Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+ \Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition $[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of $\Theta$ simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

Impact of historical tsunamis on a sandy coastal barrier: an example from the northern Gargano coast, southern Italy

International audienceThe Lesina coastal barrier is characterized by the presence of three wide washover fans. They were formed by three distinct tsunamis which struck the northern coast of the Gargano Promontory (Apulia, Italy) during historical times. A model for their formation is presented. It takes into account the geomorphological data collected and some reports about the effect of recent tsunamis on coastal barriers and beaches. Washover fans were produced by tsunami waves which ran through coseismic cracks developed on dune ridges shaping a narrow, straight and relatively deep trench which constitutes the fan throat. Moreover, each tsunami event most likely caused severe erosion of the coastal barrier, shaping erosive grooves across the dune ridges, causing beach cliffs and causing the nourishment of submarine offshore bars. After the tsunami, a phase of coastal barrier recovery began, forming new dune ridges and closing washover fan throats. Morphological, archeological and radiometric data indicate a pre-Roman age for the oldest event, which was dated at 2430 years BP. The second tsunami struck the Lesina coastal barrier with similar magnitude 1550 years BP; it was caused by the strong earthquake that occurred at Gargano Promontory in the year 493 AD as reported by a medieval sacred legend. The smallest and more recent fan formed following the tsunami that hit the northern coast of Gargano on 30 July 1627

Notulae to the Italian flora of algae, bryophytes, fungi and lichens: 9

In this contribution, new data concerning bryophytes, fungi, and lichens of the Italian flora are presented. It includes new records and confirmations for the bryophyte genera Encalypta, Grimmia, and Riccia, for the fungal genera Hericium, Inocybe, Inocutis, Pluteus, and Russula, and for the lichen genera Bryoria, Farnoldia, Hypocenomyce, Lecania, Paracollema, Peltigera, Sarcogyne, and Teloschistes

The stability of money demand in the long-run: Italy 1861–2011

Money demand stability is a crucial issue for monetary policy efficacy, and it is particularly endangered when substantial changes occur in the monetary system. By implementing the ARDL technique, this study intends to estimate the impact of money demand determinants in Italy over a long period (1861–2011) and to investigate the stability of the estimated relations. We show that instability cannot be excluded when a standard money demand function is estimated, irrespectively of the use of M1 or M2. Then, we argue that the reason for possible instability resides in the omission of relevant variables, as we show that a fully stable demand for narrow money (M1) can be obtained from an augmented money demand function involving real exchange rate and its volatility as additional explanatory variables. These results also allow us to argue that narrower monetary aggregates should be employed in order to obtain a stable estimated relation

Neustonic versus epiphytic bacteria of eutrophic lake and their biodegradation ability on deltamethrin

This study evaluated biodegradation of the insecticide deltamethrin (1 μg l−1) by pure cultures of neustonic (n = 25) and epiphytic (n = 25) bacteria and by mixed cultures (n = 1), which consisted of a mixture of 25 bacterial strains isolated from the surface microlayer (SM ≈ 250 μm) and epidermis of the Common Reed (Phragmites australis, (Cav.) Trin. ex Steud.) growing in the littoral zone of eutrophic lake Chełmżyńskie. Results indicate that neustonic and epiphytic bacteria are characterized by a similar average capacity to degrade deltamethrin. After a 15-day incubation, bacteria isolated from the surface microlayer reduced the initial concentration of deltamethrin by 60%, while the average effectiveness of the bacteria found on the Common Reed equaled 47%

Decolorization and partial mineralization of a polyazo dye by Bacillus firmus immobilized within tubular polymeric gel

The degradation of C.I. Direct red 80, a polyazo dye, was investigated using Bacillus firmus immobilized by entrapment in tubular polymeric gel. This bacterial strain was able to completely decolorize 50 mg/L of C.I. Direct red 80 under anoxic conditions within 12 h and also degrade the reaction intermediates (aromatic amines) during the subsequent 12 h under aerobic conditions. The tubular gel harboring the immobilized cells consisted of anoxic and aerobic regions integrated in a single unit which was ideal for azo dye degradation studies. Results obtained show that effective dye decolorization (97.8%), chemical oxygen demand (COD) reduction (91.7%) and total aromatic amines removal were obtained in 15 h with the immobilized bacterial cell system whereas for the free cells, a hydraulic residence time of 24 h was required for an equivalent performance in a sequential anoxic and aerobic process. Repeated-batch experiments indicate the immobilized cells could decolorize C.I. Direct red 80 and reduce medium COD in five successive batch runs with enhanced activity obtained after each consecutive run, thus suggesting its stability and potential for repeated use in wastewater treatment. UV–visible spectrophotometry and HPLC analysis were used to confirm the partial mineralization of the dye. Data from this study could be used as a reference for the development of effective industrial scale biotechnological process for the removal of dyes and their metabolites in textile wastewater