We present exact analytical calculations of scanning tunneling currents in locally disordered graphene using a multimode description of the microscope tip. Analytical expressions for the local density of states (LDOS) are given for energies beyond the Dirac cone approximation. We show that the LDOS at the A and B sublattices of graphene are out of phase by π implying that the averaged LDOS, as ...

The local, eigenfunction-weighted acoustic phonon density of states (DOS) tensor is calculated for a model substrate consisting of a semi-infinite isotropic elastic continuum with a stress-free surface. On the surface, the local DOS is proportional to the square of the frequency v, as for the three-dimensional Debye model, but with a constant of proportionality that is considerably enhanced com...

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpe...

In this Letter we discuss various properties of the local density of states (DOS) for a superconductor-ferromagnet hybrid system. The DOS is modified at small energies on both sides of the interface. Due to the interplay of superconductivity and ferromagnetism, the local DOS depends on the spin direction. The spin polarization effects extend over a long distance from the interface both in the s...

Suppose we have an n-qubit system, and we are given a collection of local density matrices ρ1, . . . , ρm, where each ρi describes some subset of the qubits. We say that ρ1, . . . , ρm are “consistent” if there exists a global state σ (on all n qubits) whose reduced density matrices match ρ1, . . . , ρm. We prove the following result: if ρ1, . . . , ρm are consistent with some state σ ≻ 0, then...