We propose a new drive mechanism for carbon nanotube (CNT) motors, based upon the torque generated by a flux of electrons passing through a chiral nanotube. The structure of interest comprises a ...double-walled CNT formed from, for example, an achiral outer tube encompassing a chiral inner tube. Through a detailed analysis of electrons passing through such a "windmill," we find that the current, due to a potential difference applied to the outer CNT, generates sufficient torque to overcome the static and dynamic frictional forces that exist between the inner and outer walls, thereby causing the inner tube to rotate.
We have studied numerically the statistics for electronic states (level-spacings and participation ratios) from disordered graphene of finite size, described by the aspect ratio \(W/L\) and various ...geometries, including finite or torroidal, chiral or achiral carbon nanotubes. Quantum chaotic Wigner energy level-spacing distribution is found for weak disorder, even infinitesimally small disorder for wide and short samples (\(W/L>>1\)), while for strong disorder Anderson localization with Poisson level-statistics always sets in. Although pure graphene near the Dirac point corresponds to integrable ballistic statistics chaotic diffusive behavior is more common for realistic samples.
We propose a new drive mechanism for carbon nanotube (CNT) motors, based upon the torque generated by a flux of electrons passing through a chiral nanotube. The structure of interest comprises a ...double-walled CNT, formed from, for example, an achiral outer tube encompassing a chiral inner tube. Through a detailed analysis of electrons passing through such a "windmill", we find that the current due to a potential difference applied to the outer CNT generates sufficient torque to overcome the static and dynamic frictional forces that exists between the inner and outer walls, thereby causing the inner tube to rotate.
We study the conductance
of 2D Dirac semimetal nanowires at the presence of disorder. For an even nanowire length
determined by the number of unit cells, we find non-integer values for
that are ...independent of
and persist with weak disorder, indicated by the vanishing fluctuations of
. The effect is created by a combination of the scattering effects at the contacts (interface) between the leads and the nanowire, an energy gap present in the nanowire for even
and the topological properties of the 2D Dirac semimetals. Unlike conventional materials the reduced
due to the scattering at the interface, is stabilized at non-integer values inside the nanowire, leading to a topological phase for weak disorder. For strong disorder the system leaves the topological phase and the fluctuations of
are increased as the system undergoes a transition/crossover toward the Anderson localized (insulating) phase, via a non-standard disordered phase. We study the scaling and the statistics of
at these phases. In addition we have found that the effect of robust non-integer
disappears for odd
, which results in integer
, determined by the number of open channels in the nanowire, due to resonant scattering.
We study the quantum self-organization of a few interacting particles with strong short-range interactions. The physical system is modeled via a 2D Hubbard square lattice model, with a ...nearest-neighbor interaction term of strength U and a second nearest-neighbor hopping t. For t=0, the energy of the system is determined by the number of bonds between particles that lie on adjacent sites in the Hubbard lattice. We find that this bond order persists for the ground and some of the excited states of the system, for strong interaction strength, at different fillings of the system. For our analysis, we use the Euler characteristic of the network/graph grid structures formed by the particles in real space (Fock states), which helps to quantify the energetical(bond) ordering. We find multiple ground and excited states, with integer Euler numbers, whose values persist from the
t
=
0
case, for strong interaction
U
>
>
t
. The corresponding quantum phases for the ground state contain either density-wave-order(DWO) for low fillings, where the particles stay apart form each other, or clustering-order(CO) for high fillings, where the particles form various structures as they condense into clusters. In addition, we find various excited states containing superpositions of Fock states, whose probability amplitudes are self-tuned in a way that preserves the integer value of the Euler characteristic from the
t
=
0
limit.
Graphic abstract
Several relaxations of envy-freeness, tailored to fair division in settings with indivisible goods, have been introduced within the last decade. Due to the lack of general existence results for most ...of these concepts, great attention has been paid to establishing approximation guarantees. In this work, we propose a simple algorithm that is universally fair in the sense that it returns allocations that have good approximation guarantees with respect to four such fairness notions at once. In particular, this is the first algorithm achieving a (ϕ−1)-approximation of envy-freeness up to any good (▪) and a 2ϕ+2-approximation of groupwise maximin share fairness (▪), where ϕ is the golden ratio (ϕ≈1.618). The best known approximation factor, in polynomial time, for either one of these fairness notions prior to this work was 1/2. Moreover, the returned allocation achieves envy-freeness up to one good (▪) and a 2/3-approximation of pairwise maximin share fairness (▪). While ▪ is our primary focus, we also exhibit how to fine-tune our algorithm and further improve the guarantees for ▪ or ▪.
Finally, we show that ▪—and thus ▪ and ▪—allocations always exist when the number of goods does not exceed the number of agents by more than two.
We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show ...that many-body states with topological features emerge at different energy bands separated by large gaps. The topology manifests in the way the particles organize in real space to form states with different energy. Each of these states contains topological defects/condensations whose Euler characteristic can be used as a topological number to categorize states belonging to the same energy band. We provide analytical formulas for this topological number and the full energy spectrum of the system for both sparsely and densely filled systems. Furthermore, we analyze the connection with the Gauss-Bonnet theorem of differential geometry, by using the curvature generated in real space by the particle structures. Our result is a demonstration of how states with topological characteristics, emerge in strongly interacting many-body systems following simple underlying rules, without considering the spin, long-range microscopic interactions, or external fields.
Graphical abstract
The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for ...sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence is so‐called strongly stable. Strong stability is satisfied by all degree sequences for which the switch chain was known to be rapidly mixing based on Sinclair's multicommodity flow method up until a recent manuscript of Erdős and coworkers in 2019. Our approach relies on an embedding argument, involving a Markov chain defined by Jerrum and Sinclair in 1990. This results in a much shorter proof that unifies (almost) all the rapid mixing results for the switch chain in the literature, and extends them up to sharp characterizations of P‐stable degree sequences. In particular, our work resolves an open problem posed by Greenhill and Sfragara in 2017.
PDF
