Localization in the Discrete Non-linear Schrodinger Equation and Geometric Properties of the Microcanonical Surface

被引:5
作者
Arezzo, Claudio [1 ,2 ]
Balducci, Federico [1 ,3 ,4 ]
Piergallini, Riccardo [5 ]
Scardicchio, Antonello [1 ,3 ]
Vanoni, Carlo [3 ,4 ]
机构
[1] Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy
[2] Univ Parma, Dipartimento Sci Matemat Fis & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy
[3] Ist Nazl Fis Nucl, Sez Trieste, Via Valerio 2, I-34127 Trieste, Italy
[4] SISSA, Via Bonomea 265, I-34136 Trieste, Italy
[5] Univ Camerino, Scuola Sci & Tecnol, Via Madonna Carceri, I-62032 Camerino, Italy
关键词
Localization; Bose-Einstein condensate; Discrete Non-Linear Schrodinger Equation; Ergodicity breaking; Morse theory; MANY-BODY LOCALIZATION; WEAK ERGODICITY BREAKING; GLASSY DYNAMICS; TRANSITION; RELAXATION; COMPLEXITY; MODEL;
D O I
10.1007/s10955-021-02870-7
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
It is well known that, if the initial conditions have sufficiently high energy density, the dynamics of the classical Discrete Non-Linear Schrodinger Equation (DNLSE) on a lattice shows a form of breaking of ergodicity, with a finite fraction of the total charge accumulating on a few sites and residing there for times that diverge quickly in the thermodynamic limit. In this paper we show that this kind of localization can be attributed to some geometric properties of the microcanonical potential energy surface, and that it can be associated to a phase transition in the lowest eigenvalue of the Laplacian on said surface. We also show that the approximation of considering the phase space motion on the potential energy surface only, with effective decoupling of the potential and kinetic partition functions, is justified in the large connectivity limit, or fully connected model. In this model we further observe a synchronization transition, with a synchronized phase at low temperatures.
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页数:23
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