Description of a system of interacting linear chains by means of the electron network model

Weger, M.; Alexander, S.; Riccia, Giacomo Della

doi:10.1063/1.1666306

Cited by 7 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) and (3), but also appropriate boundary conditions at each prong end. These conditions depend on the energy E and the specific behavior of V i (x i ) for the maximum allowed value of x i .…”

Section: Multi-prong Potentialsmentioning

confidence: 99%

“…Various aspects of the solutions of the Schrödinger equation for both scalar and vector potentials on a wide variety of networks have been discussed by several authors [1][2][3][4][5][6][7][8]. Recent investigations have been motivated in part by the considerable interest in mesoscopic systems and the experimental observation of persistent currents [9].…”

Section: Introductionmentioning

confidence: 99%

“…Recent investigations have been motivated in part by the considerable interest in mesoscopic systems and the experimental observation of persistent currents [9]. Most of the results correspond to piecewise constant scalar potentials V = V 0 [3,4,8], vector potentials A associated with uniform magnetic fields [5], or δ−function potentials at the network vertices [2,6,7]. In this paper we discuss the bound states and the scattering properties of a single particle moving in an arbitrary scalar N -prong potential.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum mechanics of multi-prong potentials

Gangopadhyaya¹,

Pagnamenta²,

Sukhatme³

1995

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar N -prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of N identical prongs exhibit an alternating pattern of non-degeneracy and (N − 1) fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in N -well potentials and of scattering for piecewise constant potentials are given. Since our treatment is for general values of N , the results can be studied in the large N limit. A somewhat surprising result is that a free particle incident on an N -prong vertex undergoes continuously increased backscattering as the number of prongs is increased.

show abstract

Section: Multi-prong Potentialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum mechanics of multi-prong potentials

Gangopadhyaya¹,

Pagnamenta²,

Sukhatme³

1995

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

A diatomic network model for electronic states of bulk, surface and thin films

Lee

1985

Journal of Physics and Chemistry of Solids

View full text Add to dashboard Cite

Quantum network theory of computing with respect to entangled flux qubits and external perturbation

Cain

2013

Journal of Applied Physics

View full text Add to dashboard Cite

In this work, we attempt to show the differences between traditional qubit-based spintronic methodology for quantum computation and the possible ballistic quantum network implementations. Flux qubits can be considered topologically similar to the persistent currents possessed as the angular momentum in Aharonov-Bohm loops, which can be coupled and thus entangled together. Since entanglement is guaranteed for coupled quantum networks, starting from a point-contacted situation, we first investigate how varying the degree of entanglement strength can affect the superposition of the four possible states for two isolated flux qubits being brought together. In general, the superposition is destroyed once the degree of entanglement is altered from the point-contact situation. However, we show that for a specific network with maximum entanglement, a Bell state situation can be produced. We then examine the effects of varying the external perturbation strength on the readout capability in quantum networks by changing the coupling strength through the cross-sectional area ratio. From the analysis of our results, we are persuaded to believe that two universally accepted components for quantum computing are not valid in the quantum network approach: the need of a weak perturbation for measurement of computational results and the requirement of fixed entanglement among qubits. We show there is an interplay between the strength of the entanglement and that of the external perturbation for high-fidelity classical readouts.

show abstract

Description of a system of interacting linear chains by means of the electron network model

Cited by 7 publications

References 9 publications

Quantum mechanics of multi-prong potentials

Quantum mechanics of multi-prong potentials

A diatomic network model for electronic states of bulk, surface and thin films

Quantum network theory of computing with respect to entangled flux qubits and external perturbation

Contact Info

Product

Resources

About