An $$H^{s,p}(\text {curl};\varOmega )$$ H s , p ( curl ; Ω ) estimate for the Maxwell system

Tunneling and quantum localization in chaos‐driven symmetric triple well potential: An approach using quantum theory of motion

“…In early nineties, Lin and Ballentine have theoretically predicted the tunneling enhancement in a driven double well, [21,22] known as chaos assisted tunneling (CAT) [23][24][25] while in 1991 Grossmann and his group have done the first theoretical work on coherent destruction of tunneling (CDT), [26] later confirmed by many other researchers. [27][28][29][30][31][32] Although CAT and CDT are top most agenda in the area of tunneling control, the experimental verifications of these two phenomena have come out only a few years back. [33][34][35] Unlike CAT and CDT, quantum localization is quiet old as the idea was first proposed by P. W. Anderson in 1958 where he had suggested the possibility of electron localization in semiconductor with large degrees of defects or impurities [36] and this type of localization is known as Anderson localization after his name.…”

Solution of the “Classical” Schrödinger equation for a driven symmetric triple well: A comparison with its classical counterpart

“…TDFGH method has already been applied to analyze the dynamics of various simple as well as complex systems. [67][68][69][70][71][72][73][74] The main advantage of using FGH as well as TDFGH method is that the methods are completely independent of the choice of basis set as here, the grid points x i ð Þ are representing the basis in the coordinate space and they are uniformly spaced with spacing Dx along the length L ð Þ of the one-dimensional system. [63,64] The orthonormalization condition on the grid is taken as…”

Fermi accelerator: A new insight from quantum theory of motion

“…On the other hand, periodically driven quantum systems have drawn attention of researchers for several decades to study a wide range of phenomena, may it be tunneling control, [6][7][8][9][10][11][12][13][14][15][16][17][18] both enhancement [6][7][8] as well as suppression [9][10][11][12][13][14][15][16][17] of tunneling, or it may be the dynamic localization [19][20][21][22][23][24] of the quantum particle. Abal et al [23] have used Fermi accelerator model to study quantum localization in one-body dissipation problem where they have got energy localization and the localization time increases when the driving frequency becomes aperiodic with addition of a second driving frequency having an irrational ratio with the first.…”