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pro vyhledávání: '"Bolte, Jens"'
Autor:
Bolte, Jens, Kerner, Joachim
Publikováno v:
Discrete and Continuous Models in the Theory of Networks (2020); Birkh\"auser: Operator Theory: Advances and Applications
In this paper we review recent work that has been done on quantum many-particle systems on metric graphs. Topics include the implementation of singular interactions, Bose-Einstein condensation, sovable models and spectral properties of some simple mo
Externí odkaz:
http://arxiv.org/abs/1805.00725
Autor:
Bolte, Jens, Garforth, George
Publikováno v:
In: Mathematical Problems in Quantum Physics, F. Bonetto, D. Borthwick, E. Harrell, M. Loss (eds.), Contemp. Math., vol. 717, AMS, Providence (2018)
We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the Hamiltonian t
Externí odkaz:
http://arxiv.org/abs/1704.00469
Publikováno v:
J. Phys. A 50 (2017) 105201
We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic osc
Externí odkaz:
http://arxiv.org/abs/1610.06472
Autor:
Bolte, Jens, Garforth, George
Publikováno v:
J. Phys. A: Math. Theor. 50 (2017) 105101
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing compatibi
Externí odkaz:
http://arxiv.org/abs/1609.00828
Publikováno v:
Rev. Math. Phys. 29 (2017) 1750027
We develop a semiclassical approximation for the dynamics of quantum systems in finite-dimensional Hilbert spaces whose classical counterparts are defined on a toroidal phase space. In contrast to previous models of quantum maps, the time evolution i
Externí odkaz:
http://arxiv.org/abs/1512.05984
Autor:
Bolte, Jens, Kerner, Joachim
Publikováno v:
Journal of Mathematical Physics 57, 043301 (2016)
In this Note we investigate Bose-Einstein condensation in interacting quantum many-particle systems on graphs. We extend previous results obtained for particles on an interval and show that even arbitrarily small repulsive two-particle interactions d
Externí odkaz:
http://arxiv.org/abs/1411.7330
We consider Schroedinger operators on compact and non-compact (finite) metric graphs. For such operators we analyse their spectra, prove that their resolvents can be represented as integral operators and introduce trace-class regularisations of the r
Externí odkaz:
http://arxiv.org/abs/1406.1045
Autor:
Bolte, Jens, Kerner, Joachim
Publikováno v:
Mathematical results in quantum mechanics, World Sci. Publ., Hackensack, NJ, 2015
We present results on Bose-Einstein condensation (BEC) on general compact quantum graphs, i.e., one-dimensional systems with a (potentially) complex topology. We first investigate non-interacting many-particle systems and provide a complete classific
Externí odkaz:
http://arxiv.org/abs/1403.0271
Publikováno v:
Annales Henri Poincar\'e, Volume 16, Issue 5, pp 1155-1189, 2015
We study zero modes of Laplacians on compact and non-compact metric graphs with general self-adjoint vertex conditions. In the first part of the paper the number of zero modes is expressed in terms of the trace of a unitary matrix $\mathfrak{S}$ that
Externí odkaz:
http://arxiv.org/abs/1311.5485
Autor:
Bolte, Jens, Kerner, Joachim
Publikováno v:
Journal of Mathematical Physics 55, 061901 (2014)
In this paper we propose quantum graphs as one-dimensional models with a complex topology to study Bose-Einstein condensation and phase transitions in a rigorous way. We fist investigate non-interacting many-particle systems on quantum graphs and pro
Externí odkaz:
http://arxiv.org/abs/1309.6091