Quantum Zeno Effect for Exponentially Decaying Systems

The quantum Zeno effect -- suppression of decay by frequent measurements -- was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected so far.Comment: 4 pages, 3 figure

Decoherence by a spin thermal bath: Role of the spin-spin interactions and initial state of the bath

We study the decoherence of two coupled spins that interact with a spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. For the anisotropic spin-bath, changing the connectivity or coupling strenghts changes the decoherence of the central system from Gaussian to exponential decay law. The initial state of the environment is shown to affect the decoherence process in a qualitatively significant manner.Comment: submitted to PR

Existence of Spinorial States in Pure Loop Quantum Gravity

We demonstrate the existence of spinorial states in a theory of canonical quantum gravity without matter. This should be regarded as evidence towards the conjecture that bound states with particle properties appear in association with spatial regions of non-trivial topology. In asymptotically trivial general relativity the momentum constraint generates only a subgroup of the spatial diffeomorphisms. The remaining diffeomorphisms give rise to the mapping class group, which acts as a symmetry group on the phase space. This action induces a unitary representation on the loop state space of the Ashtekar formalism. Certain elements of the diffeomorphism group can be regarded as asymptotic rotations of space relative to its surroundings. We construct states that transform non-trivially under a $2\pi$-rotation: gravitational quantum states with fractional spin.Comment: 26 pages, 6 figures. Changes made to section 2 and Lemma

Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems

We perform the quantitative evaluation of the entanglement dynamics in scattering events between two insistinguishable electrons interacting via Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the timedependent numerical solution of the two-particle wavefunction of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, singlet, and triplet spin state. The procedure allows to evaluate the mechanisms that govern entanglement creation and their connection with the characteristic physical parameters and initial conditions of the system. The cases in which the evolution of entanglement is similar to the one obtained for distinguishable particles are discussed.Comment: 22 pages, 7 figures, submitted to Physical Review

Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the position operator for the center of mass of the mirror, and \rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the CSL model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10^{8}. Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.Comment: 4 pages, RevTeX. Substantial changes mad

Physics of a microsystem starting from non-equilibrium quantum statistical mechanics

In this paper we address the problem to give a concrete support to the idea, originally stemming from Niels Bohr, that quantum mechanics must be rooted inside the physics of macroscopic systems. It is shown that, starting from the formalism of the non-equilibrium statistical operator, which is now a consolidated part of quantum statistical mechanics, particular correlations between two isolated systems can be singled out and interpreted as microsystems. In this way also a new framework is established in which questions of decoherence can be naturally addressed.Comment: 14 pages, latex, no figures, contribution to the Proceedings of the XXXIII Symposium on Mathematical Physics (Torun, Poland

Exact positivity of the Wigner and P-functions of a Markovian open system

We discuss the case of a Markovian master equation for an open system, as it is frequently found from environmental decoherence. We prove two theorems for the evolution of the quantum state. The first one states that for a generic initial state the corresponding Wigner function becomes strictly positive after a finite time has elapsed. The second one states that also the P-function becomes exactly positive after a decoherence time of the same order. Therefore the density matrix becomes exactly decomposable into a mixture of Gaussian pointer states.Comment: 11 pages, references added, typo corrected, to appear in J. Phys.

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.Comment: 30 pages, 3 figure

Bell inequality for pairs of particle-number-superselection-rule restricted states

Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to by-pass the superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in the pair when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.Comment: 9 pages, 6 figures; v2 is the published versio

Rate of decoherence for an electron weakly coupled to a phonon gas

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.Comment: 27 pages, 2 figure