Related papers: Adiabatic theorem in the thermodynamic limit: Syst…
We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the…
The minimum work principle states that work done on a thermally isolated equilibrium system is minimal for the adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is…
It is a fundamental problem to characterize the nonequilibrium processes. For a slowly moving one-dimensional potential, we explore the quasi adiabatic dynamics of the initial energy eigenstates for a confined quantum system interacting…
We consider a time dependent trap externally manipulated in such a way that one of its bound states is brought into an instant contact with the continuum threshold, and then down again. It is shown that, in the limit of slow evolution, the…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state…
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of…
When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow "slowly enough" is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large…
We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are…
A potential problem with adiabatic switching in perturbation theory is that divergent terms appear in the series solution. An example of this was presented by C. Brouder et al [4] for a simple 2 state system where the evolution of system in…
We investigate the performance of an adiabatic evolution protocol when initialized from a Gibbs state at finite temperature. Specifically, we identify the diagonality of the final state in the energy eigenbasis, as well as the difference in…
Assuming that Bogoliubov's theory of weakly interacting dilute Bose gas defines a self-consistent model Hamiltonian, we investigate its thermodynamic limit as we take the volume to infinity. The infinite volume is taken via a sequence of…
We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
The development of advanced quantum technologies and the quest for a deeper understanding of many-particle quantum mechanics requires control over the quantum state of interacting particles to a high degree of fidelity. However, the quickly…
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…
We investigate microscopically the tunneling dynamics in spontaneous fission of atomic nuclei. To this end, we employ a schematic solvable model with a pairing-plus-quadrupole interaction. The spontaneous decay of a system is simulated by…
Adiabatic elimination is a standard tool in quantum optics, which produces an effective Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher unperturbed energy. It shares with…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…