible by qubit tunneling spectroscopy (QTS). In the standard
QTS experiments, an incoherent probe qubit is strongly coupled to one of the
qubits of the system in such a way that its incoherent tunneling rate provides
information about the energy eigenvalues of the original (source) system. In
this paper, we generalize QTS by coupling the probe qubit to many source
qubits. We show that by properly choosing the couplings, one can perform
projective measurements of the source system energy eigenstates in an arbitrary
basis, thus performing quantum eigenstate tomography. As a practical example of
a limited tomography, we apply our scheme to probe the eigenstates of a kink in
a frustrated transverse Ising chain.Comment: 8 pages, 4 figure
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