scholarly journals Matrix operator approach to the quantum evolution operator and the geometric phase

2013 ◽  
Vol 63 (10) ◽  
pp. 1871-1886 ◽  
Author(s):  
Sang Pyo Kim ◽  
Jewan Kim ◽  
Kwang Sup Soh
Keyword(s):  
Geometric Phase ◽  
Evolution Operator ◽  
Matrix Operator ◽  
Quantum Evolution ◽  
Operator Approach

Exploring scalar quantum walks on Cayley graphs

2008 ◽  
Vol 8 (1&2) ◽  
pp. 68-81
Author(s):  
O.L. Acevedo ◽  
J. Roland ◽  
N.J. Cerf
Keyword(s):  
Evolution Operator ◽  
Cayley Graphs ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Constructive Method ◽  
Quantum Evolution ◽  
Necessary Condition ◽  
Internal Space ◽  
Special Cases ◽  
Scalar Quantum

A quantum walk, \emph{i.e.}, the quantum evolution of a particle on a graph, is termed \emph{scalar} if the internal space of the moving particle (often called the coin) has dimension one. Here, we study the existence of scalar quantum walks on Cayley graphs, which are built from the generators of a group. After deriving a necessary condition on these generators for the existence of a scalar quantum walk, we present a general method to express the evolution operator of the walk, assuming homogeneity of the evolution. We use this necessary condition and the subsequent constructive method to investigate the existence of scalar quantum walks on Cayley graphs of groups presented with two or three generators. In this restricted framework, we classify all groups -- in terms of relations between their generators -- that admit scalar quantum walks, and we also derive the form of the most general evolution operator. Finally, we point out some interesting special cases, and extend our study to a few examples of Cayley graphs built with more than three generators.

Spin and Charge Currents from Applying a Microwave Field to a Quantum Dot

2010 ◽  
Vol 663-665 ◽  
pp. 1337-1340
Author(s):  
Yun Qing Zhou ◽  
Jian Ming Yao ◽  
Ling Min Kong ◽  
Rui Wang
Keyword(s):  
Quantum Dot ◽  
Bias Voltage ◽  
Microwave Field ◽  
Evolution Operator ◽  
Operator Approach ◽  
Zero Bias ◽  
Spin Pumping

The evolution operator approach is applied to studying photon-electron pumping effects on a quantum dot connected to two magnetic leads in the presence of both via-dot and over-dot tunneling channels. It is found that a microwave field applied to the quantum dot may give rise to charge and spin pumping at zero bias voltage for asymmetric magnetic junctions.

scholarly journals Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization

2014 ◽  
Vol 25 (06) ◽  
pp. 1450060 ◽  
Author(s):  
Roberto Paoletti
Keyword(s):  
Phase Space ◽  
Evolution Operator ◽  
Quantum Evolution ◽  
Classical Dynamics ◽  
Semiclassical Asymptotics ◽  
Local Scaling ◽  
Space And Time

This paper deals with the local semiclassical asymptotics of a quantum evolution operator in the Berezin–Toeplitz scheme, when both time and phase space variables are subject to appropriate scalings in the neighborhood of the graph of the underlying classical dynamics. Global consequences are then drawn regarding the scaling asymptotics of the trace of the quantum evolution as a function of time.

Pumping Currents from Applying a Microwave Field and a Magnetic Field to a Quantum Dot

2011 ◽  
Vol 181-182 ◽  
pp. 993-997
Author(s):  
Yun Qing Zhou ◽  
Jian Ming Yao ◽  
Ling Min Kong ◽  
Rui Wang
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
Bias Voltage ◽  
Microwave Field ◽  
Evolution Operator ◽  
Operator Approach ◽  
Zero Bias ◽  
Spin Pumping

The evolution operator approach is applied to studying photon-electron pumping effects on a quantum dot connected to two magnetic leads in the presence of both via-dot and over-dot tunneling channels. It is found that a microwave field applied to the quantum dot may give rise to charge and spin pumping at zero bias voltage for asymmetric magnetic junctions.

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