相关论文: Long-term stability of driven quantum systems and …

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…

We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of…

A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.

Quantum information processing has greatly increased interest in the phenomenon of environmentally-induced decoherence. The spin boson model is widely used to study the interaction between a spin-modelling a quantum particle moving in a…

The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration $\tau$ is upper bounded by $C/\tau$ for some positive…

We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic…

The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium…

We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these…

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated…

The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time…

We present a gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann-Robertson-Walker universe filled by multiple interacting fluids. We resolve arbitrary perturbations into adiabatic and entropy…

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…

This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting…

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…

In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…

The time evolution of wavepackets in crystals in the presence of a homogeneous electric field is formulated in k-space in a numerically tractable form. The dynamics is governed by separate equations for the motion of the waveform in k-space…

We investigate Bloch oscillations of interacting cold atoms in a mean-field framework. In general, atom-atom interaction causes dephasing and destroys Bloch oscillations. Here, we show that Bloch oscillations are persistent if the…

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on…

We study the Cauchy problem for the reduced Maxwell-Bloch equations with initial data for the electric field in weighted Sobolev spaces, assuming that all atoms initially reside in their ground state. Using the d-bar steepest descent…