Related papers: On the Initial State and Consistency Relations
Superconductivity owes its properties to the phase of the electron pair condensate that breaks the $U(1)$ symmetry. In the most traditional ground state, the phase is uniform and rigid. The normal state can be unstable towards special…
A small system in contact with a macroscopic environment usually approaches an asymptotic state, determined only by some macroscopic properties of the environment such as the temperature or the chemical potential. In the long-time limit,…
Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr\"odinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…
We study time evolution of entanglement between two qubits, which are part of a larger system, after starting from a random initial product state. We show that, due to randomness in the initial product state, entanglement is present only…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
A variety of quantum computing algorithms exist for the preparation of approximate Hamiltonian ground states. A natural and important question is how these ground-state approximations can be further improved using adiabatic state…
We consider the 1d interacting Bose gas in the presence of time-dependent and spatially inhomogeneous contact interactions. Within its attractive phase, the gas allows for bound states of an arbitrary number of particles, which are…
We describe repulsively interacting Bose-Einstein condensates in spatially correlated disorder potentials of arbitrary dimension. The first effect of disorder is to deform the mean-field condensate. Secondly, the quantum excitation spectrum…
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate…
We point out that by the ``smoothness means fast decay'' principle in Fourier analysis, it is possible to infer the smoothness (or nonsmoothness) of the autocorrelation function from a mere glimpse of the initial state. Specifically, for a…
The uncertainty in the determination of the Z line-shape parameters coming from the precision of the calculation of the Initial-State Radiation and Initial--Final-State Interference is 2 10**(-4) for the total cross section sigma zero(had)…
Input-to-state stability (ISS) allows estimating the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is…
Given a diagonalizable matrix $A$, we study the stability of its invariant subspaces when its matrix of eigenvectors is ill-conditioned. Let $\mathcal{X}_1$ be some invariant subspace of $A$ and $X_1$ be the matrix storing the right…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for…
A general deterministic analysis to state the necessary conditions with a coefficient determination for the variational source condition to hold is provided. Of particular interest in terms of the choice of the regularization parameter, it…
We present an analysis of the adiabatic approximation to understand when it applies, in view of the recent criticisms and studies for the validity of the adiabatic theorem. We point out that this approximation is just the leading order of a…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…