On the ground state for quantum graphs

被引：15
作者：
Kurasov, Pavel [1 ]
机构：
[1] Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2019年 / 109卷 / 11期
关键词：
Quantum graphs; Positivity preserving semigroups; Ground state;
D O I：
10.1007/s11005-019-01192-w
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Ground-state eigenfunctions of Schrodinger operators can often be chosen positive. We analyse to which extent this is true for quantum graphs-differential operators on metric graphs. It is shown that the theorem holds in the case of generalised delta couplings at the vertices-a new class of vertex conditions introduced in the paper. It is shown that this class of vertex conditions is optimal. Relations to positivity preserving and positivity improving semigroups are clarified.
引用
收藏
页码：2491 / 2512
页数：22
相关论文
共 50 条
  • [31] QUANTUM GRAPHS AND THEIR RESONANCE PROPERTIES
    Lipovsky, J.
    ACTA PHYSICA SLOVACA, 2016, 66 (04) : 265 - 364
  • [32] Quantum graphs with spin Hamiltonians
    Harrison, J. M.
    ANALYSIS ON GRAPHS AND ITS APPLICATIONS, 2008, 77 : 261 - 277
  • [33] On the Essential Spectrum of Quantum Graphs
    Vladimir Rabinovich
    Integral Equations and Operator Theory, 2017, 88 : 339 - 362
  • [34] Standing waves on quantum graphs
    Kairzhan, Adilbek
    Noja, Diego
    Pelinovsky, Dmitry E.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2022, 55 (24)
  • [35] Nonlinear optics of quantum graphs
    Lytel, Rick
    Shafei, Shoresh
    Kuzyk, Mark G.
    OPTICAL PROCESSES IN ORGANIC MATERIALS AND NANOSTRUCTURES, 2012, 8474
  • [36] On the Essential Spectrum of Quantum Graphs
    Rabinovich, Vladimir
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2017, 88 (03) : 339 - 362
  • [37] Spectral Fluctuations of Quantum Graphs
    Pluhar, Z.
    Weidenmueller, H. A.
    FOURTH CONFERENCE ON NUCLEI AND MESOSCOPIC PHYSICS 2014, 2014, 1619
  • [38] Thermodynamics at zero temperature: Inequalities for the ground state of a quantum many-body system
    Il'in, N.
    Shpagina, E.
    Lychkovskiy, O.
    PHYSICS LETTERS A, 2021, 414
  • [39] Control problems on quantum graphs
    Avdonin, Sergei
    ANALYSIS ON GRAPHS AND ITS APPLICATIONS, 2008, 77 : 507 - 521
  • [40] Trace formulae for quantum graphs
    Bolte, Jens
    Endres, Sebastian
    ANALYSIS ON GRAPHS AND ITS APPLICATIONS, 2008, 77 : 247 - +
12345