Excess noise of the silicon surface barrier detectors

From our experiments the following conclusions follow:

On the construction of monopoles for the classical groups

ForG a classical group, an equivalence is exhibited between:

Nonlinear Reformulation of Heisenberg's Dynamics

A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of scalar fields for classical position/momentum observables Q/P, QM evolves (in Heisenberg's picture) according to the formally similar Lie algebra of commutator brackets of the corresponding operators:

Nuclear physics with hyperfine methods

In this talk the discussion of nuclear physics studied by hyperfine methods is limited to a few topics of high actuality:

Further Results on the Smoothability of Cauchy Hypersurfaces and Cauchy Time Functions

Recently, folk questions on the smoothability of Cauchy hypersurfaces and time functions of a globally hyperbolic spacetime M, have been solved. Here we give further results, applicable to several problems:

On Asymptotic Properties of a Number Theoretic Function Arising out of a Spin Chain Model¶in Statistical Mechanics

Let

The physics and mathematics of the second law of thermodynamics

     

11.

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property   总被引：1，自引：1，他引：0  

Valter Moretti 《Communications in Mathematical Physics》2008,279(1):31-75

This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M. It is now focused on the quantum state λ _M , of a massless conformally coupled scalar field propagating in M. λ _M is “holographically” induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity of M. It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one, M͂, are globally hyperbolic and M admits future time infinity i ⁺. λ _M coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M, the state λ _M enjoys the following further remarkable properties:

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M. It is now focused on the quantum state λ _M , of a massless conformally coupled scalar field propagating in M. λ _M is “holographically” induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity of M. It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one, M͂, are globally hyperbolic and M admits future time infinity i ⁺. λ _M coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M, the state λ _M enjoys the following further remarkable properties:

Laser Stark spectroscopy in the 9.4-μm region: The ν2 and ν5 bands of methyl chloride-d3

About two hundred Stark resonances of the ν₂ and ν₅ vibration-rotation bands of CD₃³⁵Cl, using a 9.4 μm CO₂ laser as a source, have been measured. By combining these data with the zero-field microwave spectra the following molecular constants have been determined (with the standard deviations in parentheses):

     

13.

On the Computational Power of Molecular Heat Engines     

Dominik Janzing 《Journal of statistical physics》2006,122(3):531-556

A heat engine is a machine which uses the temperature difference between a hot and a cold reservoir to extract work. Here both reservoirs are quantum systems and a heat engine is described by a unitary transformation which decreases the average energy of the bipartite system. On the molecular scale, the ability of implementing a (good) unitary heat engine is closely connected to the ability of performing logical operations and classical computing. This is shown by several examples:

		$\text{ν}{}_2$		$\text{ν}{}_5$
$\text{ν}{}_0$		1 028.67275 (15)		1 059.96970 (11)		(cm?1)
$\text{A}$		78 765.20 (89)		78 030.21 (109)		(MHz)
$\text{B}{}^1$		10 805.29 (26)		10 860.10 (13)		(MHz)
$\text{Aζ}{}_5$				?25 080.77 (99)		(MHz)
$\text{D}$			8 756.0 (43)			(MHz)
μ		1.90741 (33)		1.90607 (36)		(D)
μ(ground state)			1.90597 (33)			(D)

(1)	The most elementary heat engine is a SWAP-gate acting on 1 hot and 1 cold two-level systems with different energy gaps.
(2)	An optimal unitary heat engine on a pair of 3-level systems can directly implement OR and NOT gates, as well as copy operations. The ability to implement this heat engine on each pair of 3-level systems taken from the hot and the cold ensemble therefore allows universal classical computation.
(3)	Optimal heat engines operating on one hot and one cold oscillator mode with different frequencies are able to calculate polynomials and roots approximately.
(4)	An optimal heat engine acting on 1 hot and n cold 2-level systems with different level spacings can even solve the NP-complete problem KNAPSACK. Whereas it is already known that the determination of ground states of interacting many-particle systems is NP-hard, the optimal heat engine is a thermodynamic problem which is NP-hard even for n non-interacting spin systems. This result suggests that there may be complexity-theoretic limitations on the efficiency of molecular heat engines.

     

On the Computational Power of Molecular Heat Engines

A heat engine is a machine which uses the temperature difference between a hot and a cold reservoir to extract work. Here both reservoirs are quantum systems and a heat engine is described by a unitary transformation which decreases the average energy of the bipartite system. On the molecular scale, the ability of implementing a (good) unitary heat engine is closely connected to the ability of performing logical operations and classical computing. This is shown by several examples:

Laser Stark spectroscopy of formaldehyde-d2: The Coriolis coupled ν4 and ν6 fundamentals

Using CO₂ and N₂O lasers, we have measured and assigned nineteen ν₄ and nine ν₆ rotation-vibration resonances of the type ΔM = 0 and M = J. These transitions were combined with the zero-field pure rotational spectra in order to determine the two fundamental vibrational frequencies, the rotational constants of both excited states, the Coriolis coupling constant, and the dipole moments of each of the three states. The ground-state rotational constants and centrifugal distortion constants were taken from a microwave study and the centrifugal distortion constants of the excited states were assumed equal to those of the ground state. The following results were obtained (standard deviations in parentheses):

     

15.

Electronic structure of PrO: An analysis summary     

M. Dulick  R.W. Field 《Journal of Molecular Spectroscopy》1985,113(1):105-141

The (0,0) bands of nine prominent electronic transitions, Systems X, XI, and XVI through XXII, in the wavelength region 500–800 nm were studied. High-precision (±0.005 cm^?1), Doppler-limited, selectively detected cw-dye laser fluorescence excitation spectra for Systems XVI through XXII were recorded and analyzed. Definitive Ω assignments for the upper and lower states of these transitions were established from identified first lines in the P and R branches. Resolved fluorescence studies revealed 22 additional electronic transitions in the same wavelength region, many of which provide energy linkages between the upper or lower states of previously observed transitions. The comprehensive energy level diagram assembled from 31 electronic transition linkages comprises a total of 22 upper and lower electronic levels. Ω assignments and relative energies for the electronic states of the transitions studied (including Systems XIV and IX identified in fluorescence and the proposed assignment for System VI) are

		$\text{ν}{}_4$		$\text{ν}{}_6$
$\text{ν}{}_0$		938.0345 (6)		989.2519 (18)		(cm?1)
$\text{A}$		139 579 (150)		143 323 (150)		(MHz)
$\text{B}$		31 873.6 (5)		32 379.5 (7)		(MHz)
$\text{C}$		26 242.9 (6)		25 994.4 (8)		(MHz)
$\text{ξ}{}_{64}{}^{\mathrm{(a)}}$			136 178 (770)			(MHz)
μ		2.319 (10)		2.347 (4)		(D)
μ(ground state)			2.3464 (8)			(D)

     

16.

A Numerical Approach to Copolymers at Selective Interfaces     

Francesco Caravenna  Giambattista Giacomin  Massimiliano Gubinelli 《Journal of statistical physics》2006,122(4):799-832

We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known. In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include:

System	Ω′	$\text{T′}{}_0\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$	$\text{Ω″}$	$\text{T″}{}_0\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$
VI	5.5	11102	4.5	2157
IX	4.5	16597	3.5	3887
X	5.5	13259	4.5	220
XI	5.5	13865	4.5	220
XIV	5.5	16595	4.5	2157
XVI	5.5	19169	4.5	3720
XVII	4.5	16597	3.5	0
XVIII	7.5	21321	6.5	3965
XIX	6.5	19687	5.5	2111
XX	5.5	18069	4.5	220
XXI	4.5	18885	4.5	220
XXII	5.5	19169	4.5	220

–	Various numerical observations that suggest that the critical line lies strictly in between the two bounds.
–	A rigorous statistical test based on concentration inequalities and super–additivity, for determining whether a given point of the phase diagram is in the localized phase. This is applied in particular to show that, with a very low level of error, the lower bound does not coincide with the critical line.
–	An analysis of the precise asymptotic behavior of the partition function in the delocalized phase, with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a Brownian scaling.
–	A new proof of the lower bound on the critical line. This proof relies on a characterization of the localized regime which is more appealing for interpreting the numerical data.

2000 MSC: 60K37, 82B44, 82B80     

Electronic structure of PrO: An analysis summary

The (0,0) bands of nine prominent electronic transitions, Systems X, XI, and XVI through XXII, in the wavelength region 500–800 nm were studied. High-precision (±0.005 cm^?1), Doppler-limited, selectively detected cw-dye laser fluorescence excitation spectra for Systems XVI through XXII were recorded and analyzed. Definitive Ω assignments for the upper and lower states of these transitions were established from identified first lines in the P and R branches. Resolved fluorescence studies revealed 22 additional electronic transitions in the same wavelength region, many of which provide energy linkages between the upper or lower states of previously observed transitions. The comprehensive energy level diagram assembled from 31 electronic transition linkages comprises a total of 22 upper and lower electronic levels. Ω assignments and relative energies for the electronic states of the transitions studied (including Systems XIV and IX identified in fluorescence and the proposed assignment for System VI) are

A Numerical Approach to Copolymers at Selective Interfaces

We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known. In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include:

The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation

We consider two-dimensional Bernoulli percolation at densityp>p _c and establish the following results:

The A1Π-X1Σ band system of CD+: Spectroscopic constants and isotope shifts

Six bands of the A¹Π-X¹Σ system of CD⁺ in the region 3800–4800 Å have been recorded in emission using an aluminum hollow-cathode discharge in the HeC₂H₂ mixture. From the vibrational and rotational analysis of the observed bands, the following constants (cm^?1) are obtained:

     

19.

Rotational analysis of some electronic transitions in the spectrum of PrO     

E.A. Shenyavskaya  L.A. Kaledin 《Journal of Molecular Spectroscopy》1982,91(1):22-34

Rotational analysis of 13 emission bands of PrO belonging to 10 different systems was carried out. The derived constants are as follows:

		$\text{T}{}_{00}$		$\text{ω}{}_{\mathrm{e}}$		$\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}$		$\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}$		$\text{B}{}_{\mathrm{e}}$		$\text{D}{}_{\mathrm{e}}\text{·10}{}^4$		$\text{α}{}_{\mathrm{e}}$
$\text{A}{}^1\text{Π}$		23 747.5		1367.3		60.6		0.75		6.428		5.7		0.388
$\text{X}{}^1\text{Σ}$		0		2035						7.650		4.1		0.190
				(2101.6)		(33.3)

     

20.

A unified approach to string scattering amplitudes     

A. A. Voronov 《Communications in Mathematical Physics》1990,131(1):179-218

$\text{ν}{}_0$	$\text{B′}$	$\text{D′ × 10}{}^7$	$\text{B″}$	$\text{D″ × 10}{}^7$
18 665.19(1)	0.3530(1)	1.80(5)	0.3622(1)	2.85(1)
18 613.22(1)	0.3517(1)	0.4(3)	0.3606(1)	2.4(2)
17 842.32(1)	0.3560(1)	3.0(1)	0.3621(1)	2.7(1)
17 796.09(4)	0.3532(3)	2.4(8)	0.3604(2)	2.7(6)
18 628.22(3)	0.3530(6)	1.8(8)	0.3620(5)	2.7(7)
14 426.12(2)	0.3519(1)	5.5(6)	0.3620(1)	1.9(6)
13 541.44(2)	0.3500(2)	3.7(5)	0.3605(2)	2.3(5)
13 645.78(8)	0.3511(3)	3.1(5)	0.3620(2)	2.8(5)
12 961.98(4)	0.3445(4)	4.5(4)	0.3603(3)	2.3(7)
9 600.47(1)	0.3454(1)	2.8(2)	0.3620(1)	3.0(3)
16 591.29(1)	0.3536(1)	0.5(2)	0.3610(1)	2.6(1)
11 912.89(1)	0.3480(2)	8.5(8)	0.3610(1)	2.2(6)
10 429.62(2)	0.3450(1)	3.1(1)	0.3610(1)	3.0(3)

1)

Physics. In the calculation of g-loop string tachyon amplitudes withn scattering points the distinguished Polyakov measure d g,n on the moduli spaceM g,n of Riemann surfaces of genus g withn punctures arises. We give an interpretation of this measure as the modulus squared of a holomorphic section g,n (the Mumford form) of a certain holomorphic line bundle, i.e., we prove an analog of the Belavin-Knizhnik theorem d g,n =| g,n |2 in the amplitudic case. We give an expression for this measure through the determinants of the Laplace operators over ghosts and over multivalued fields with monodromy prescribed by momenta at the scattering points. We show also that the form g,n (n0) (n0) for the partition function andn-point amplitudes can be obtained from a unified over alln, universal Mumford form.

2)

Mathematics. The following new concepts from the theory of complex algebraic curves are investigated: divisors with complex coefficients, complex powers of holomorphic line bundles, determinants of Laplace operators over multivalued functions, etc. The corresponding generalizations of the determinant line bundles, the Weil-Deligne pairings, the Quillen and the Arakelov-Deligne metrics are constructed. A suggested by string amplitude considerations analog of the Mumford theorem on holomorphic triviality of the bundle 2 1 -13 over the moduli space is given. This analog asserts the existence of a canonical flat metric on a certain line bundle (see the main body of the text). There exist two differences: the latter bundle is not holomorphically trivial but has a canonical flat metric, and, being defined on the Teichmüller spaceT g, n , this bundle can be pulled down only on an infinite-sheeted covering of the moduli spaceM g,n . The universal isometries and the relative curvatures from the second part of the paper may be interesting, too.

Communicated by A. Jaffe     

Rotational analysis of some electronic transitions in the spectrum of PrO

Rotational analysis of 13 emission bands of PrO belonging to 10 different systems was carried out. The derived constants are as follows: