Quantum Bifurcations

Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions

“…To distinguish between the two cases, we introduce the term quantum bifurcation, which describes non-analyticities of the ground state energy of infinitely-connected, semiclassical (e.g. mean-field) models; see also [18][19][20]. Such quantum bifurcations are encountered in the semiclassical limit of our arXiv:1509.08429v2 [quant-ph] 26 Apr 2016 model even if N is finite, whereas for finite S we observe a quantum phase transition in the thermodynamic limit.…”

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“…In order to solve the coupled differential equations for the soliton-pair propagation we divide the two differential equations in (5) and we obtain…”

“…Nonlinearity represents the origin of several intriguing phenomena in classical and quantum physics. We adress Rogue waves [1,2,3], bifurcation [4,5] Bistability [6,7,8], chaos [9,10,11,12], and solitons [13,14,15] as few examples. Russel discoveres Solitons in 1834 [16] .…”

Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=αEleuch1 2018Advances in Mathematical Physics24010View full textAdd to dashboardCite

“…Nonlinearity has generated crucial effects and phenomena not only in the macroscopical systems but also in the microscopical systems governed by quantum physics. We can cite as examples Rogue waves [10][11][12], bifurcation [13,14], bistability [15][16][17][18], chaos [19][20][21][22], phase transition [23][24][25][26], lasing [27][28][29][30][31], superradiance [32][33][34], correlations [35][36][37], squeezing [38][39][40][41], and solitons [42][43][44][45][46][47][48]. A particular interest is focused on solitons due to their potential new application perspectives in several fields of physics and engineering [49][50][51][52][53][54][55][56].…”