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- 저자 : Fistul, M. V. (검색결과 3 건)
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Anderson localization in generalized discrete-time quantum walks
Vakulchyk, I.,Fistul, M. V.,Qin, P.,Flach, S. American Physical Society 2017 Physical Review B Vol.96 No.14
<P>We study Anderson localization in a generalized discrete-time quantum walk-a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle, which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic-energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows one to obtain analytical expressions for spectrally independent localization length, which is highly useful for various applications.</P>
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Andreanov, A,Fistul, M V IOP 2019 JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Vol.52 No.10
<P>We present a theoretical study of resonant frequencies and spatial correlations of Josephson phases in frustrated arrays of Josephson junctions. Two types of one-dimensional arrays, namely, the diamond and sawtooth chains, are discussed in detail. For these arrays in the linear regime the Josephson phase dynamics is characterized by multiband dispersion relation <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/52/10/105101/aab013dieqn001.gif'/>, and the lowest band becomes completely <I>flat</I> at a critical value of frustration, <I>f</I> = <I>f</I> <SUB> <I>c</I> </SUB>. In a strongly nonlinear regime such critical value of frustration determines the crossover from non-frustrated (0 < <I>f</I> < <I>f</I> <SUB> <I>c</I> </SUB>) to frustrated (<I>f</I> <SUB> <I>c</I> </SUB> < <I>f</I> < 1) regimes. The crossover is characterized by the thermodynamic spatial correlation functions of phases on vertices, <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/52/10/105101/aab013dieqn002.gif'/>, i.e. <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/52/10/105101/aab013dieqn003.gif'/> displaying the transition from long- to short-range spatial correlations. We find that higher-order correlations functions, e.g. <I>p</I> = 2 and <I>p</I> = 3, restore the long-range behavior deeply in the frustrated regime, <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/52/10/105101/aab013dieqn004.gif'/>. Monte-Carlo simulations of the thermodynamics of frustrated arrays of Josephson junctions are in good agreement with analytical results. We also outline the extension of our results to the case of kagome lattice, prototypical 2D frustrated lattice, and other higher dimensional lattices.</P>
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