Forze non conservative nella meccanica quantistica

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

“…. .Û 2Û1 is applied to the Shrödinger eqution (16), the Floquet operator is reduced to the energy operatorp t , namelŷ…”

“…In many applications as radio-frequency ion traps [1][2][3][4][5][6][7][8], quantum optics [9][10][11][12], cosmology [13,14], quantum field theory [15], quantum dissipation [16][17][18][19][20][21][22], magneto transport in lateral heterostructures [23][24][25][26] and even gravitational waves [27] the time evolution of particles in quadratic potentials is frequently examined. The one-dimensional, generalized time-dependent quadratic Hamiltonian is given bŷ H = a 1 (t) + a 2 (t)x + a 3 (t)p + a 4 (t)x 2 + a 5 (t)p 2 + a 6 (t) (xp +px) ,…”

“…Aside from the simple harmonic oscillator, a large number of interesting systems arise from this Hamiltonian as the linear potential [28,29], the driven harmonic oscillator [30,31], Kanai-Caldirola Hamiltonians [16][17][18][19][20][21], and time dependent harmonic oscillators i.e. an oscillator with time-varying frequency [21,32,33].…”

Relativistic and Non-Relativistic Quantum Brownian Motion in an Anisotropic Dissipative Medium

“…In the Heisenberg picture, the equations of motion for canonical variables X ω and Q ω are the same equations (26) and (27) with the formal solution (29) and likewise the R field is defined by Eq. (30).…”

Mesoscopic circuits with charge discreteness: Quantum transmission lines

“…From this, the classical Hamiltonian could be written in the standard way. So, quantization becomes attainable from the usual correspondence between position-momentum and its associated operators [8,9,10]. In our case, a similar procedure could be implemented and we obtain the time depending Hamiltonian:…”