Related papers: Weakly nonlinear time-adiabatic theory
We introduce non-adiabatic semiclassical dressed states for a quantum system interacting with an electromagnetic field of variable amplitude and phase, and presence of dumping. We also introduce a generalized adiabatic condition, which…
We consider a nonlinear semi-classical Schroedinger equation for which quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. The relevance of the nonlinearity was discussed by R. Carles, C.…
In this paper we show that the typical effects of quantum resonances, namely, the exponential-type decay of the survival amplitude, continue to exist even when a nonlinear perturbative term is added to the time-dependent Schroedinger…
We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in…
We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation was derived from a model of active Brownian particles…
We establish adiabatic theorems with and without spectral gap condition for general operators $A(t): D(A(t)) \subset X \to X$ with possibly time-dependent domains in a Banach space $X$. We first prove adiabatic theorems with uniform and…
We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…
We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for…
We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in the undamped NLS, the solution of the…
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation.…
Several misprints and small mistakes were in the initial version. They have been corrected. Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz…
We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe. Such theories can possess an adiabatic regime in which the quintessence field…
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach…
It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching.…
We construct an extensive adiabatic invariant for a Klein-Gordon chain in the thermodynamic limit. In particular, given a fixed and sufficiently small value of the coupling constant $a$, the evolution of the adiabatic invariant is…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
The adiabatic particle number in mean field theory obeys a quantum Vlasov equation which is nonlocal in time. For weak, slowly varying electric fields this particle number can be identified with the single particle distribution function in…