Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.Comment: 4 pages, 1 figur

The dynamical hole in ultrafast photoassociation: analysis of the compression effect

Photoassociation of a pair of cooled atoms by excitation with a short chirped laser pulse creates a dynamical hole in the initial continuum wavefunction. This hole is manifested by a void in the pair wavefunction and a momentum kick. Photoassociation into loosely bound levels of the external well in Cs_2 0$_g^-$(6S + 6P$_{3/2}$ is considered as a case study. After the pulse, the free evolution of the ground triplet state wavepacket is analyzed. Due to a negative momentum kick, motion to small distances is manifested and a compression effect is pointed out, markedly increasing the density of atom pairs at short distance. A consequence of the hole is the redistribution of the vibrational population in the ground triplet state, with population of the last bound level and creation of pairs of hot atoms. The physical interpretation makes use of the time dependence of the probability current and population on each channel to understand the role of the parameters of the photoassociation pulse. By varying such parameters, optimization of the compression effect in the ground state wavepacket is demonstrated. Due to an increase of the short range density probability by more than two orders of magnitude, we predict important photoassociation rates into deeply bound levels of the excited state by a second pulse, red-detuned relative to the first one and conveniently delayed.Comment: 31 pages, 11 figure

Density-functional theory of nonequilibrium tunneling

Nanoscale optoelectronics and molecular-electronics systems operate with current injection and nonequilibrium tunneling, phenomena that challenge consistent descriptions of the steady-state transport. The current affects the electron-density variation and hence the inter- and intra-molecular bonding which in turn determines the transport magnitude. The standard approach for efficient characterization of steady-state tunneling combines ground-state density functional theory (DFT) calculations (of an effective scattering potential) with a Landauer-type formalism and ignores all actual many-body scattering. The standard method also lacks a formal variational basis. This paper formulates a Lippmann-Schwinger collision density functional theory (LSC-DFT) for tunneling transport with full electron-electron interactions. Quantum-kinetic (Dyson) equations are used for an exact reformulation that expresses the variational noninteracting and interacting many-body scattering T-matrices in terms of universal density functionals. The many-body Lippmann-Schwinger (LS) variational principle defines an implicit equation for the exact nonequilibrium density.Comment: Title, abstract, and text are adjusted to precise formulations (the original version contained a logical error

Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons

Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schroedinger equation. Here we begin important tests of the relativistic sixteen component wave function solutions obtained in a recent work on meson spectroscopy, extending a method developed previously for positronium decay into two photons. Preliminary to this we examine the positronium decay in the 3P_{0,2} states as well as the 1S_0. The two-gamma quarkonium decays that we investigate are for the \eta_{c}, \eta_{c}^{\prime}, \chi_{c0}, \chi_{c2}, \pi^{0}, \pi_{2}, a_{2}, and f_{2}^{\prime} mesons. Our results for the four charmonium states compare well with those from other quark models and show the particular importance of including all components of the wave function as well as strong and CM energy dependent potential effects on the norm and amplitude. The results for the \pi^{0}, although off the experimental rate by 15%, is much closer than the usual expectations from a potential model. We conclude that the Two-Body Dirac equations lead to wave functions which provide good descriptions of the two-gamma decay amplitude and can be used with some confidence for other purposes.Comment: 79 pages, included new sections on covariant scalar product and added pages on positronium decay for 3P0 and 3P_2 state

Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation with Maximal Entropy Production and Other Nonunitary Processes

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.Comment: To appear in Reports on Mathematical Physics. Presented at the The Jubilee 40th Symposium on Mathematical Physics, "Geometry & Quanta", Torun, Poland, June 25-28, 200

Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

Tensor model and dynamical generation of commutative nonassociative fuzzy spaces

Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous proposal is applied to dynamical generation of commutative nonassociative fuzzy spaces. It is numerically shown that fuzzy flat torus and fuzzy spheres of various dimensions are classical solutions of the rank-three tensor model. Since these solutions are obtained for the same coupling constants of the tensor model, the cosmological constant and the dimensions are not fundamental but can be regarded as dynamical quantities. The symmetry of the model under the general linear transformation can be identified with a fuzzy analog of the general coordinate transformation symmetry in general relativity. This symmetry of the tensor model is broken at the classical solutions. This feature may make the model to be a concrete finite setting for applying the old idea of obtaining gravity as Nambu-Goldstone fields of the spontaneous breaking of the local translational symmetry.Comment: Adding discussions on effective geometry, a note added, four references added, other minor changes, 27 pages, 17 figure

Relational Quantum Mechanics

I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the "measurement problem") could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion is the notion of observer-independent state of a system (or observer-independent values of physical quantities). I reformulate the problem of the "interpretation of quantum mechanics" as the problem of deriving the formalism from a few simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.Comment: Substantially revised version. LaTeX fil

Bound, virtual and resonance SS-matrix poles from the Schr\"odinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and 4 table