We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a nonlinear ramp which crosses a critical point. Using Kibble-Zurek-like scaling arguments we derive general scaling laws for the density of excitations and energy excess generated during the nonlinear sweep of the confining potential. It is shown that, with respect to the sweeping rate, the densities follow algebraic laws with exponents that depend on the space-time properties of the potential and on the scaling dimensions of the densities. We support our scaling predictions with both analytical and numerical results on the Ising quantum chain with an inhomogeneous transverse field varying in time.
A nonlinear device capable of handling multiple wavelength channels simultaneously by using spectral-hole burning in the inhomogeneous broadening of the gain in self-assembled quantum dots is proposed. The multichannel property of this device stems from the localized absorption or gain change at the pump wavelength within the inhomogeneously broadened gain spectrum. The spectral width of the modulation and its time evolution was also evaluated. The result indicates the applicability of this device to multichannel operation.
Abstract A system of <?CDATA
N≫1?> N ≫ 1 interacting spinless quantum particles, described by a statistical operator F(t), is considered. A time-dependent projection operator formalism for a family of projectors, which select a statistical operator <?CDATA
FS(t)?> F S ( t ) for a group of S < N relevant particles by integration of the variables of the irrelevant N − S ‘environment’ particles, is presented. This formalism results in a nonlinear version of the inhomogeneous Nakajima–Zwanzig generalized master equation (GME) for the relevant part of the statistical operator F(t), which contains an undesirable initial condition term related to the irrelevant part of the statistical operator depending on N variables. By introducing an additional operator identity, the obtained nonlinear inhomogeneous Nakajima–Zwanzig equation is exactly converted into a homogeneous nonlinear equation, accounting for initial correlations in the kernel governing its evolution. Both of these equations are equivalent to the corresponding evolution equations for <?CDATA
FS(t)?> F S ( t ) and take into account the dynamics of the environment particles. The equations for <?CDATA
FS(t)?> F S ( t ) are specialized in the linear approximation for the particle density n and analyzed for a one-particle statistical operator <?CDATA
F1(t)?> F 1 ( t ) . It turns out that, in addition to the correlations caused by interparticle interaction, the irrelevant initial condition term in the inhomogeneous equation for <?CDATA
F1(t)?> F 1 ( t ) , defined by the two-particle correlations, also contains quantum correlations conditioned by the quantum particle statistics. The latter do not vanish with time and cannot be disregarded in the conventional way by applying e.g. Bogoliubov’s principle of weakening of initial correlations. In order to take initial quantum and other correlations (commonly discarded in an unconvincing way) into consideration, the obtained nonlinear homogeneous GME has been applied. Exact in the first approximation in n, we obtain a new homogeneous equation for <?CDATA
F1(t)?> F 1 ( t ) , which accounts for correlations and is valid for any time moment t. It is shown how this reversible-in-time equation changes at different timescales and converts into the irreversible quantum Boltzmann equation on the macroscopic timescale without the use of the conventional approximations.