Explicitly Solvable Cases of One-Dimensional Quantum Chaos

Explicit spectral formulas for scaling quantum graphs

“…In what follows the bond potentials are considered to be scaling potentials, U ij = ij E, ij = ji = const. The physical meaning and the reason for introducing the scaling assumption are discussed in [7][8][9][10]. In addition, in Sec.…”

“…Many theoretical investigations, which are difficult to conduct for more familiar quantum chaotic systems [4][5][6], can be carried out explicitly for quantum graphs, both in the classical and in the quantum regimes. An example are recently obtained spectral formulas [7][8][9][10], which provide explicit analytical expressions for the individual quantum energy eigenvalues of a subset of scaling quantum graphs.…”

Experimental Investigation of Reflection Coefficient and Wigner's Reaction Matrix for Microwave Graphs

“…Among the systems modeled by quantum graphs are, e.g., electromagnetic optical waveguides [3,4], mesoscopic systems [5,6], quantum wires [7,8] and excitation of fractons in fractal structures [9,10]. Recent works have shown that quantum graphs provide an excellent system for studying quantum chaos [11][12][13][14][15][16][17][18][19][20][21]. Quantum graphs with external leads (antennas) have been analyzed in detail in [16,17].…”

Quantum Graphology

“…Quantum graphs have recently attracted a lot of interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A special volume containing a number of contributions can be found in [18].…”