Quantum and Classical Correlations of Spatial and Spin Degrees of Freedom in Quantum Rings

2006 ◽  
Vol 13 (04) ◽  
pp. 455-462 ◽  
Author(s):  
O. Kálmán ◽  
P. Földi ◽  
M. G. Benedict
Keyword(s):  
Quantum Interference ◽  
Degrees Of Freedom ◽  
Beam Splitter ◽  
Spin Correlation ◽  
Important Special Case ◽  
One Dimensional ◽  
Specific Input ◽  
Spatial Degree ◽  
Special Case ◽  
Quantum And Classical Correlations

A one-dimensional mesoscopic ring with one input and two output leads acts as a spintronic beam splitter. The spatial degree of freedom, i.e., the presence of two different possible output channels, gets intertwined with the spin direction as a consequence of quantum interference and spin-orbit interaction. We investigate this kind of spatial-spin correlation, and show that the output density operator contains no quantum entanglement in the important special case when the device polarizes a perfectly random input spin state. However, the correlations are in general not purely classical, we also present specific input states with maximal spatial-spin entanglement after the ring.

scholarly journals Constraints on somite formation in developing embryos

2019 ◽  
Author(s):  
Jonas S. Juul ◽  
Mogens H. Jensen ◽  
Sandeep Krishna
Keyword(s):  
Phase Measurement ◽  
Ex Vivo ◽  
Clock Period ◽  
Important Special Case ◽  
One Dimensional ◽  
Phase Profile ◽  
Somite Formation ◽  
Vertebrate Embryos ◽  
The Waves ◽  
Special Case

Segment formation in vertebrate embryos is a stunning example of biological self-organisation. Here, we present an idealized model of the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the model to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex-vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our model makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

scholarly journals Constraints on somite formation in developing embryos

2019 ◽  
Vol 16 (158) ◽  
pp. 20190451
Author(s):  
Jonas S. Juul ◽  
Mogens H. Jensen ◽  
Sandeep Krishna
Keyword(s):  
Phase Measurement ◽  
Ex Vivo ◽  
Clock Period ◽  
Important Special Case ◽  
One Dimensional ◽  
Phase Profile ◽  
Somite Formation ◽  
Vertebrate Embryos ◽  
The Waves ◽  
Special Case

Segment formation in vertebrate embryos is a stunning example of biological self-organization. Here, we present an idealized framework, in which we treat the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the framework to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our analysis makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

Mechanically-Tunable Quantum Interference in Ferrocene-Based Single-Molecule Junctions

2020 ◽  
Author(s):  
María Camarasa-Gómez ◽  
Daniel Hernangómez-Pérez ◽  
Michael S. Inkpen ◽  
Giacomo Lovat ◽  
E-Dean Fung ◽  
...  
Keyword(s):  
Single Molecule ◽  
Quantum Interference ◽  
Degrees Of Freedom ◽  
Building Blocks ◽  
Ferrocene Derivative ◽  
Single Molecule Junctions ◽  
Molecule Junction ◽  
Single Molecule Junction ◽  
The Impact ◽  
D Orbitals

Ferrocenes are ubiquitous organometallic building blocks that comprise a Fe atom sandwiched between two cyclopentadienyl (Cp) rings that rotate freely at room temperature. Of widespread interest in fundamental studies and real-world applications, they have also attracted<br>some interest as functional elements of molecular-scale devices. Here we investigate the impact of<br>the configurational degrees of freedom of a ferrocene derivative on its single-molecule junction<br>conductance. Measurements indicate that the conductance of the ferrocene derivative, which is<br>suppressed by two orders of magnitude as compared to a fully conjugated analog, can be modulated<br>by altering the junction configuration. Ab initio transport calculations show that the low conductance is a consequence of destructive quantum interference effects that arise from the hybridization of metal-based d-orbitals and the ligand-based π-system. By rotating the Cp rings, the hybridization, and thus the quantum interference, can be mechanically controlled, resulting in a conductance modulation that is seen experimentally.<br>

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

Sub-half-wavelength atom localization via two standing waves

2017 ◽  
Vol 95 (3) ◽  
pp. 305-309 ◽  
Author(s):  
Haifeng Xu
Keyword(s):  
Quantum Interference ◽  
High Efficiency ◽  
Quantum Information Processing ◽  
One Dimensional ◽  
Half Wavelength ◽  
Potential Applications ◽  
Phase Gate ◽  
Quantum Error ◽  
Excited State Population ◽  
Atom Localization

We present a simple scheme of high-efficiency one-dimensional (1D) atom localization via manipulation of excited state population in a four-level inverted-Y atomic system. Because of the joint quantum interference induced by the two standing-wave fields, the 100% detecting probability of the atom in the subwavelength domain appears when the corresponding conditions are satisfied. The proposed scheme may open a promising way to achieve high-precision and high-efficiency 1D atom localization, which provides some potential applications to spatially selective single-qubit phase gate, entangling gates, and quantum error correction for quantum information processing.

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

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