Resonances, Unstable Systems and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting, 7-22 July 2004, University of Denver. Accepted for publication in the Internation Journal of Theoretical Physic

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

Adiabatic theorems for linear and nonlinear Hamiltonians

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation. It is shown that in some cases the found condition is necessary and sufficient. The adiabatic theorem is generalized for the case of nonlinear Hamiltonians

Electronic spin precession and interferometry from spin-orbital entanglement in a double quantum dot

A double quantum dot inserted in parallel between two metallic leads allows to entangle the electron spin with the orbital (dot index) degree of freedom. An Aharonov-Bohm orbital phase can then be transferred to the spinor wavefunction, providing a geometrical control of the spin precession around a fixed magnetic field. A fully coherent behaviour is obtained in a mixed orbital/spin Kondo regime. Evidence for the spin precession can be obtained, either using spin-polarized metallic leads or by placing the double dot in one branch of a metallic loop.Comment: Final versio

The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation

The usual quantitative condition has been widely used in the practical applications of the adiabatic theorem. However, it had never been proved to be sufficient or necessary before. It was only recently found that the quantitative condition is insufficient, but whether it is necessary remains unresolved. In this letter, we prove that the quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation.Comment: 4 pages,1 figue

Two-Frequency Jahn-Teller Systems in Circuit QED

We investigate the simulation of Jahn-Teller models with two non-degenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits isolating the effective single frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.Comment: 8 pages, 4 figures, figures revise

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure

Gauge-Invariant Formulation of Spin-Current-Density Functional Theory

Spin-currents and non-abelian gauge potentials in electronic systems can be treated by spin-current-density functional theory, whose main input is the exchange-correlation (xc) energy expressed as a functional of spin-currents. Constructing a functional of spin currents that is invariant under U(1)$\times$SU(2) transformations is a long-standing challenge. We solve the problem by expressing the energy as a functional of a new variable we call "invariant vorticity". As an illustration we construct the xc energy functional for a two-dimensional electron gas with linear spin-orbit coupling and show that it is proportional to the fourth power of the spin current.Comment: 8 pages, 3 figures, submitte

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions. Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from $p$- and $sd$-shell regions. Method: We use the real-energy and complex-energy continuum shell model approaches. Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical situations, including capture reactions to weakly-bound and unbound states. Conclusions: We demonstrated that the single-particle ANCs exhibit generic behavior that is different for charged and neutral particles. We verified the previously proposed relation [N.K. Timofeyuk, R.C. Johnson, and A.M. Mukhamedzhanov, Phys. Rev. Lett. 91, 232501 (2003); Phys. Rev. Lett. 97, 069904(E) (2006); N. K. Timofeyuk and P. Descouvemont, Phys. Rev. C 72, 064324 (2005)] between proton and neutron mirror ANCs. We find minor modifications if the spectroscopic strength is either localized in a single state or broadly distributed. For cases when several states couple strongly to the decay channel, these modifications may reach 30%.Comment: 18 pages, 17 figures, 9 table