Minimal Quantum Research Articles

The principle of minimal quantum fluctuations for the time-dependent Schrödinger equation

It is shown that the optics-mechanics analogy which originally led Schrödinger to his famous equation stops at the time-independent level. For potentials involving time explicitly, the time-dependent Schrödinger equation cannot be deduced in a similar manner. Instead, a variational principle for the time-dependent Schrödinger equation is established. It minimizes the total quantum fluctuations of a newly defined Hamilton-Jacobi function about its limiting classical value over space-time, thereby demonstrating the existence of a deeper relationship between classical and quantum mechanics beyond the simple optics-mechanics analogy. This principle is similar in spirit to Feynman's space-time approach to quantum mechanics.

Alignment caused by photoionization and in radiative electron capture into excited states of hydrogenic high-Zions

In high-energy atomic collisions between bare high-$Z$ projectiles and low-$Z$ target atoms, an electron may be captured radiatively into the ground state or, alternatively, into an excited projectile state, which subsequently decays by x-ray emission. These processes are the inverse of a single-step or a two-step ionization, in which the first photon resonantly excites an electron from the hydrogenic ${1s}_{1/2}$ ground state and a second photon ionizes the excited electron. In this paper, we present a theoretical analysis with a particular emphasis on a detailed multipole decomposition of the photon wave function. This treatment is suitable for connecting angular correlations with alignment studies of the excited state. The anisotropy factors for angular correlations beween the beam axis and the decay x rays following radiative electron capture (REC) into the ${2p}_{3/2}, {3p}_{3/2}, {3d}_{3/2},$ and ${3d}_{5/2}$ levels of bare ${\mathrm{Xe}}^{54+}, {\mathrm{Au}}^{79+}, {\mathrm{Pb}}^{82+},$ and ${\mathrm{U}}^{92+}$ projectiles with energies ranging from 10 MeV/u to 10 GeV/u are explicitly presented and the connection with the alignment is given. It is predicted that REC occurs predominantly into states with the minimal magnetic quantum number $\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$ indicating a strong alignment perpendicular to the beam axis.

Minimal irreversible quantum mechanics: The mixed states and the diagonal singularity

A formalism for minimal irreversible quantum mechanics is extended from pure states to mixed states. In the latter case the problem of their diagonal singularity is explained and solved. In addition to the pure and mixed states of the usual approach, more general states are obtained. The Friedrichs model is studied. Decoherence is found and decoherence characteristic times are computed.

Sufficient Conditions for Conservativity of Minimal Quantum Dynamical Semigroups

The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a “generalized” subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this criteria in mathematical physics and quantum probability.

Changes in Chlorophyll Fluorescence of Apple Fruit during Maturation, Ripening, and Senescence

Trends in chlorophyll fluorescence for `Starking Delicious', `Golden Delicious' and `Law Rome' apple (Malus ×domestica Borkh.) fruit were examined during the harvest season, during refrigerated-air (RA) storage at 0 °C, following RA and controlled-atmosphere (CA) storage, and during a poststorage holding period at 22 °C. Fluorescence parameters of minimal fluorescence (Fo), maximal fluorescence (Fm), and quantum yield [(Fm-Fo)/Fm, otherwise denoted as Fv/Fm] were measured. During `Starking Delicious' fruit maturation and ripening, Fv/Fm declined with time, with the rate of decline increasing after the ethylene climacteric. During RA storage, all fluorescence parameters remained constant for approximately 2 weeks, then steadily declined with time for `Starking Delicious' fruit. Superficial scald was detected after Fv/Fm had declined from an initial value of 0.78 to ≈0.7. Fv/Fm was consistently higher for CA-stored fruits than for RA-stored fruits. We were able to resegregate combined populations of “high-quality” (CA) and “low-quality” (RA) `Law Rome' fruit with 75% accuracy using a threshold Fv/Fm value of 0.685, with only 5% RA-stored fruit incorrectly identified as being of high quality. During a poststorage holding period, Fo, Fm, and Fv/Fm correlated well with firmness for `Starking Delicious', but not for `Golden Delicious' fruit, which were already soft. Fo and Fm were linearly correlated with hue angle for 'Golden Delicious' fruit, decreasing as yellowness increased. The accuracy, speed of assessment, and light-based nature of fluorescence suggests that it may have some practical use as a criterion to assist in sorting apple or other chlorophyll-containing fruit or vegetables on commercial packing lines.

Problem of unitarity and quantum corrections in semiclassical quantum gravity

Using both the Born-Oppenheimer idea and the de Broglie-Bohm interpretation of wavefunction we represent in a different way the semiclassical quantum gravity from the Wheeler-DeWitt equation in an oscillating regime which can preserve completely the unitary quantum evolution of a matter field at the expense of a nonlinear gravitational field equation, but has the same asymptotic limit as the others. We apply the de Broglie-Bohm interpretation to the nonlinear gravitational field equation to develop a perturbation method to find the quantum corrections of a matter field to the gravity. The semiclassical Einstein equation with the quantum corrections is found for a minimal quantum FRW cosmological model.

Path integrals and pseudoclassical description for spinning particles in arbitrary dimensions

The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of the one in four dimensions (which is already known). In this case the gauge invariant part of the effective action in the path integral has the form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the Hamiltonization of the pseudoclassical theory with the new action we show that the operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized for the case of a particle with an anomalous magnetic moment.

Pseudoclassical Description of Higher Spins in 2 + 1 Dimensions

A pseudoclassical supersymmetric model to describe massive particles with higher spins (integer and half-integer) in 2 + 1 dimensions is proposed. The quantization of the model leads to the minimal (with only one polarization state) quantum theory. In particular, the Bargmann–Wigner type equations for higher spins arise in the course of canonical quantization. The cases of spin one-half and one are considered in detail. Here one gets Dirac particles and Chern–Simons particles respectively. A relation with the field theory is discussed. On the basis of the model proposed, and using dimensional reduction considerations, a model to describe Weyl particles with higher spins in 3 + 1 dimensions is constructed.

On the lindblad equation with unbounded time-dependent coefficients

We prove newa priori estimates for the resolvent of a minimal quantum dynamical semigroup. These estimates simplify well-known conditions sufficient for conservativity and impose continuity conditions on the time-dependent operator coefficients ensuring the existence of conservative solutions of the Markov evolution equations.

Pseudoclassical description of massive Dirac particles in odd dimensions

A pseudoclassical model is proposed to describe massive Dirac (spin one-half) particles in arbitrary odd dimensions. The quantization of the model reproduces the minimal quantum theory of spinning particles in such dimensions. A dimensional duality between the model proposed and the pseudoclassical description of Weyl particles in even dimensions is discussed.

Sorting Fruit by Quality: What Chloroplast Fluorescence Can Tell Us

Chloroplast fluorescence as a nondestructive tool for assessing `Red Delicious', `Golden Delicious' and `Law Rome' apple fruit quality was examined after approximately 4.5 months storage. Fluorometry parameters of minimal fluorescence (Fo), maximal fluorescence (Fm) and quantum yield (Fm-Fo)/Fm (otherwise denoted as Fv/Fm) were determined. All fluorescence parameters declined with time as apple fruit were maintained at 22°C in air. Fv/Fm was found to correlate well with firmness for `Red Delicious' fruit. A decline in Fo with time correlated very well with the development of yellow coloration of `Golden Delicious' fruit. The Fv/Fm value was consistently higher for controlled-atmosphere (CA) stored fruit than for regular-air (RA) stored fruit. When CA and RA stored `Law Rome' fruit were combined and a Fv/Fm value of 0.685 was used to resegregate fruit from the two storage regimes. Resegregation was achieved with 75% accuracy, with only 5% RA-stored fruit incorrectly identified as CA-stored. The accuracy, speed of assessment and light-based nature of fluorometry suggest it may have some practical use as a tool for sorting apple and other chlorophyll-containing fruit on commercial packinglines.

Proof theory for minimal quantum logic: A remark

It is remarked that the inference rule (‘ → ’) is superfluous for the sequential system GMQL introduced by H. Nishimura for the minimal quantum logic.

Proof theory for minimal quantum logic I

In this paper we give a sequential system of minimal quantum logic which enjoys cut-freeness naturally. The duality theorem, the cut-elimination theorem, and the completeness theorem with respect to the relational semantics of R. I. Goldblatt are presented. Due to severe limitations of space, technically heavy proofs of the first two theorems are relegated to a subsequent paper.

Fuzzy quantum logic II. The logics of unsharp quantum mechanics

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operatorsF on a Hilbert spaceℋ such that∀ψ∈ℋ, 0≤〈ψ¦Fψ〉≤∥ψ∥2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to “sharp” effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (afuzzy-like and anintuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.

Stochastic dilation of minimal quantum dynamical semigroup

A necessary and sufficient condition is formulated for minimal quantum dynamical semigroups to be conservative. The paper also provides a Markovian dilation of the minimal semigroups, as a contractive solution of an associated quantum stochastic differential equation in Boson-Fock space, which is isometric if and only if the minimal semigroup is conservative. Using the reflection principle of Brownian motion a necessary and sufficient condition for the contractive solution to be co-isometric is also obtained.

Minimal area problems and quantum open strings

We discuss minimal area problems for surfaces with boundaries and both open and closed string punctures. We define open-closed string diagrams to be surfaces with metrics of minimal area under the condition that any nontrivial Jordan open curve be longer or equal to π and any nontrivial Jordan closed curve be longer or equal to 2π. It is proven that the double of an open-closed string diagram is a closed string diagram of covariant closed string field theory.

N=3 AND N=4 SUPERCONFORMAL WZNW SIGMA MODELS IN SUPERSPACE I: GENERAL FORMALISM AND THE N=3 CASE

In the present and accompanying papers we develop a manifestly invariant superfield description of N=3 and N=4 2D superconformal WZNW sigma models with U(1)×O(3) and U(1)×U(1)×O(4) as the bosonic target manifolds. In the first paper we start by recalling the basic elements of 2D superconformal superfield calculus. As a new result, we generalize the latter to the newly discovered U(1) -extended O(4) N=4 superconformal algebra. In particular, the existence of a new class of N=4 primary superfields labelled by the eigenvalues of the U(1) generator is pointed out. Further, we construct the N=3 superspace formulation of the U(1)×O(3) model. The self-contained definition of the N=3 supercurrent via the basic primary superfields of this model is given, both in classical and quantum cases, and the relevant SOPEs are written down. It is shown that the model, being actually N=4 supersymmetric, admits one more supercurrent which extends the N=3 superconformal algebra to the N=4 one mentioned above. We define the minimal quantum N=3 superfield representations adequate for the two important cases of fermionization of the [Formula: see text] Kac-Moody current corresponding to the levels k=0 and k=2 of the bosonic part of one of its [Formula: see text] components.

Adaptation of the Photosynthetic Apparatus to Irradiance in Dunaliella tertiolecta

The time course of adaptation from a high to a low photon flux density was studied in the marine chlorophyte Dunaliella tertiolecta. A one-step transition from 700 to 70 micromole quanta per square meter per second resulted in a reduction of doubling rate from 1.1 to 0.4 per day within 24 hours, followed by a slower accumulation of photosynthetic pigments, light harvesting antenna complexes, Photosystem II reaction centers and structural lipids that constitute the thylakoid membranes. Photoregulated changes in the biochemical composition of the thylakoid proteins and lipids were functionally accompanied by decreases in the minimal photosynthetic quantum requirement and photosynthetic capacity, and an increase in the minimal turnover time for in vivo electron transport from water to CO(2). Analysis of de novo synthesis of thylakoid membranes and proteins indicates that a high light to low light transition leads to a transient in carbon metabolism away from lipid biosynthesis toward the synthesis of the light harvesting antenna protein complexes, accompanied by a slower restoration rate of reaction centers and thylakoid membranes. This pattern of sequential synthesis of light harvesting complexes followed by reaction centers and membranes, appears to optimize light harvesting capabilities as cells adapt to low photon flux densities.

Quantum wave packets on Kepler elliptic orbits.

Wave-packet solutions of the Schr\"odinger equation for the Coulomb potential are obtained that travel along classical elliptic orbits of fixed mean eccentricity and angular momentum. These wave packets are coherent states that have minimal quantum fluctuations in the noncommuting components of the Lenz vector in the plane of the orbit. For large quantum numbers the asymptotic form of the wave packet and the classical equations of the orbit are obtained analytically.

Minimal quantum logic with merged implications

It is shown that the property of orthomodularity can be interpreted as a particular reduction of the operations of implication to the relation of implication, and a physical interpretation of the result is given.