Jacek Jurkowski

Quantum damped oscillator I: Dissipation and resonances

Abstract Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

Quantum states with strong positive partial transpose

We construct a large class of bipartite

Memory in a nonlocally damped oscillator

M\ensuremath{\bigotimes}N

A Class of Bound Entangled States of Two Qutrits

quantum states which defines a proper subset of states with positive partial transposes (PPTs). Any state from this class has PPT but the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator. We propose to call elements from this class states with strong positive partial transposes (SPPTs). We conjecture that all SPPT states are separable.

On separable decompositions of quantum states with strong positive partial transposes

We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quantum propagator.

Local Numerical Range for a Class of 2 ⊗ d Hermitian Operators

We provide a new class of states of two qutrits displaying the so-called bound entanglement. We investigate the states using various versions of computable cross-norm and realignment criteria recently introduced in [7].

q-discord for Generalized Entropy Functions

We analyze a class of positive partial transpose (PPT) states such that the positivity of its partial transposition is recognized with respect to the canonical factorization of the original density operator (Cholesky block decomposition). We call such PPT states strong PPT (SPPT) states. This property, in contrast to PPT, is basis dependent. It is shown that there exists a proper subset of SPPT states which are separable and provide a separable decomposition for any of these states.

Observed light yield of scintillation pixels: Extending the two-ray model

Local numerical range is analyzed for a family of circulant observables and states of composite 2 ⊗ d systems. It is shown that for any 2 ⊗ d circulant operator

Estimating concurrence via entanglement witnesses

\mathcal{O}

Algorithms for calculating the leading quantum electrodynamics P(1/r 3) correction with all-electron molecular explicitly correlated Gaussians

there exists a basis giving rise to the matrix representation with real nonnegative off-diagonal elements. In this basis the problem of finding the extremum of