Superradiant laser: First-order phase transition and non-stationary regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well-separated pulses may occur. Received: 19 June 1998 / Accepted: 19 October 1998     

Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

By generalizing recently obtained results we calculate the excess noise factor (Petermann factor) for a laser system with non-orthogonal eigenmodes. The quantum consistency of the calculation is shown through the explicit conservation of input-output commutation rules. As a result of the calculation, the excess noise in the lasing mode is shown to depend on the laser gain below threshold, and on the noise analysis frequency below and above threshold. Received: 27 October 1998 / Received in final form: 11 March 1999     

The complete symmetrization of quantum operators: new thoughts on an old problem

The complete symmetrization with respect to x, p _x,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A ²)=(op A)². For example, angular momentum operators M _z ² and M ² are modified by the additive constants ²/2 and 3 ²/2 respectively (M ²0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.     

A functionalized dianthryl tetraaza macrocycle having the recognizing and switching ability

The synthesized macrocycle L is the novel fluorescent receptor having the switching ability by the external stimuli as well as having the recognizing ability of various metal ions. In particular, this macrocycle L shows the possibility of the selectivity of metal ions even in the same charge ions of a different metal, and the values of association constant (M⁻¹) of that for metal ions are consistent with the tendency of increasing charge number of metal ion. In addition, the values of quantum yield (Φ_F) of metal complexes of macrocycle L were ranged from 0.021 to 0.111 enough to recognize the metal ions in macrocycle L. We know from the fluorescent pH titration of macrocycle L by acid/base that the change of fluorescence intersects at about pH=5.     

Quantum key distribution using three basis states

This note presents a method of public key distribution using quantum communication of n photons that simultaneously provides a high probability that the bits have not been tampered. It is a variant of the quantum method of Bennett and Brassard (BB84) where the transmission states have been decreased from 4 to 3 and the detector states have been increased from 2 to 3. Under certain assumptions regarding method of attack, it provides superior performance (in terms of the number of usable key bits) for n<18m, where m is the number of key bits used to verify the integrity of the process in the BB84-protocol.     

Towards a field theory of the plateau transitions in the integer quantum Hall effect

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the integer quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL( )/SU(2) WZNW model (at the usual Ka –Moody point and with the level 6≤k≤8 ). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.     

Dirichlet Forms and Dirichlet Operators for Gibbs Measures of Quantum Unbounded Spin Systems: Essential Self-Adjointness and Log-Sobolev Inequality

For each [0, 1] we consider the Dirichlet form and the associated Dirichlet operator for the Gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential. The Gibbs measure is related to the Gibbs state of the system via a (functional) Euclidean integral procedure. The configuration space for the spin systems is given by We formulate Dirichlet forms in the framework of rigged Hilbert spaces which are related to the space . Under appropriate conditions on the potential, we show that the Dirichlet operator is essentially self-adjoint on the domain of smooth cylinder functions. We give sufficient conditions on the potential so that the corresponding Gibbs measure is uniformly log-concave (ULC). This property gives the spectral gap of the Dirichlet operator at the lower end of the spectrum. Furthermore, we prove that under the conditions of (ULC), the unique Gibbs measure satisfies the log-Sobolev inequality (LS). We use an approximate argument used in the study of the same subjects for loop spaces, which in turn is a modification of the method originally developed by S. Albeverio, Yu. G. Kondratiev, and M. Röckner.     

Photochemical preparation of tricyclic hydroxyketones by transanular cyclization of bridged 4-benzoylcyclohexanones

Summary The bridged 4-benzoyl-cyclohexanones3a–f were synthesized by ,-annelation of cyclic ketones. Irradiation of3a–f revealed a strong dependence of the photochemical behaviour on the ring size and the introduction of a nitrogen atom. Ketones which are able to form 1,6-biradicals (3b,c,e) undergo unselective photolytic decomposition, whereas3a,d,f afforded tricyclic hydroxyketones. The diastereoselectivity of ring closure is remarkably improved by introduction of a protected nitrogen atom (3d,f) in comparison to the carbocyclic diketone3a. Moreover, the N protective group of 4-azatricyclo-4.3.1.0^3,8]decan-7-one (7) could be removed affording the free hydroxy amino ketone8 in good yields. An explanation of the diastereoselective cyclization of3a and of the surprisingly low quantum yield of3d was found by conformational analysis of the corresponding triplet biradicals.

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Photochemische Darstellung tricyclischer Ketone durch transanulare Cyclisierung verbrückter 4-Benzoylcyclohexanone

Zusammenfassung Die verbrückten 4-Benzoyl-cyclohexanone3a–f wurden durch ,-Anellierung cyclischer Ketone synthetisiert. Das photochemische Verhalten von3a–f hängt in starkem Maße von der Ringgröße und von der Einführung eines Stickstoffatoms ab. Ketone, die in der Lage sind, 1,6-Biradikale zu bilden (3b,c,e), unterliegen einer unselektiven photolytischen Zersetzung, während3a,d,f tricyclische Hydroxyketone liefern. Die Diastereoselektivität des Ringschlusses wird durch Einführung eines Stickstoffatoms (3d,f) im Vergleich zum carbocyclischen Analogon3a deutlich gesteigert. Weiterhin gelang es, die N-Schutzgruppe im 4-Azatricyclo-[4.3.1.0^3,8]decan-7-on (7) unter Bildung des freien Hydroxyaminoketons8 in guten Ausbeuten zu entfernen. Eine Erklärung für die diastereoselektive Cyclisierung von3a und für die überraschend geringe Quantenausbeute von3d wurde durch Konformationsanalyse der entsprechenden Triplett-Biradikale gefunden.

     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.