Coherence and incompatability inWu* -algebraic quantum theory

In the framework of generalized quantum theory using aW ^*-algebraic formalism, we introduce a completely symmetric coherence relation for states which is also applicable to nonpure states. Making use of lattice theoretic results the properties of this relation, especially its connection with incompatibility, are investigated. By means of algebraic decomposition theory the investigation is reduced to the case of factors where a complete classification of the coherence classes is given.     

On the quantum density of states and partitioning an integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For N bosons in a one-dimensional harmonic oscillator potential, it is well known that the asymptotic (N→∞) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of sth powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d²(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the s=1 case, we use the modified technique to obtain a new formula for distinct restricted partitions.     

The temporal evolution of population densities of excited states in atomic oxygen thin plasmas

Population densities of transient oxygen plasmas have been calculated solving a system of differential equations, which describes the temporal evolution of the considered quantum levels. The results, which refer to a temperature of 1 eV and to electron number densities ranging from 10⁸ to 10¹⁴ cm^-3, show the strong importance of the metastable 3s⁵S state in determining the evolution of these plasmas. The present results are then applied to the calculation of relaxation times of selected quantum levels and to the definition of quasistationary conditions of plasmas having low lying excited states (i.e. states belonging to the same principal quantum number as the ground state).     

Temperature dependence of bound state spectra in field theory

We analyze the behaviour of kinks and semiclassical bound states at finite temperatures by applying quantum statistics to the fluctuations which determine the quantum dynamics of these states. We consider two theories in one space dimension — the ?⁴ theory with a dynamical symmetry breaking and the Gross-Neveu model. For the ?⁴ theory, the one-loop temperature corrections are obtained by using temperature-dependent Green function techniques. We show that the same result can be obtained by applying quantum statistics to the fluctuations around the kink. For the Gross-Neveu model, the temperature dependence of the bound states, which correspond to time-independent field configurations, is obtained. We show that for every bound state there exists a critical temperature at which this state breaks up into its constituents. This critical temperature increases with the number of constituents of the bound state.     

Spectroscopy and Regge trajectories of heavy quarkonia in the relativistic quark model

The mass spectra of charmonia and bottomonia are calculated in the framework of the relativistic quark model up to high orbital and radial excitations. The Regge trajectories of heavy quarkonia are constructed both in the (J,M ²) and (n _r ,M ²) planes, where J is the total angular momentum and nr is the radial quantum number. All daughter trajectories turn out to be almost linear and parallel, while parent trajectories exhibit some nonlinearity. Such nonlinearity occurs only in the vicinity of ground states and few lowest excitations and is more pronounced for bottomonia, while it is only marginal for charmonia. The obtained results are compared with available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.     

A Migdal-Kadanoff renormalization-group approach for the XY spin glass

Superconducting rings with mesoscopic Josephson junctions are considered in the presence of a do voltage bias V _o and of non-classical electromagnetic fields (coherent states, squeezed states, number eigenstates etc.). Due to the quantum nature of these devices the current I is a quantum mechanical operator and therefore «I²» is in general different from «I»². Using «I ²» we define the rms current I _rms, and using the various harmonics of «I» as if they belong to a classical current we define the “classical rms current” I _{rms, class}. In the case of classical currents these two quantities are identical, but for quantum currents they are different. We study their difference for various non-classical fields, and find that in some cases this difference is large. These predictions could be observed experimentally through the electromagnetic power that these currents radiate. An experiment that confirms the I _rms and refutes the Irms, class would prove the quantum nature of these currents.     

Product Vacua with Boundary States and the Classification of Gapped Phases

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state, but which on the left and right half-infinite chains have additional zero energy edge states. The models, which we call Product Vacua with Boundary States, form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its SO(2J + 1)-invariant generalizations fit into this classification.     

Bohr correspondence principle for large quantum numbers

Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI ^?1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is that of a particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies.     

Manifestation of nonplanarity effects and charge-transfer interactions in spectral and kinetic properties of triplet states of sterically strained octaethylporphyrins

Properties of the triplet states of octaethylporphyrins with the steric hindrance (free bases and Pd complexes) are studied by the methods of stationary and kinetic spectroscopy in the temperature range from 77 to 293 K. The mono-mesophenyl substitution results in a decrease in the quantum yield and shortening of the phosphorescence lifetime of Pd complexes by 250–3500 times in degassed toluene at 293 K. The phosphorescence quenching is caused by nonplanar dynamic conformations of the porphyrin macrocycle in the T ₁ state, which also lead to the appearance of new bands at λ～1000 nm in the T-T absorption spectra. As the number of meso-phenyls (Pd-octaetyltetraphenylporphyrin) increases, the quantum yield of phosphorescence further decreases (<10^?5) at 293 K, the lifetime of the T ₁ state shortens (<50 ns), and the efficiency of the singlet oxygen generation abruptly decreases (<0.01). The intense bathochromic emission of this compound at 705 nm with a lifetime of 1 ms at 77 K is assigned to the phosphorescence of a nonplanar conformation. Upon meso-orthonitrophenyl substitution, the quenching of phosphorescence of Pd complexes (by more than 10⁴ times at 293 K) is caused by direct nonadiabatic photoinduced electron transfer from the T ₁ state to the nearest charge-transfer state with the probability k _et ^T =(1.5–4.0)×10⁶ s^?1. The induced absorption of ortho-nitro derivatives in the region between 110 and 1400 nm is caused by mixing of pure ππ* states with charge-transfer states.     

Role of semicore electrons in the lattice dynamics of a cubic ZnS crystal

The phonon dispersion in a ZnS crystal has been studied by the density functional theory method with different pseudopotentials containing 10 (Zn¹²⁺) and 18 (Zn²⁰⁺) semicore electrons of the shell with the principal quantum number n = 3 in a zinc atom. It has been found that the pseudopotential of Zn²⁰⁺, unlike the pseudopotential of Zn¹²⁺ describes the phonon dispersion more accurately. An analysis has demonstrated that, in this case, the degree of d-p hybridization of semicore d states of zinc with the valence p states of sulfur decreases.     

Drag effect of one-dimensional electrons upon photoionization of D<Superscript>(−)</Superscript> centers in a longitudinal magnetic field

A theory is elaborated for the impurity photon drag effect in a semiconductor quantum wire exposed to a longitudinal magnetic field B directed along the axis of the quantum wire. The phonon drag effect is associated with the transfer of the longitudinal photon momentum to localized electrons in optical transitions from D^(?) states to hybrid-quantized states of the quantum wire, which is described by a confinement parabolic potential. An analytical expression for the drag current density is derived within the model of a zero-range potential in the effective mass approximation, and the spectral dependence of the drag current density is examined at different magnitudes of B and parameters of the quantum wire upon electron scattering by a system of impurities with short-range potentials. It is established that the spectral dependence of the drag current density exhibits a Zeeman doublet with a clear beak-shaped peak due to optical transitions of electrons from D^(?) states to states with the magnetic quantum number m=1. The possibility of using the photon drag effect in a longitudinal magnetic field for the development of laser radiation detectors is analyzed.     

Quantum field theories around a large-Z nucleus: metastable states in supercritical phase

We show that new metastable charge-neutral excitations exist in the supercritical phase of QED around a hypothetical large-Z nucleus. They are the vibration modes of the electron cloud induced around the external charge, and therefore do not have their counterpart in the normal phase. To uncover their properties we utilize our bosonized formulation of QED with proper care of renormal-ordering. In this framework the states can be described as small fluctuations on the solitonic ground state. Their energy levels and the widths are estimated by using the WKB approximation. Some of them are found to be very narrow, of the order of 1–10 keV, and have energies around ～1.6 MeV. The nature of the states is clarified and their quantum numbers are determined:J ^PC =O^+? and 1⁺⁺. Possible relevance of these states to the anomalous peak structure found in heavy ion collision experiments is briefly discussed and a new coincidence experiment is proposed to test this picture.     

High-temperature infrared spectrum of HCN near 3300 cm−2

The infrared absorption of HCN near the fundamental band at 3311 cm^?1 has been measured at temperatures up to 1200 K. Transitions involving high rotational states (up to J = 62) have been measured. These give an improved value for the sextic centrifugal distortion term H₀. Many hot-band transitions have been observed and assigned to transitions originating in vibrationally excited states up to 4000 cm^?1 above the ground state. These measurements give new data on vibrational states involving moderately high bending quantum numbers and indicate that new terms are needed to fit the ro-vibrational energy levels.     

QCD studies and discoveries with e + e − colliders and future perspectives

Observations of new charmonium(-like) and bottomonium(-like) states (sometimes refered to as “XYZ” states) at e ^?+? e ^??? colliders have changed our picture of quarkonia systems as QCD bound states. Potential models with a linear confinement ansatz, which were able to predict many conventional states with an accuracy of ～1 MeV, absolutely fail in describing many of the new states. Symmetries play an important role e.g. in the determination of the quantum numbers (such as charge conjugation in the radiative decays) or in trying to explain surprising properties such as isospin violation.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

Electron capture and scaling anomaly in polar molecules

We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D₀=1.63×¹⁰⁻¹⁸ esu cm. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.     

Observation of the 5pΠu Rydberg state of Li2

Some weak, collisionally induced transitions in ⁷Li₂ have been recorded by Fourier transform spectrometry in the near infrared, following excitation of the 5d¹Π_g state by optical-optical double resonance. They have been assigned as transitions to the 1 ¹Δ_g state from levels v=0 and 1 of a new ungerade Rydberg state, 5p¹Π_u. Quantum defect considerations indicate that the principal quantum number for this new state is 5, and that the assignment to 5p is compatible with a Rydberg series of which the lowest members would be the B¹Π_u and C¹Π_u states.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Frequency stabilization of multiple lasers and Rydberg atom spectroscopy

In this paper we report details of the apparatus and experimental techniques used to excite Rydberg states of ⁷Li using multiple diode lasers. Special attention is paid to frequency stabilization of the lasers and we show how three lasers can be stabilized using the fluorescence from a single atomic state. Laser spectroscopy of the 8p,9p, and 11p–15p states is then performed to determine the quantum defects of these states. Our measurement precision exceeds that of previous measurements of these defects by as much as a factor of 25. This work substantially extends our previous measurement of the 10p quantum defect, and we compare our measured defects with recent theoretical calculations for the np states across the range 8≤n≤15. The agreement with theory is excellent.