Shannon information entropies for rectangular multiple quantum well systems with constant total lengths

We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum(FWHM) of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki(BBM)inequality.     

Darboux related quantum integrable systems on a constant curvature surface

We consider integrable deformations of the Laplace–Beltrami operator on a constant curvature surface, obtained through the action of first-order Darboux transformations. Darboux transformations are related to the symmetries of the underlying geometric space and lead to separable potentials which are related to the KdV equation. Eigenfunctions of the corresponding operators are related to highest weight representations of the symmetry algebra of the underlying space.     

Determining the orientation of single quantum systems by means of scanning fluorescence microscopy

It shown via computational methods that the orientation and coordinates of single quantum electric dipole emitters in an isotropic medium can be clearly determined from scanned confocal luminescent images acquired using a circular inhomogeneous incoming beam. The efficiencies of circular inhomogeneous and radial beams are compared.     

Determination of the diffusion and viscosity coefficients from the properties of dual fluorescence of molecules in solutions

We have proposed and substantiated an approach that makes it possible to determine the diffusion and microviscosity coefficients in solutions from characteristics of the dual fluorescence of molecular probes. This approach uses the Stern-Volmer constants obtained upon fluorescence dynamic quenching in solutions. The relations that follow from the balance equations in terms of the formalism of two-level reactions in the excited state for the case of photoreactions of the kinetic character yield the dependences of the intensity ratio of the fluorescence bands of the normal form and tautomer on the degree of quenching. In accordance with these dependences, the dynamic quenching of the diffusion character (including the temperature quenching) changes the intensity distribution, and, based on these dependences, the Stern-Volmer constants and the bimolecular quenching constants can be determined, from which, using appropriate models, the diffusion and viscosity coefficients can be found. The merit of the method is its simplicity and availability, since it is based on the use of the data of steady-state measurements of fluorescence spectra with widespread standard instruments.     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

Unimodular quantum gravity and the cosmological constant

It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.     

Determination of the gravitational constant with a beam balance

The Newtonian gravitational constant G was determined by means of a novel beam-balance experiment with an accuracy comparable to that of the most precise torsion-balance experiments. The gravitational force of two stainless steel tanks filled with 13 521 kg mercury on 1.1 kg test masses was measured using a commercial mass comparator. A careful analysis of the data and the experimental error yields G=6.674 07(22)x10(-11) m(3) kg(-1) s(-2). This value is in excellent agreement with most values previously obtained with different methods.     

Coupling constant thresholds in nonrelativistic quantum mechanics

We extend the analysis of absorbtion of eigenvalues for the two body case to situations where absorbtion occurs at a two cluster threshold in anN-body system. The result depends on a Birman-Schwinger kernel for such anN-body system, an object which we apply in other ways. In particular, we control the number of discrete eigenvalues in the 0 limit.Research partially supported by U.S.N.S.F. under Grant MCS-78-01885.     

Cosmological constant and quantum gravitational corrections to the running fine structure constant

The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.     

Dynamic quenching of the dual fluorescence of molecules

Mathematical relations describing the properties of spontaneous steady-state dual fluorescence under conditions of dynamic quenching of excited states by foreign impurities are derived. It is shown that, in the case of a kinetic character of the reaction, the initial form of the dye and its photoproduct are quenched, the intensity ratio of the fluorescence bands of the initial form and the product linearly increasing with the quencher concentration. Analysis performed is applicable to a wide range of photoreactions accompanied by the dual fluorescence (charge transfer, proton transfer, complexation, etc.). The properties of the fluorescence, absorption, and dual fluorescence excitation for 3-hydroxyflavone in acetonitrile under conditions of dynamic quenching by the TEMPO spin quencher with a concentration below 1.25 × 10^?2 M are studied. 3-Hydroxyflavone is characterized by the excited-state intramolecular proton transfer and by the fluorescence spectrum consisting of two well-spaced bands. The observed dependences of the intensity of both fluorescence bands on the quencher concentration correspond to the theoretical conclusions. The Stern-Volmer constants calculated from the experimental data on the assumption of diffusion quenching of the excited states are 858 and 1141 M^?1 for the normal and tautomeric fluorescence bands, respectively. The experimental results reveal the kinetic character of the excited-state proton transfer in 3-hydroxyflavone in acetonitrile.     

About coupling constant singularities in quantum electrodynamics

The contribution of the multibubble insertions in the photon propagator to the anomalous magnetic moment of the electron is reexamined. Using the asymptotic form of the photon propagator one finds a softer singularity than that found in a recent analysis.     

Taming the cosmological constant in 2D causal quantum gravity with topology change

As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of causal dynamical triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the four-dimensional Euclidean path integral. Remarkably, in the continuum limit we obtain a finite spacetime density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense of a gravitational path integral which includes a sum over topologies, provided suitable causality restrictions are imposed on the path integral histories.     

Chaplygin gas quantum universe in the presence of the cosmological constant

We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant. We apply the Schutz’s variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the effective cosmological constant during the transition from the early times to the late times. For the case of an effective negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale factors never tend to the singular point, we have an initial indication that this model may not have singularities at the quantum level.     

Constructing the davies process of resonance fluorescence with quantum stochastic calculus

The starting point is a given semigroup of completely positive maps on the 2×2 matrices. This semigroup describes the irreversible evolution of a decaying two-level atom. By using the integral-sum kernel approach to quantum stochastic calculus, the two-level atom is coupled to an environment, which in this case will be interpreted as the electromagnetic field. The irreversible time evolution of the two-level atom then stems from the reversible time evolution of the atom and the field together. Mathematically speaking, a Markov dilation of the semigroup has been constructed. The next step is to drive the atom by a laser and to count the photons emitted into the field by the decaying two-level atom. For every possible sequence of photon counts, a map is constructed that gives the time evolution of the two-level atom implied by that sequence. The family of maps obtained in this way forms a so-called Davies process. In his book, Davies describes the structure of these processes, which brings us into the field of quantum trajectories. Within the model presented in this paper, the jump operators are calculated and the resulting counting process is briefly described.     

The dual of a quantum group

It is shown that the bialgebra (two dimensional pseudo-group) of Woronowicz, with some mild technical conditions, can be embedded into the enveloping algebra of a solvable Lie algebra, with the usual Lie structure and a deformed coproduct. The bialgebra dual of this bialgebra is calculated and found to coincide with U _q,q' (sl₂) after fixing the center. The (associative) bialgebra dual form is calculated explicitly and found to be a product ofq-exponentials. Implications about quantum transfer matrices are discussed.     

Determination of the gravitational constant G

A precise knowledge of the Newtonian gravitational constant G has an important role in physics and is of considerable meteorological interest. Although G was the first physical constant to be introduced and measured in the history of science, it is still the least precisely determined of all the fundamental constants of nature. The 2002 CODATA recommended value for G, G = (6.6742 ± 0.0010) × 10⁻¹¹m³ · kg⁻¹ · s⁻², has an uncertainty of 150 parts per million (ppm), much larger than that of all other fundamental constants. Reviewed here is the status of our knowledge of the absolute value of G, methods for determining G, and recent high precision experiments for determining G.     

Determination of the axial-vector weak coupling constant with ultracold neutrons

A precise measurement of the neutron decay β asymmetry A? has been carried out using polarized ultracold neutrons from the pulsed spallation ultracold neutron source at the Los Alamos Neutron Science Center. Combining data obtained in 2008 and 2009, we report A? = -0.119?66±0.000?89{-0.001?40}{+0.001?23}, from which we determine the ratio of the axial-vector to vector weak coupling of the nucleon g{A}/g{V}=-1.275?90{-0.004?45}{+0.004?09}.     

Stochastic processes associated with quantum systems

Stochastic processes have been useful in constructing and studying states in Quantum Field Theory (e.g., the Erice Lectures [3], Simon [2], Glimm and Jaffle [6] and in Quantum Statistical Mechanics (e.g., Ginibre [5], Høegh-Khron [7], Fröhlich [4], Driessler, Landau and Perez [2]). By analytically continuing into imaginary time, we may in certain cases replace the non-commulative algebra of observables of the quantum system by a commulative algebra consisting of functions of a stochastic process.In this article we are going to discuss an appropriate mathematical framework for this connection between quantum systems and stochastic processes.     

On the thermodynamic and quantum fluctuations of the cosmological constant

We discuss, from a condensed-matter point of view, the recent idea that the Poisson fluctuations of the cosmological constant about zero could be a source of the observed dark energy [1, 2]. We argue that the thermodynamic fluctuations of Λ are much bigger. Since the amplitude of the fluctuations is ∝ V^?1/2, where V is the volume of the universe, the present constraint on the cosmological constant provides a lower limit for V that is much larger than the volume within the cosmological horizon.